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[Assistant] It is an application of stacked data structure that is these conversions. But for now, we are just understanding how you can do the conversions manually. And now let's move on to the vice versa process that is how to convert a postfix expression to infix expression.


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[Assistant] Okay so we just did the infix to postfix and now we are doing the reverse process that is we have to convert a postfix expression to the infix expression so over here in the question you can see convert the following


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[Assistant] Postfix expression to its infix format. We've been given a postfix expression and the steps involved are first we have to start from right to left.


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[Assistant] So we already did prefix to infix in the previous tutorial.


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[Assistant] There we were starting from left to right over here we are gonna start from right to left that is in this order.


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[Assistant] And we will keep moving till we get the first instance of one operator followed by two operands.


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[Assistant] Over here, this is another operator, right? This is an operand. So you can say operand 1, but this is not an operand, it is an operator. So we again move forward.


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[Assistant] So we come over here, this is an operand, so we are not involved with this. Then we come over here and we see this is


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[Assistant] One operator and after this the two elements are operands.


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[Assistant] So A and B are operands and this is an operator. So this is the ideal situation over your start from right to left till you get first instance of one operator. So this is one operator.


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[Assistant] And these are the two operands which are following minus in right to left direction.


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[Assistant] So now we have to convert that to infix notation and substitute it with a temporary variable. So what we did, we went from right to left.


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[Assistant] And we came at this operator and we saw


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[Assistant] That after this operator, we have two operands B and A.


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[Assistant] So step number two says just convert it to infix. So ultimately we have to convert this smaller sub-expression into infix format. So it is in postfix right now and when we convert it to infix, this operator will come in between these two, right? So ultimately the result will be a minus b because minus will come in between a and b in the infix version.


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[Assistant] We'll consider as x1. So this expression will become x1 c


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[Assistant] So let's move on to step 3. Step 3 is proceed forward from there to the left or end. That is completely scan this entire expression from right to left and start again and again if end of the expression is arrived.


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[Assistant] Right to left. We see that we have one operator. Is this operator followed by two operands? From right to left. So we'll see this and this. And you can see these two are operands now. Because x1 resembles a-b.


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[Assistant] So an operand can also be a sub-expression, right? So now we have to convert this again to infix. So we'll get plus over here in between. And ultimately we'll get x1 plus c.


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[Assistant] And now we have pretty much arrived at our solution. So now we just have to re-substitute x1's value which is a-b. So instead of x1, I'm gonna write a-b and then we have plus c. And this is the proper infix format of this postfix expression.


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[Assistant] Okay, so this was question number one and if you are a little confused, let's see question number two for better practice and understanding and things will be very clear there.


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[Assistant] Okay, so here's question number two and it says convert the following postfix expression to the infix format. So this time we have a little larger expression. So again, we'll start from


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[Assistant] Right to left, that is step number one, start from right to left.


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[Assistant] Till you get the first instance of one operator followed by two operands. So we'll start with this operator. Is it followed by two operands? No, because we have one more operator over here. So we'll move forward.


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[Assistant] Now we'll take this divide operator. Is it followed by two operands? Yes, we have DNE.


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[Assistant] So after divide by operator, we have two operands. So step number two says convert that to infix notation and assume and substitute it with a temporary variable. So when we convert this, we get


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[Assistant] Then we have plus operator, is it followed by two operands? No, we have star over here. So we move forward. Then we see star operator, is it followed by two operands? Yes, we have C and B. So after star operator,


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[Assistant] We have c and b, so we have to convert that to infix format so star will come in between. So after conversion we will get b star c and again we'll assume b star c as x2.


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[Assistant] Then we'll move forward. We only have one operand left. So in one sweep from right to left, we did two conversions and the remaining things will be as it is. So a will be as it is. We will have plus as it is and we will have minus as it is.


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[Assistant] So ultimately when we substitute b star c to x2 and d by e as x1, we will get a, b star c is x2, then we have a plus operator, then d by e is become x1, so I'll write x1, and then we have a minus operator. Okay.


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[Assistant] So again, proceed forward from there to the left or end which means after one sweep we reach the end. And then we start again. And we scan again with all the operators. So we'll start from right to left. So over here we have a minus operator.


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[Assistant] Is minus operator followed by two operands? No. Because x1 is there one operand but then we have one operator. That is plus. So we move forward. Then we see this plus operator.


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[Assistant] After plus operator we can see that there are two operands x2 and a. So then we convert this to infix format. So ultimately we are left with a plus x2 and x1 is as it is and we have minus. So a plus x2.


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[Assistant] Can now be converted to x3 or considered as x3. So we have x3, x1 and we have minus operator. So lastly minus operator is left.


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[Assistant] After minus operator, do we have two operands? We have x1 and x3. So we convert this to infix by taking minus in between and ultimately we reach to


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[Assistant] x3 minus x1. Now the only thing left out is to re-substitute these values of x3, x1 and x2. So x3 is a plus x2, right? What is the value of x3? It is a plus x2. Then we have a minus over here, so we have minus. And what is the value of x1? x1 is d by e.


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[Assistant] We still have to re-substitute x2's value. What is x2's value? It is b star c.


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[Assistant] So ultimately we will be left with a plus, then we have b star c, then we have minus d divided by e. And this is the final answer which is in proper infix format from this postfix expression.


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[Assistant] Okay, so I hope you've understood now clearly of how to convert postfix to infix. We simply have to scan the entire expression from right to left.


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[Assistant] And we have to find out a pattern where we get one operator followed by two operands. And as soon as we get that, we have to convert it to infix and substitute it with a temporary variable and then move again to the left.


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[Assistant] And you have to keep doing it till we get the final answer, till we get all the infix version of the entire postfix expression. And that's how you reach your final answer. So let's take one last example so that this idea is very clear.


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[Assistant] Okay, so here's another postfix expression a b c raised to plus d star e plus and you have to convert it to infix. So we'll start from right to left. We'll see plus is it followed by two operands? No, we have e but we have one more operator over here. So we'll go ahead. We'll see this star


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[Assistant] Is it followed by two operands? We have d, but we have one more plus over here, so no. So even this is not resolved.


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[Assistant] Then we see plus, plus has one more operator over here, that is raise two, so this is also not resolved. But when you see this raise two sign, this caret, after this caret, we have c and b, that is two operands. So you have to convert this to infix, so caret comes in between.


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[Assistant] So everything else will be as it is, we have A and then we have B raised to C and everything else is as it is and we have to substitute B raised to C


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[Assistant] Okay, so again we have to go from right to left. If you observe after this plus sign, now we have two operands x1 and a. The remaining operators do not follow two operands. So after this plus, we do not have two operands. After this star, we do not have two operands. So that pattern only exists.


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[Assistant] So we will convert this to infix, we will get a plus x1 because plus sign comes in between in infix format and rest things remain as it is.


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[Assistant] That is D star EN plus. Then we assume A plus X1 as X2. So we get X2 D star EN plus. So again when we scan from right to left, we can see that after star, we have D and X2. That is two operands. So star comes in between. Then we say X2


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[Assistant] So, convert it to infix and remaining e plus is kept as it is. Then we substitute x2 star d as x3. So, we have x3 e plus. So, ultimately this plus operator is left followed by two operands e and x3. So, we get x3 plus e. So, we've arrived at our result.


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[Assistant] Now we just have to re-substitute the values. So x3 is x2 star d. So we get x2 star d in place of x3 and then we have plus e as it is. What is the value of x2? x2 is a plus x1. So we get a plus


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[Assistant] x1 in the place of x2 remaining star d plus e is as it is and lastly


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[Assistant] After substituting x1's value that is b raised to c, we get the final answer of a plus at the place of x1 we substitute b raised to c, we have b raised to c and then we have star, we have d plus e. And this is the final infix format of this postfix expression.


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[Assistant] Okay, so this was the last example of postfix to infix conversion and by now I'm assuming you guys are having a good hang of it. You can, as I mentioned, practice more examples, try to convert them manually, take a pen and paper, that's the best way you can practice.


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[Assistant] And I hope this video was understandable. If you like this video, please give this video a thumbs up. Let me know in the comments how this video was.


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[Assistant] Do share it with your friends and in further video tutorials now, we will see these same conversions using the stack data structure. So stay tuned for that. Those videos will also be there in this playlist itself. So with that being said, I'm gonna wrap this video over here. Thanks for watching. See you in the next one. Peace.


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[Assistant] Everyone wanted to give trees.


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[Assistant] Hi kids! How are you today? I'm your teacher, Brian. Today, we're going to read another book in the Brain Bank series.


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[Assistant] What is the title of the book? We can see it here.


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[Assistant] A year with mother goose. Mother goose


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[Assistant] What is a goose? A goose is a kind of bird. In Korean, you say ko-wi.


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[Assistant] Koh-wee, it's a big bird, right? We see them flying in the fall.


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[Assistant] Mother, of course, ohmah, ohmah. So, ohmah kowee, right? Okay. And we're spending a year, a whole year. Spring, summer, fall, winter.


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[Assistant] Okay, so a whole year with Mother Goose. Are you ready? I'm interested. What's going to happen? Let's find out. In the first picture,


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[Assistant] We have a year with Mother Goose. We see Mother Goose here. Here is Oma Koi, right? This is Mama, Mama or Mother Goose.


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[Assistant] How many babies does she have? How many baby?


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[Assistant] Geese, do you see? By the way, goose? Hanuman. Geese? Mani. Geese.


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[Assistant] Geese. Mani. Goose. Hana.


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[Assistant] How many geese do you see? How many? We see one, two, three, four, five. There are five geese


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[Assistant] Following Mama Goose. What are they doing?


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[Assistant] They are following Mama Goose or Mother Goose. Let's read together.


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[Assistant] It is spring. Pum. Right? It is spring. I like spring. Do you like spring?


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[Assistant] It's warm in the spring. New flowers, ah.


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[Assistant] Mother goose makes a nest.


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[Assistant] Father Goose helps too.


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[Assistant] So, in the picture, what do we see? Who is that? That looks like Father Goose, Appa, Appa Koi, right? What is Father Goose doing?


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[Assistant] Okay, this is his beak. So he helps to make the nest.


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[Assistant] Did you know a male goose is called a gander? Here this is Papa Goose, Father Goose, Appa, Appa Goose, right? Father Goose. And he helps make the nest.


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[Assistant] He has a special name. His name is called a gander.


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[Assistant] Gander is namja koi. Okay?


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[Assistant] Male goose or father goose. He is a gander.


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[Assistant] His name is a gander. We say he is a gander.


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[Assistant] Here is the nest. How many eggs are in the nest? Look at the eggs. Uh, how many eggs do you see?


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[Assistant] One, two, three, four, five. Five eggs. How many baby geese? We saw five geese. Okay, so this is before they were born. Let's read.


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[Assistant] Mother Goose lays five big white eggs.


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[Assistant] Big white insect, right? White eggs.


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[Assistant] She sits on the eggs.


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[Assistant] Why does she sit on the eggs? Eggs are weak. You might break them. But Mother Goose is very careful. She sits on the eggs. Why?


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[Assistant] This keeps them warm. Ahh.


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[Assistant] The eggs must be warm, not cold. So Mother Goose, joshamal, she sits on the eggs to keep them warm.


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[Assistant] What does Father Goose do? Mother Goose is sitting on the eggs. What does Father Goose do?


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[Assistant] Father Goose watches. He watches for danger. Look at the picture.


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[Assistant] Do you see danger in this picture?


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[Assistant] Let's see, over here, what do we see? We see Mother Goose.


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[Assistant] She is sitting on the eggs.


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[Assistant] Over here, we see Father Goose. He is watching for danger. Where is the danger?


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[Assistant] What is this? Do you see this? What is that?


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[Assistant] Father goose, 조심해요. Mother goose, 조심해요. Be careful. The fox is hungry. 배고파. The fox wants to eat the eggs. 조심해요. Right? But father goose,


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[Assistant] Is watching. He sees the fox.


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[Assistant] He will keep Mother Goose safe.


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[Assistant] He will scare away the fox. Go away, fox!


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[Assistant] Right? So Father Goose will keep Mother Goose safe.


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[Assistant] Keep someone safe. You keep something safe, you protect it. You keep away danger. Keep it safe.


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[Assistant] Here's a good picture. What's happening? Here are the eggs, but the eggs are breaking.


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[Assistant] What's happening? What comes out of the eggs? What comes out of the eggs? Baby geese. Baby birds.


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[Assistant] We say they hatch. This word we say they hatch. So.


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[Assistant] The eggs hatch. The babies come out. Yay!


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[Assistant] Mother goose takes her babies to the lake.


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[Assistant] Wow, Bollyhill, right? They are hatched. They're new babies.


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[Assistant] Right away, let's go to the lake.


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[Assistant] Okay, Mother Goose takes her babies to the lake. This is the lake.


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[Assistant] Remember, a lake is a little small. Water. It's a lake. Okay? And the water is fresh. We can drink it. Mmm, 좋아요. Right? Okay.


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[Assistant] Geese. How many? Well, one, two, three, maybe four.


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[Assistant] Five, six, seven, eight. We see about eight, maybe seven or eight baby geese in this picture. Wow. Look at this baby goose.


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[Assistant] He's eating. Oh, pego pa! What is he eating?


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[Assistant] He's eating grass. Okay? So baby geese eat grass.


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[Assistant] Do you want to know about the next season? What happens in the summer? Well, that will be in part two. So let's take a break now. I will see you in part two.


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[Assistant] Hello everybody, welcome back to part two of A Year with Mother Goose. Before, we saw the geese after they were hatched. It's spring. It's still spring now.


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[Assistant] What happens also in the spring? Let's take a look.


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[Assistant] In this picture, what do you see? How many adult geese do you see? How many adult geese do you see? We see two. Here is one. Here is two.


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[Assistant] Where is Mother Goose? Where is Mother Goose? Mother Goose is in the front.


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[Assistant] Where is Father Goose? Father Goose is in the back. What is Father Goose doing?


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[Assistant] He's keeping the babies safe.


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[Assistant] Here is danger. What is this? This is a fox. So, let's read together.


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[Assistant] Mother goose walks at the front. Mother goose walks at the front.


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[Assistant] Father Goose walks at the back.


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[Assistant] Father Goose chases away. Chase away?


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[Assistant] Anything that comes near his family. Here is a fox. The fox is coming near the family. He's coming near the baby geese. The fox wants to eat.


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[Assistant] The baby geese, right? The fox is hungry.


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[Assistant] This is lunch. Okay? So Father Goose will chase away


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[Assistant] The fox. He will keep the baby geese safe.


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[Assistant] Baby geese. That's maybe a little difficult to say. There's another word we can use for baby geese. Did you know?


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[Assistant] A baby goose is called a gosling. Gosling.


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[Assistant] How many goslings are in the picture? One gosling, two goslings, three goslings, four goslings, five goslings.


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[Assistant] There are five goslings in the picture.


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[Assistant] How many ganders are in the picture? Do you remember? Gander is a male goose.


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[Assistant] Like Father Goose. There is one gander in the picture. Father Goose is here. And Mother Goose is here. Where are they going? They are going to the lake.


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[Assistant] Mother and father goose eat marsh grasses. The goslings eat too. So what do geese eat? They eat grass. They eat grass in the marsh.


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[Assistant] The marsh is like a land covered with water. See, this is land and


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[Assistant] Just choke em. It's a little deep. It's not very deep. It's a little deep. If you have a wide area like this, we say it is a marsh.


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[Assistant] A lot of grass grows in the marsh. We say marsh grass.


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[Assistant] So they have a lot of food. They are very lucky. They will not be hungry. They have a lot of food. Okay.


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[Assistant] What do they do at the lake? They eat marsh grass, but they also, what are they doing here? Looks like they're diving into the water and they're swimming. Do you like to swim?


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[Assistant] At the bottom of the lake. At the bottom. Right? What do you see at the bottom of the lake?


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[Assistant] More grass. There's more grass on the bottom of the lake.


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[Assistant] Father Goose is getting the grass. Let's read.


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[Assistant] Mother and Father Goose swim in the lake.


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[Assistant] They dive, dive, go down under the water. They dive to find, oops, they dive to find lake weed. This is lake weed, lake weed under the water.


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[Assistant] The goslings copy them. Copy?


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[Assistant] Do what I do. If I do this, you do the same thing.


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[Assistant] When Papa Goose dives under the water?


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[Assistant] The goslings also dive under the water. The goslings copy father goose and mother goose. That's how the goslings learn.


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[Assistant] We learn by copying our parents.


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[Assistant] Okay, all animals do that. Most animals do that. Okay, next.


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[Assistant] Look at the picture. Do you see that something has changed? What has changed in the picture? Here is Father Goose. Here is Mother Goose.


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[Assistant] Here are the goslings. Do they look the same? No, they're different.


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[Assistant] How are they different? Right? How are they different? They are bigger. Their wings, their wings are bigger. When is it? It is summer.


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[Assistant] Right? It is summer.


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[Assistant] The goslings follow mother and father goose. They are bigger now. They are growing up. They are growing up. When we grow up, we get bigger.


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[Assistant] So, they are still following Father and Mother Goose. Do you see anything else in the picture? Here is the lake. What is this in the lake?


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[Assistant] That's a beaver, okay? That's another animal.


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[Assistant] Is the beaver dangerous? Does Father Goose have to keep the gosling safe?


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[Assistant] No, don't worry. The beaver is not dangerous. The beaver will not eat the goslings. Okay, let's continue.


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[Assistant] The goslings swim with other goslings.


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[Assistant] How many goslings are there? Oh, too many. I can't count. There are many, many goslings. More than five. So the goslings meet other goslings. They meet many other goslings and they swim together.


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[Assistant] They learn to watch for danger.


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[Assistant] So uhm, watch for danger. Soon they will learn to fly. Soon, they will learn to fly. Right now, can they fly? Look at their wings. Their wings are too small. They can't fly.


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[Assistant] They have to wait till their wings get bigger like mama goose. Then they can fly. So they can't fly.


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[Assistant] Soon they will learn to fly. They have to get bigger. Did you know, goslings go to daycare?


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[Assistant] Daycare, that's like Oroni Jeep, right? Oroni Jeep. It's daycare. When father goes to work and mother goes to work, sometimes the children go to Oroni Jeep, right? Daycare center.


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[Assistant] So they are safe, and they meet other children.


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[Assistant] Adult geese take care of them while their parents feed.


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[Assistant] So the adult geese, other moms, other dads, watch the baby geese.


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[Assistant] Mother goose and father goose, they're eating somewhere else. Then they come back, and these geese, the other adult geese, go to eat too. So it's like daycare, right? It's like ornijiip for


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[Assistant] Okay, that brings us to the end of part two. Let's take a short break and we'll begin part three. I want to know


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[Assistant] What happens to the geese in the fall and the winter? So we'll find out next. See you then. Bye bye.


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[Assistant] Hello kids! Welcome back to part 3 of A Year with Mother Goose. Take a look at the picture.


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[Assistant] What season is it now? Spring, summer, fall, or winter. Which season? It's fall. It is fall in this picture. What are the geese doing? The geese are flying.


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[Assistant] Are there any goslings? No. There are no goslings.


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[Assistant] All the geese are adult geese. And they are flying. Where are they going? Where are they flying to? They're flying south, nam-uro. Why? Why do they fly south?


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[Assistant] Because it's getting cold here. In the south, it's warmer. Ah, nice weather. So the geese fly south for the winter. Let's read together. It is fall.


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[Assistant] Right now, right? It is fall now.


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[Assistant] Mother and father goose fly with the other geese. They fly together and they have some special shape. Okay, we'll talk about that soon.


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[Assistant] So mother and father goose fly with the other geese.


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[Assistant] So do the gosling.


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[Assistant] Well the goslings, they aren't goslings anymore. They're grown up. They're almost adults. Okay? They fly with mother goose and father goose.


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[Assistant] They fly in this shape. What is this shape?


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[Assistant] It's a V shape, but it's an upside down V shape. Not this way, this way, right? It's a V shape.


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[Assistant] Why do they fly in a V shape?


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[Assistant] Why don't they all fly together in a straight line? Why not?


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[Assistant] Well, because a V shape is easier. Okay? Think about this.


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[Assistant] These birds here, okay, these birds are behind


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[Assistant] Do you know that he is working very hard?


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[Assistant] These birds, they're ah, shiwayo, kinchanayo.


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[Assistant] Because this bird is breaking the wind.


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[Assistant] So these birds, they are, they can fly easier.


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[Assistant] They can rest, okay? They can take a break. Can this bird be in front all the time?


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[Assistant] No, it's too hard. So after some hours, after some time, this bird goes behind. He goes


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[Assistant] In the back. Okay, so he goes back and he, oh, he takes a break.


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[Assistant] It's easier for all the birds to fly south.


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[Assistant] They work together. They help each other.


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[Assistant] That's a good idea. We should all help each other so that we can do what we need to do. Birds help each other.


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[Assistant] We should help each other too. So.


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[Assistant] When we work, let's work together. Let's help each other.


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[Assistant] They fly to a warmer place. A warmer place. Where is it? What direction? What did I say before? What did I say? I said south.


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[Assistant] It is south of their summer home.


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[Assistant] In the summer, they live in the north, like in Korea.


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[Assistant] In the fall they fly south, maybe to the Philippines. In the Philippines it is very warm. In Korea during the winter


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[Assistant] It's cold, right? So many Koreans go to the Philippines in the winter, like the geese. Okay? So it is south of their summer home.


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[Assistant] They will spend the winter there.


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[Assistant] So the geese go to the south, to the Philippines, or to South America, or some other place in the south, and they spend the winter. They spend the winter, they take that time there, in the south.


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[Assistant] Did you know we use the word geese to mean more than one goose? I taught this to you before in section one, in part one. Remember, geese, goose, hanaman, geese, manayo.


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[Assistant] In this picture, do you see a goose or many geese? Of course, you see many geese. Not just one, many. One, two, three, four, five, six. Six geese. Not goose.


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[Assistant] It looks like they're flying back north.


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[Assistant] Before they were in the south, now they're flying back north. Winter is over. It is spring.


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[Assistant] Not cold anymore. So the geese can fly back to their summer home.


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[Assistant] The geese fly back north to their lake.


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[Assistant] The goslings are big geese now.


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[Assistant] They can take care of themselves. Take care of.


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[Assistant] Can you take care of yourself?


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[Assistant] Maybe not now. You're too young. Your mother and father take care of you. They give you a home. They give you food. They give you their love. They protect you.


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[Assistant] They keep you safe from danger. They take care of you


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[Assistant] But in this picture the goslings are big. They're big now. They are adult geese. They can take care of themselves. They can protect themselves. They can find food for themselves. Okay.


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[Assistant] Mother and father goose make a new nest. A new nest. It's a new year. One year later. They make a new nest.


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[Assistant] Goose do. They make a new nest.


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[Assistant] Mother goose will lay new eggs. She will sit on them.


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[Assistant] How many days later will the eggs hatch? Do you remember? How many days later?


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[Assistant] 28 days later, new goslings, new baby geese will come out and father and mother goose will care for the new goslings. Aha.


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[Assistant] So we have a circle.


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[Assistant] A circle. And a circle is like a cycle. This is the circle of the life of the geese.


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[Assistant] If you think about all animals have a life cycle, right? They're born, they get, uh, they get older, they learn from their mother and father, they grow up.


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[Assistant] They become adult geese and then they have babies again. Let's take a look here.


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[Assistant] What are these here? These are eggs. How many eggs? One, two, three, four, five. There are five eggs. What happens here? When? These are chicks.


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[Assistant] Chicks or goslings for the geese. How many? One, two, three, four, five. There are five chicks. All of the eggs, what did all the eggs do? All the eggs hatched. All of the eggs hatched. What's going on here? What's happening? This is day one.


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[Assistant] No sleeping. As soon as they hatch, let's go to the lake.


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[Assistant] Day one, the baby geese, the goslings, are following mother goose to the lake.


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[Assistant] What are they doing here? They're swimming in the lake. They're learning how to swim and they're eating the marsh grass. This is day two or day three. And they do this for a long time, all through the spring.


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[Assistant] Two months later, two months later, they fly. They learn how to fly. And then, one year later, they come back to their home on the lake.


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[Assistant] And the cycle starts again.


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[Assistant] Right? They start again. So it is a life cycle for geese. The goose life cycle.


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[Assistant] Of course, all animals do the same thing, as I said before.


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[Assistant] This is the life cycle for geese. Can you think about the life cycle for human beings?


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[Assistant] Think about that. Maybe you can make a picture like this. Draw the different times in your life and in the future. And maybe when you have kids too, that cycle will start again. Very interesting.


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[Assistant] Well, that's about it. That's all we have for part three of A Year with Mother Goose. We've spent one year with the goose family. I hope you learned a lot. I sure did. And I'll see you next time. Take care.


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[Assistant] This push is nice.


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[Assistant] This push is not nice.


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[Assistant] This kick is nice.


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[Assistant] This kick is not nice.


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[Assistant] This hit is nice.


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[Assistant] This hit is not nice.


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[Assistant] This poll is nice.


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[Assistant] This poll is not nice.


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[Assistant] Dreamed a dream in time gone by


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[Assistant] Come with me where chains will never bind you.


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[Assistant] All your grief at last, at last.


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[Assistant] Is there any better way to hit the road whenever and wherever you want than to take your entire house with you on your travels? The proud Australian people will tell you that camper traveling has allowed them to make their vast and beautiful land country all part of their own backyard.


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[Assistant] This country has highly developed facilities for camper travel, which allows you to enjoy its beauty at perfect ease, with sunrises and starry nights to keep you company.


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[Assistant] You'll never have to worry about packing your luggage, checking out, etc.


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[Assistant] However, before you hit the road, you should take the time to get familiar with your new home.


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[Assistant] Such a wonderful vehicle naturally needs to be paired with a stunning round.


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[Assistant] Today, we're taking a ride on the Great Ocean Road. One of the world's most beautiful roads, and an absolute must-see attraction in Australia.


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[Assistant] The road stretches almost 300 kilometers, bringing you to all of its coasts, beaches, cliffs, waterfalls, and forests along the way.


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[Assistant] There are scenic lookouts placed throughout the route. So remember not to let your driving be distracted by the scenery.


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[Assistant] Well, because today's Friday, we're gonna deal with a lot of traffic. It's about a good 45 minutes.


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[Assistant] Yeah, let's definitely do that. Okay. It's getting a little chilly. Okay. How about the sun roof?


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[Assistant] Wow, passengers. I've picked up probably over 10,000 people already.


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[Assistant] It's a pretty bad rating, and uh, drivers will tend to cancel on your rides, they'll...


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[Assistant] So uhm, there's this one time where the front passenger threw up.


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[Assistant] Yeah, sure. You know, LA, there's so many things to do. Uh, do you like basketball? Yeah. The LA Lakers, Clippers, and you're at LA at a perfect time.


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[Assistant] Because this is the time of the year where there's a lot of things going on. The Lakers are on. They're playing.


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[Assistant] You know, I might go to that game too. Really? I got some friends that are coming into town. Oh, no joke. I'm serious. Oh dude, that'd be cool if we could do that. Did you guys buy the tickets already? I think so. Oh wow, okay.


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[Assistant] You know, this is pretty standard in LA. Yeaah. If we're going one mile, ten minutes, yeaah. This is pretty standard.


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[Assistant] So we have to get used to, as drivers, we have to get used to the traffic.


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[Assistant] Yeah, there are a lot of good places to drink around here. Tons of bars. The night scene.


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[Assistant] Is ridiculous. Lots of places where you can go. Just keep in mind that the bar is here close early. 2 o'clock in the morning. Last call is always at 1.30.


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[Assistant] And, uh, Shaquille O'Neal, a lot of the NBA players, they love to frequent that bar. And when they go, their tabs are run up in the thousands, every time.


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[Assistant] Oh yes, yes, he is generous. I actually picked up one of the bartenders and he told me that story where famous celebrities go into his bar all the time and they tip very well.


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[Assistant] There are a lot of places that are overrated in LA. I gotta say, uh, Santa Monica is pretty overrated.


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[Assistant] The cities here are really safe. Uh, crime rates have dropped. A lot. So, you'd be surprised how safe you are in Beverly Hills.


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[Assistant] When tourists come to Los Angeles, one of the places they tend to visit is Koreatown.


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[Assistant] About 10 minutes away from downtown LA and it has over 300 Korean barbecues there. Everything's open very late. There are bars there.


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[Assistant] And you're gonna have to look into that. Yeaah. The Korean Channel's a good place.


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[Assistant] Actually, I'm from Bangladesh. Ooh, the women hot there. Here's a picture of my wife.


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[Assistant] Or Mandragora is used to return those who've been petrified to their original state.


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[Assistant] Mandrake or Mandragora is used to return those who've been petrified to their original state.


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[Assistant] It's also quite dangerous. The mandrake's cry is fatal to anyone who hears it.


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[Assistant] Mandrake or Mandragora is used to return those who've been petrified to their original state.


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[Assistant] It's also quite dangerous. The mandrake's cry is fatal to anyone who hears it.


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[Assistant] You're lying! Not just to me, that doesn't matter. To yourself as well. That's what a fool does.


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[Assistant] Hello, grammarians. Let's talk about reflexive pronouns, and just as a word of warning, this means I'm going to be talking about myself a lot. What I mean is that in English we have this distinction between the personal pronoun, uhm, so for example, me, and its reflexive pronoun, which is myself.


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[Assistant] And we use these pronouns in very specific cases. So I'm gonna show you what all of those reflexive pronouns look like, uh, contrasted with their personal pronoun forms, and then we're gonna talk about how we use them. So, so in the first person we say, uhm, personal pronoun is me, the reflexive pronoun is myself.


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[Assistant] The first person plural personal pronoun is us, and the reflexive form of that is ourselves. Then in the second person, both plural and singular, personal pronoun is you.


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[Assistant] And then in the reflexive it can either be yourself when you're addressing one person or yourselves when the you you are talking to consists of more than one person.


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[Assistant] The singular third-person pronouns look like this. It, her, and him. And the reflective versions are as follows. Itself, herself, and himself.


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[Assistant] Finally, the personal pronoun them becomes the reflexive pronoun themselves.


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[Assistant] Now all of these are what we would call object pronouns. They can all be the object of a verb. So they're never the doers, they're always the doees.


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[Assistant] With the exception of you or it, none of these pronouns, uh, can be the subject of a sentence. In standard American English, it is not grammatical to say, me eat a cookie, for example. It's part of why Cookie Monster sounds so funny.


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[Assistant] So then the question becomes, when do you use these? So the place for these object pronouns to go is in the back end of the sentence, what we call the predicate, uh, where the object of the verb lives. So for example, she poked me, she is the subject of the sentence.


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[Assistant] It is the do-ee, it is the thing that something is done to and not the do-er. So that's when you'd use object pronouns generally. But, when do you use reflexive pronouns?


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[Assistant] As opposed to the other possibility, which is Janelle making breakfast for someone else, Janelle made us breakfast. And in this case, this, this usage is not reflective. She's not doing a thing for herself or to herself. She's doing, she's making breakfast for other people. And so you just use the regular personal object pronoun there.


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[Assistant] You can only use a reflexive pronoun when the subject and the object of the sentence are the same thing. Janelle is the same thing as herself. Janelle is not the same thing as us, so we would say us here and not ourselves.


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[Assistant] How about this one? Roderick saw me in the mirror. Now I am not named Roderick. I'm not the same thing as Roderick. And if I were writing a sentence about myself, I would say, I saw myself in the mirror.


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[Assistant] Roderick and I and me are not the same person. I and myself are the same person. The same person as Roderick is Roderick.


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[Assistant] So, if we were to say Roderick saw Roderick in the mirror, we would render that as Roderick saw himself.


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[Assistant] Because the subject here and the object here are the same thing.


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[Assistant] So remember, you use reflexive pronouns when the subject and the object of a sentence are the same thing.


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[Assistant] It's really easy to get tripped up this way, especially if there's a compound object in the sentence.


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[Assistant] And it's easy to get confused because you're talking about two, two people here in this, uh, in this object. And that's a little befuddling. It kind of throws you off. And so there's a test you can do. If you're unsure of whether or not it should be Vidya or myself, or Vidya or me, which is what I would say, how do you tell?


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[Assistant] Take the other person out of the object. Just for a little bit. So would you say, you can talk to myself? Or would you say, you can talk to me?


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[Assistant] Well, since we know that you is not the same thing as myself, and you can only use reflexive pronouns when the subject


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[Assistant] And the object are the same thing, the answer is me.


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[Assistant] So then, we bring Vidya back, we bring the other part of the object back, and it becomes, you can talk to Vidya, or me.


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[Assistant] So when in doubt, sub it out. Take the other part of the object and just pretend it's not there and just think about how the subject and the object connect.


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[Assistant] Chances are you won't actually end up using a reflexive pronoun. Perform that little check and you'll never go wrong. You can learn anything. David out.


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[Assistant] She steps through the door. And where's Ted? Not eagerly waiting by the door.


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[Assistant] Nah, I'm across the room at my drafting table. Showing some foxy young thing all my cool architecture stuff.


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[Assistant] So Robin strolls over, and I casually give her one of these. Hey, what's up?


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[Assistant] Okay, yes, you got me. One of the reasons I threw these parties was so that I could introduce you to, uhm, this guy. Uh, I figured, you know, since it didn't work out between us and now we can just laugh about it.


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[Assistant] Previously, I had covered three of the basic aspects of English, and that's simple, perfect, and progressive. And so there's just one more. And it's a combination of the last two, and it's called the perfect progressive. And to recap what those two things do, is what the perfect does, is it denotes something that is complete,


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[Assistant] And the progressive notes something that has been ongoing. And it seems like those two things together don't make a whole lot of sense, but I promise that they do. You can use the perfect progressive aspect.


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[Assistant] To say that you've been doing something for a long time or you will have done something for a long time or that you had been doing something continuously in the past and now it's stopped. So let me explain how the perfect progressive is constructed. You take the verb to have and then you combine it with the word been and then the verb in question and then the ending ing.


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[Assistant] So as with all of our aspects, the only part that changes is this have stuff. This is the only word that changes depending on which tense you situate it in.


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[Assistant] So in the past you would say I had. I had been eating cookies.


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[Assistant] In the present, you would say, I have been eating cookies. In the future, you can say, I will have been eating cookies.


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[Assistant] So you can use the perfect progressive aspect in a couple of different ways. You can say that something


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[Assistant] If it had been ongoing in the past and is now done, you can say that it's been ongoing in the past and is still happening now. You know, I have been eating cookies all morning and I have no intent to stop. Or you can use the perfect progressive to say how long something has been going on. So you can say, I've been eating, I will have been eating cookies for 40 years come next Thursday and I have no regrets.


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[Assistant] You know, you can say how long something has been going on using this aspect.


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[Assistant] But you get the idea. So the perfect progressive is formed by combining have and have is the part that changes. I had been, I have been, I will have been with been and the verb in question with an ing ending. You can learn anything. David out.


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[Assistant] So there we were. Stuck on an airplane to Philadelphia with two very un-single girls. All thanks to your Uncle Barney.


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[Assistant] So, Barney and I hit the town. Philadelphia, PA. Our first and only stop, Sasha's party.


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[Assistant] Hello boys and girls. My name is Larry. Today we are going to study this book. This is Brain Bank Science Book Number 15.


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[Assistant] Can you help me read the title of this book? Let's read together. Diary of a pumpkin. Diary of a pumpkin. What is a diary? A diary is a journal. A diary is when you write information about your day.


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[Assistant] So we are going to write information about this pumpkin. Pumpkin in Korean is hobak. Hobak. What color is this pumpkin? Orange. Orange. Some people say orange. Orange or orange. Depending on where you come from and learn English.


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[Assistant] I say orange. So this hobak is orange.


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[Assistant] Let's read about the diary of this very big pumpkin.


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[Assistant] Wow. Diary of a pumpkin. Let's look at this picture.


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[Assistant] Pumpkins. Now, there might be some underneath, but I cannot see them.


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[Assistant] Are all the pumpkins the same size? No. This one is very small.


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[Assistant] So we have small pumpkins and we have big pumpkins or big hobaks or small hobaks.


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[Assistant] I like wagon because it has wheels. Wheels. And we can pull it.


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[Assistant] This is a red wagon.


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[Assistant] And this wagon has many pumpkins in it. Now can you see here? Looks like some wood chips.


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[Assistant] Okay, now in a diary, we always have to put the date. So this is April 26th. Let's look at some of the pictures. Here we have pumpkin seeds or hobak seot. Seeds in Korean is seot. Seot. Here we have a happy little girl.


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[Assistant] She has many seeds in her hand. And here we have granddad or haraburji, haraburji, and granddaughter. And what are they doing?


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[Assistant] They are planting the seeds. They are planting siat. Siat.


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[Assistant] Let's read. Do you have your reading glasses on?


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[Assistant] Granddad has a pumpkin plot.


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[Assistant] Pumpkin plot is an area of land. An area of land. So this area here


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[Assistant] The area of land for growing fruits and vegetables. This is a pumpkin plot.


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[Assistant] Which means granddad is only


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[Assistant] Going to grow pumpkins in this area.


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[Assistant] Today, I helped him plant pumpkin seeds. I.


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[Assistant] Who is I? Who is writing this diary?


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[Assistant] The little girl. This is her diary about planting pumpkins with her granddad, her haraburji. So she's helping. Granddad gave me, gave to give.


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[Assistant] Gave me some pumpkin seeds of my own. This means these seeds belong to her. They are not granddad seeds. They are her seeds. Her siat. Her siat. Here we have a shovel used for digging and here


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[Assistant] We have a gardening fork. And we use that to clear the land, put the seeds in the hole right here.


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[Assistant] She says, I am planting pumpkin seeds with granddad. Very exciting time for her. Have you ever planted seeds before?


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[Assistant] Let's see what happens the next day or many days later. Are you ready?


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[Assistant] I have my own part of the pumpkin plot. My own. This area belongs to this little girl. Granddad gave it to her.


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[Assistant] And said, grow your pumpkins here.


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[Assistant] Who will grow the biggest pumpkin? Biggest pumpkin. Very large. Huge. Maybe this big. Bigger than you. Will it be granddad or me? Who do you think will grow the biggest pumpkin? The biggest hobak.


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[Assistant] Okay, let's see what happens next.


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[Assistant] We have granddad and the little girl watering the pumpkin seeds. This is called a watering can.


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[Assistant] We have the first leaves here. Oh, this is very interesting. What is this?


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[Assistant] This is called a water pump. The little girl will lift the handle up.


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[Assistant] And then water comes out. This water


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[Assistant] Comes from a very deep well. A very deep well. Let's read.


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[Assistant] It is sunny in my part of the pumpkin plot.


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[Assistant] You can see the sun shining down here.


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[Assistant] What do these seeds need to grow? They need water and they need sun. They need water and sun.


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[Assistant] Granddad told me to water my pumpkin seeds every day. Every day. And that's what she is doing. Now, we have the first leaves. Right here, growing.


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[Assistant] The pumpkin seeds are growing into pumpkins. Isn't this exciting?


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[Assistant] Let's look at the next journal entry in her diary.


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[Assistant] To get a closer look, we can see, look how big this watering can is. It's almost as big as she is.


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[Assistant] That's why Grandad is helping her hold it. It's too big for her. And the water comes out.


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[Assistant] Okay, we are still May 5th. The same day. I waited and waited.


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[Assistant] Why aren't my pumpkins growing?


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[Assistant] Today, I saw some little green shoots. I showed granddad. These are little green shoots. Shoots in Korean, sesak. Sesak. Right here. The pumpkin plant is growing.


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[Assistant] All from the little seeds. Now we have the first green shoots. We're gonna finish with section one.


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[Assistant] Come back in section two and let's find out.


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[Assistant] The growth of these pumpkins. I'll see you soon.


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[Assistant] Hello boys and girls. Welcome back for part two of a diary of a pumpkin. If you remember in part one,


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[Assistant] More than one month later. Let's see how much the pumpkin has grown. Let's look at the pictures. Here we have the young girl watering her pumpkin. And we can see there's some more green plants there. Here is a picture of a green plant. And here we have a drawing.


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[Assistant] On a stem with a very big green leaf. Let's read this story. Do you have your reading glasses on?


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[Assistant] My pumpkin plants are growing fast now. This means they're growing very quickly. They're getting big very quickly.


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[Assistant] The big leaves soak up the sun. Here is a big leaf and they soak up the sun. Soak up. The difficult word. Let me explain something differently to you. If you have a towel and you pour water on the towel, will the water


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[Assistant] Fall to the ground? No. The towel soaks up the water.


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[Assistant] Collects, gathers, absorbs, soak up.


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[Assistant] So the leaves soak up the sun. They love the sun.


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[Assistant] And the stems are prickly. Prickly.


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[Assistant] Now, the opposite of prickly would be smooth. Smooth skin. Sometimes men have prickly skin here. Okay? Prickly. You can see right here. These little bumps make this stem prickly. And the snail is trying to climb up this prickly stem.


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[Assistant] Why? Why is this snail here? Maybe we can find out the answer here.


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[Assistant] The prickly stems help stop, stop the snail from crawling up to eat the leaves.


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[Assistant] So the snail wants to, uh, wants to eat this leaf. The pumpkin doesn't want that. So the pumpkin plant grows prickly stems. Okay, let's see what happens.


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[Assistant] Now, July 9th, about one month later. Here we can see a beautiful flower.


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[Assistant] Big flowers are growing on my pumpkin plants now. What color is this flower? Very good, yellow. What is this? This is a bee.


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[Assistant] And if you look very closely, you can see the prickly stem.


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[Assistant] A very tiny baby pumpkin. And this is a pumpkin life cycle.


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[Assistant] This is the changes the pumpkin goes through. Let's take a closer look. Just a minute. We picked some of the flowers.


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[Assistant] Picked has many different meanings. Picked means to choose. I pick you to be on my team. This, a little bit different. This means to...


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[Assistant] Plants or to pick vegetables or to pick fruit means to harvest, to gather.


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[Assistant] Grandad, or remember the Korean word for grandad? Harabarji. Harabarji.


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[Assistant] Said that would help me get bigger pumpkins. So the little girl takes the flowers off and maybe now the pumpkin will get bigger and bigger.


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[Assistant] Let's look at the pumpkin life cycle. The pumpkins start here.


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[Assistant] The first one has seeds, or siat, siat.


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[Assistant] They grow into kind of like a plant. A beautiful green plant with big leaves that soak up the sun, get even bigger. Then, we have some beautiful flowers.


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[Assistant] Do you remember the color of these flowers? Red? Blue? Orange?


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[Assistant] No. What is orange? Do you remember from the very first page what was orange? Hobak. Or pumpkin. The pumpkin was orange. But these flowers are yellow. Yellow. And then this.


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[Assistant] It gets bigger and bigger. Is this a big pumpkin yet? What color is that pumpkin? This one. This is a green pumpkin. And finally, it turns into a orange pumpkin or a ripe pumpkin. Let's see if we're correct. Pumpkin seeds


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[Assistant] Flower on a pumpkin, very good. A growing pumpkin, it's green.


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[Assistant] And finally, a ripe pumpkin. Now this pumpkin means


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[Assistant] Ripe means it's able to be eaten. If you want, you can eat that pumpkin. If you try to eat this pumpkin, it will not taste good.


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[Assistant] So you always want to eat ripe vegetables and ripe fruit.


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[Assistant] Ripe means mature or ready to be eaten.


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[Assistant] Granddad drew this diagram.


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[Assistant] It shows the stages of a pumpkin's growth.


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[Assistant] So this is a diagram. It shows you the stages or the steps.


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[Assistant] One, two, three, four, five. In this diagram, there are five stages of the pumpkin's growth. Let's look at the next.


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[Assistant] Now we have July 14th, a couple of days later. It is hot weather now. The sun is there.


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[Assistant] My pumpkin flowers have turned into green pumpkins. Right here.


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[Assistant] Lots of sun and lots of water. What is this called? A watering can.


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[Assistant] Is this a ripe pumpkin? Hmm. No. Do you remember what color a ripe pumpkin is from our diagram? Very good.


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[Assistant] In our diagram, a ripe pumpkin is orange, not green. This is a growing pumpkin.


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[Assistant] The water helps the pumpkins grow bigger.


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[Assistant] Is this a big pumpkin? What about this? Is this a big pumpkin? Can you imagine having a pumpkin this big? Bigger than you? It could be possible. Let's find out. On this day, it is August 4th. The next month. And it looks like in August, it is very sunny.


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[Assistant] In the month of August, how is the weather where you live? Is it sunny? Is it raining? Is it snowy? Is it cloudy? Is it hot? Is it warm? Is it cold? Here, I think it is sunny and hot. What is the little girl going to do?


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[Assistant] I am going on vacation today.


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[Assistant] Granddad is going to take care of my pumpkin. The little girl is leaving. Where is she going? We don't know. She is going on a trip some place. Which means she cannot take care of her pumpkins. What does she need to do? She needs to water her pumpkins.


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[Assistant] So she asked granddad to do it. If a pumpkin has no water, what happens?


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[Assistant] The pumpkins will die. She even wrote a little note here for grandad. Let's see what it says. Note to grandad.


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[Assistant] Please remember to water the plants in the morning and at night.


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[Assistant] So how many times does Grandad have to water the pumpkin plants? Just once?


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[Assistant] Two times? Three times? Four? Five? Six?


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[Assistant] Granddad has to water the pumpkin seeds or the pumpkin plant two times. In the morning and at night. And then the pumpkins will continue to grow. And hopefully there is plenty of sunlight. Remember the pumpkins need sun and water.


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[Assistant] I'll see you again very soon for part three. Goodbye.


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[Assistant] Hello boys and girls. Welcome back for part three of Diary of a Pumpkin. If we look at this date, September 30th.


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[Assistant] We are now five months later. Five months later, we planted the seeds, the siats, in April. The end of April. She looks very happy, doesn't she? Why? Because her pumpkin is fully grown. Let's read this diary.


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[Assistant] My pumpkins are huge now. Huge. Very big. Bigger than me.


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[Assistant] But very big. That is what huge mean. They are ready to pick. Do you remember pick means here means to harvest.


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[Assistant] It means to take the vegetables or take the fruit


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[Assistant] From the trees or the plants or the ground.


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[Assistant] So they're ready to harvest, they're ready to pick, and if I want, I can eat.


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[Assistant] Granddad got a measuring tape. We measured my pumpkins. Remember, granddad and the little girl want to see who has the biggest pumpkin. Who do you think? Granddad or the little girl? Okay, let's look and find out.


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[Assistant] We measured granddad's pumpkins too. Who will have the biggest pumpkin? Now, they're going to measure around, around the pumpkin. They're going to see whose is bigger and maybe how much they weigh the weight. You can see all the pumpkins back there, many of them.


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[Assistant] Here is the green plant, there's the leaves, the stem, and now the big pumpkin.


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[Assistant] Let's look at the next page. October 1st. I won! I won! She is the winner. She has the biggest pumpkin.


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[Assistant] Let's find out how big her pumpkin is. My biggest pumpkin. That means...


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[Assistant] She has many, she grew many pumpkins. But the biggest one, the biggest one was 23 inches around. Around here.


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[Assistant] Right here, 23 inches around, which is about


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[Assistant] Fifty-seven centimeters. About fifty-seven centimeters.


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[Assistant] And it weighed 18 pounds. That's about 8 kilograms. That's a pretty big pumpkin!


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[Assistant] So granddad's pumpkin will be smaller. Let's find out how big granddad's pumpkin is.


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[Assistant] Grandad's biggest pumpkin was 20 inches around. 20 inches is about


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[Assistant] 50 centimeters. About 50. Very close to the little girls. Very close.


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[Assistant] And it weighed 16 pounds, which is about...


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[Assistant] So Grandpa got second place.


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[Assistant] But the two pumpkins were very close. Very similar.


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[Assistant] What are you going to do with all those pumpkins? Mom asked. Just wait and see, we said. Hmm. What can you do with these pumpkins?


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[Assistant] Do you think she is going to eat these pumpkins? Maybe something very different.


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[Assistant] And if you can look, you see all these leaves on the ground. Do you know what season this is? Does it look like winter? No. Does it look like summer? No. This season has two names. Fall or autumn.


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[Assistant] Let's see, em and en. Okay, this is autumn or fall.


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[Assistant] Let's find out what granddad and the little girl are going to do with their pumpkins.


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[Assistant] Wow! They didn't eat the pumpkins at all!


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[Assistant] This is what granddad and I did with those pumpkins. What did they do?


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[Assistant] To say what they did with these pumpkins? I know one. I'll give you a little secret. C A R V E D. Carved. Granddad and the little girl carved the pumpkins. What did they make?


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[Assistant] What kind of face is this? This one looks like, uh, a silly face. Can you make a silly face? Try.


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[Assistant] This is a scary face? Or a surprise face?


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[Assistant] Maybe this pumpkin is frightened.


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[Assistant] And this one here. This pumpkin looks sad?


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[Assistant] This is a happy pumpkin. Can you look happy? Very good. Why did granddad and the little girl carve the pumpkins? I think I know why. Let's find out.


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[Assistant] Wow! They made jack-o-lanterns. Can you say jack-o-lantern? Jack-o-lantern. I'll spell it for you.


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[Assistant] Jack-o'-lantern. Very good. Now, you can see this here. And this one. These are called lanterns. A lantern is a kind of light. Now, these jack-o'-lanterns have light. But they're made in a pumpkin. Do you know when we use and make


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[Assistant] Jack-O-Lanterns. It's a special holiday called Halloween. H-A-L-L-O W-E-E-N Halloween. Now they use these to kind of frighten off any ghosts that may be around your home.


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[Assistant] Have you ever made a jack-o-lantern? They're very fun. So maybe this year...


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[Assistant] You can make a jack-o-lantern with your mom and dad. We've finished the story of a diary of a pumpkin. I hope you've enjoyed it, and I will see you in the next book. Goodbye!


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[Assistant] We are actually in the island of Hawaii. Now in Hawaii, do you know what their traditional dance is called?


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[Assistant] Daocheng Yading is a magical and mysterious land.


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[Assistant] Located in the southwest of China's Sichuan province.


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[Assistant] This is a kingdom surrounded by breathtaking views.


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[Assistant] It's like placing people into a colorful fairy tale world.


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[Assistant] The focal point is the three mountain peaks in Daocheng Yading.


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[Assistant] The most beautiful is called young my young.


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[Assistant] It is about 6,000 meters in height and has the shape of a perfect pyramid.


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[Assistant] The American explorer Joseph Rock first introduced it to the world with photos taken for the National Geographic Magazine.


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[Assistant] He wrote, She is the most beautiful snow peak my eyes have ever seen.


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[Assistant] The crest of the mountains is covered by snow most of the time.


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[Assistant] No one has yet ever been able to reach the top.


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[Assistant] It is an irreplaceably sacred place in the hearts of the local people.


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[Assistant] The locals say that if one could walk round the holy mountains three times,


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[Assistant] Then your wishes for this life will be fulfilled.


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[Assistant] But it is such a great challenge to both one's physical ability and mind, because of its altitude.


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[Assistant] But also earth that can purify the soul.


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[Assistant] Put 25 pennies into one coin and you'll have a quarter worth 25 cents, hope you understood.


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[Assistant] Yo, what's going on guys? Tanmay here for simple snippets and welcome back to another video tutorial on data structures and algorithms. And today finally, we are starting off with our very first nonlinear data structure, which is tree data structure.


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[Assistant] So this is just an introduction and it's a very very important video.


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[Assistant] Because this is where we start off with the non-linear type of data structures and don't worry we'll take a differentiation.


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[Assistant] But this is just an introduction to the tree data structure, which is a nonlinear data structure.


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[Assistant] This video is very important guys and the topics that we are gonna cover in this video is as shown on the screen.


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[Assistant] What is a tree data structure? We'll try to understand how a tree data structure looks by taking a real world example and then comparing it with our data structure example. We'll also see what is a binary tree.


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[Assistant] We will also understand some important tree terms and some important tree properties. Those are absolute important. Those are fundamentals which you need to know.


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[Assistant] We will see the logical diagram in the terms of implementation of how it would look like when we actually implement a tree data structure programmatically.


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[Assistant] And then at the end we will simply list down some of the types of trees, some of the variations as well as the applications of tree data structure.


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[Assistant] Please make sure you watch this video till the end. This is a very, very important data structure. It has a wide range of applications, many variations and


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[Assistant] It is one of the most widely used data structure in real world applications also. So with that being said, let's get started.


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[Assistant] If you're new to my channel, my name is Tanmay Sakpal and I do a lot of computer science and information technology video tutorials like computer programming, development, technology talks and a lot more on this channel.


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[Assistant] So if that's something you are interested into, then definitely subscribe and turn on the notifications to get the latest updates and never miss out on such important topics.


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[Assistant] A quick recap, you can skip this, but we've already seen this in this DSA course, in this DSA playlist.


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[Assistant] We know what is a data structure, right? If you've seen this DSA course, we already know what is data structure. Data structure is simply a way of storing and organizing data in the memory in such a way that access management and modification becomes efficient.


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[Assistant] So it's nothing but how you store the data, right? Now, why am I taking a recap? It is because which data structure to use depends upon many different criterias. Some of them have listed as follows.


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[Assistant] Depending upon which is more efficient. So for some applications, maybe a queue data structure is much more efficient than compared to a stack.


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[Assistant] So same on those lines. Another criteria is memory usage and efficiency.


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[Assistant] And of course there are many other criterias, but the point being said over here is every data structure has its own pros and cons with its own unique properties and some drawbacks. So it depends upon the application, depends upon the condition on which we decide which data structure is supposed to be used. So I just wanted to give you this recap.


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[Assistant] So now that you've understood what is a data structure, which you already had, but this was just a recap. So far in this entire tutorial course, as I mentioned, we've covered quite a lot of linear data structures and to give you a basic explanation of what is linear and nonlinear.


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[Assistant] So if you see on this screen, I have denoted the four basic linear data structures, which we've already covered, arrays, stack, queue, and linked list.


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[Assistant] If you observe array, you can see data is arranged in a sequence in a proper sequential order in a linear order. In a queue also you can see we have data coming in from one end and going out from the other. So we have a rear and a front.


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[Assistant] That is a logical start and end. In a stack also, data is pushed in this direction and popped out from the same end, but it is still arranged in a linear way in a sequential way.


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[Assistant] And linked list again you can see we have every node arranged one after each other.


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[Assistant] So all of these data structures are linear in a sense that the data is arranged in a sequential manner.


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[Assistant] So the definition of a tree data structure is, a tree is a non-linear data structure


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[Assistant] That simulates a hierarchical tree structure with a root value and sub trees of children with parent node represented as a set of linked nodes. Okay.


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[Assistant] So before we understand the technical aspect, let's take a real world example of what is a hierarchical tree. So let's take an example of a typical college hierarchy, you know. So in a college we have a chairman, we would have a director. So a director is under the chairman.


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[Assistant] Then under the director, we have multiple HODs that is head of departments. So let's say in a college, we have multiple departments.


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[Assistant] So we have the science, we have commerce and we have arts department. So we have their individual HODs. They all report to the director. Under the HOD, we have senior faculty 1 and 2.


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[Assistant] Over here we have only one senior faculty and over here we have three senior faculties and


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[Assistant] And you have many different types of hierarchical data in the real world.


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[Assistant] So a tree data structure is a data structure that simulates this behavior. Okay.


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[Assistant] So in data structures now coming into the data structures side, our data structure is going to try to simulate this same hierarchical behavior. When I say that it would mean that the data is going to be organized in a hierarchical tree kind of scenario. So let's see how that looks and then we will again go through this definition.


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[Assistant] Okay, so on the right hand side, this is where a logical tree diagram would look like for a nonlinear data structure of a tree. So again, let's go through the definition now.


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[Assistant] So tree is a nonlinear data structure and the reason why it is nonlinear is because data is not organized in a linear way. You can see over here you have multiple


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[Assistant] But you can clearly see that it is not linear. So this tree is a nonlinear data structure that simulates a hierarchical tree structure. So this looks pretty much like this with a root value. So the top node is going to be called as the root node. So this is root, which is at the top.


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[Assistant] So I've just named them randomly, okay. This is not like there is a way to name them. This is just for our reference for now. And you can see root node is root node number one. After that, it has two nodes right below it, which is node two and node three.


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[Assistant] So, these can be individually considered as sub-trees of children. So, for 1, the children are node 2 and 3. So, if you only see everything below 2,


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[Assistant] It can be also called as a tree only, right? So it is a subtree.


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[Assistant] Similarly, this is also a tree data structure itself. So these are sub-trees with a parent node, parent node being root node over here. And it is represented as a set of linked nodes.


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[Assistant] So these yellow arrows are nothing but links or they are also called as edges. Okay.


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[Assistant] Let's try to get into more details about some important terms of tree data structure.


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[Assistant] Okay, so on the left hand side, we have some important tree terms. Let's go one by one. If you're making notes, you can take a screenshot. You can note them down, but don't worry. I'm going to be sharing all this theory.


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[Assistant] Along with the diagrams on our official website. So you can just copy paste it and prepare your notes for your exams.


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[Assistant] There's a link in the video description to our official website for this article. Just go there and you can refer these notes later on. But now let's go one by one through all these different tree terms. So point number one, root.


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[Assistant] And it does not have a parent. So that would be the top node, which is node number one and it is called as root node. So it's a special node because there is only one root node.


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[Assistant] And the entire tree is referenced through it. So you can go to any node starting from the root node.


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[Assistant] Also, it does not have anything above it. So there is no parent of this root node. So obviously the next question is what is a parent node?


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[Assistant] So that is point number two and parent node is


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[Assistant] A node, which is an immediate predecessor of a node. Predecessor means the node that comes before it. So, for node 2 and 3,


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[Assistant] Which node comes before it, immediately it is root node, which is node 1. So for node 2 and node 3,


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[Assistant] So that is point number three, child node. Child node is all immediate successors of a node are its children. So after node one, node one is directly linking to node three and node two.


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[Assistant] I hope I'm making sense over here. Please do note these points. Do note these terms. These are absolutely important. In further tutorials, in further videos, we will constantly refer to these terms directly. And I'm going to assume that you already know. So hence, please pay attention.


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[Assistant] Now moving on we have the concept and the term of siblings. Nodes with the same parent are called siblings. So over here if you see node 2 and 3 have the same parent as node 1 so they can be considered as siblings. If you see below, let's go one level down.


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[Assistant] Is the parent of node 4, node 5 and node 6 because it is immediately predecessor of the node. That is node 2 is directly linked to node 4, node 5 and node 6.


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[Assistant] So this makes node 4 and 5 and 5 and 6 and 4 and 6, all of these three as siblings, as well as all of them as child node of node 2.


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[Assistant] Okay, if you go one level below again, node 9 and 10 are siblings because their immediate predecessor is node 5 which is their parent.


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[Assistant] Which makes 9 and 10 as children of 5. Makes sense? Alright. So siblings is done. Let's move down. We have point number 5 which is leaf. So leaf is the last node in the tree and there is no node after this node. So at the bottom is where we will find the leaf nodes. So over here that would be node 9, node 10, node 11,


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[Assistant] And also at this level we have node 8 because all these nodes do not have any node below it. So is 9 linked or is 9 pointing to any other node? No. Is 10 pointing to any other node? No.


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[Assistant] Is 11 pointing to any node? No. And 8 is also not pointing to any node, which makes them leaf nodes. Alright?


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[Assistant] Okay, let's see point number six. Point number six is edge. Edge is the connection between one node to another. It is the line between two nodes or a node and a leaf. So this yellow line is what I'm trying to say is a edge. It is also known as a link.


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[Assistant] So it can be link and edge. Please remember both these two terms. It is just the line that is connecting between the two nodes.


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[Assistant] Now do note that these lines are not bi-directional. They only go in one direction which means that you can go from node 1 to 3, but you cannot come back. This is not valid. So when you actually implement a tree data structure,


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[Assistant] The traversal of nodes will only start from root node and it will go to


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[Assistant] The child nodes and it will go below only and not in reverse order. Okay, so hence the arrow is also in one direction. It is not like this. So keep in mind that.


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[Assistant] The edges and the links are not bidirectional, they are only in one direction and that is the downward direction. The next term is the path.


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[Assistant] So, path is a number of successive edges from source node to the destination node.


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[Assistant] So if the destination node is 7 and I just mentioned that we will start from the root node only, the path would be this edge and then this edge, right? So this is going to be our path. Another example, if


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[Assistant] This is the destination where we want to reach. We will have to traverse from 1 to 2. We will have to traverse from 2 to 5.


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[Assistant] And then we'll have to traverse from 5 to 10. So three edges come between


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[Assistant] Root node 1 and the destination node which is a leaf node of 10 and that is the path. The 8th term over here is the degree of the node. So what is degree of the node? So degree of a node is equal to the number of children a node have. So if you try to calculate the degree of the root node,


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[Assistant] You simply count the direct children it has. So we have node 2 and node 3 as


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[Assistant] Which is node n2 or node 2 which has the maximum number of children which is 3.


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[Assistant] So the degree of the tree you can say is also 3, okay.


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[Assistant] Okay, so these were some important tree terms. I hope they were easy to understand.


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[Assistant] Let's see a few properties of tree data structure. Okay, so property number one.


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[Assistant] Says that a tree can be termed as a recursive data structure. So what does this mean?


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[Assistant] Now I am assuming you already know what is recursive behavior or recursion or recursive function. Recursion basically means that


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[Assistant] Repetition of same entity or same activity over and over again till a particular condition is met.


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[Assistant] So what does this mean? So if you see, if you start from root node 1, this whole data structure is a tree.


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[Assistant] Now, if you go to its child nodes and divide it into two subtrees, that is this is subtree 1 and this as subtree 2,


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[Assistant] You can safely say that even these two are tree data structures.


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[Assistant] Now you can again further divide these sub trees into smaller sub trees.


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[Assistant] And you can keep on going till you ultimately reach a single node.


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[Assistant] And as I mentioned, recursive in this context simply means that a tree data structure can be divided into smaller subtree data structures recursively till you reach a single entity that is the node. Okay.


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[Assistant] Okay, let's move forward, point number two. So in a valid tree,


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[Assistant] So if you calculate the number of nodes over here, we have 11 nodes. Let's calculate the number of links. 1, 2,


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[Assistant] So this is always going to be true for a valid tree. When I say valid tree, it means that it is a proper tree data structure and not something other than a tree data structure.


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[Assistant] This property only applies to a valid tree data structure. So if you simply have one more edge to one more node, let's say this is node 12, so this would be edge number 11.


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[Assistant] And node will become 12. So, number of nodes again will become 12 and edges will become 11. So, again the same property is followed. Okay, alright. Now, let's see three important properties or you can see these are


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[Assistant] Important attributes of a tree. The first one is depth of node.


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[Assistant] This node 6. I simply have to calculate the number of edges from this root node. So, this is the root node till this node 6. So, we have this one first link which goes from 1 to 2. Then we have this second link which goes to our node 6. So, the depth for node 6 is equal to these two edges. So, that is 2. Okay. Let's calculate depth for this node.


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[Assistant] For node 9 is going to be equal to this first edge. Then we will go from 2 to 5. This is the second edge.


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[Assistant] And then we will go from 5 to 9 which is our destination. So this is the third edge. The depth over here is 3. Okay. Basic enough.


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[Assistant] Because there is no node above root node.


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[Assistant] So the depth of root node is always gonna be zero, okay? Keep that in mind. It can be asked in your exams or as a trick question. Moving forward, what is height of the node?


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[Assistant] So height of a node is the number of edges. Again, it is number of edges only, but it is different than depth of node. So height of node


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[Assistant] Is the number of edges on the longest path between that node and a leaf. So when you calculate depth, you start from root to the particular node. But when you calculate height, you start from that node and take the longest path till you reach a leaf. Okay?


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[Assistant] So let's see what that means. Let's calculate the height of


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[Assistant] Node 3. So let me write over here. Height of node 3 is equal to the number of edges on the longest path between that node and a leaf. So for node 3, if you go from 3 to 8, this 8 is also a leaf. We have one edge. But for 3, we can go in this direction also. We will go from 3 to 7, which is one edge.


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[Assistant] And then we can go from 7 to 11 which is second edge and this is also leaf node. So, we have two options of leaf nodes starting from node 3.


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[Assistant] We have to select the longest path. Which is the longest path? Obviously we will go from 3 to 7 and 7 to 11 because there are two edges. So 2 is greater than 1. So height is gonna be 2. Okay. So height of node 3 is gonna be 2. Let's calculate the height of node 2. Which is this node. So we have first path going from node 2 to 4. And 4 is also a leaf node. We have one path going from 2 to 5.


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[Assistant] So, one edge and second edge. Again, we can also go from 2 to 5 and 5 to 10.


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[Assistant] Again one edge and second edge and both 9 and 10 are leaf nodes.


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[Assistant] And last direction which we can go is from 2 to 6. 6 is also a leaf node, so this is 1. So obviously, the longest path is


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[Assistant] Lastly, height of root node can be considered as this path.


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[Assistant] How to calculate height of node and depth of node? A lot of times students get confused between depth and height. It can be different, so please


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[Assistant] Note these points down and how to calculate them very properly. And last point, last property is height of tree.


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[Assistant] And the height of tree is always equal to the height of root node. So height of 1 which is this root node is equal to 3 which is also equal to height of tree. Okay, alright.


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[Assistant] So these were some important tree terms and properties. And now let's move forward.


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[Assistant] So, so far what we've understood is what is a tree data structure. We saw the definition. We saw the comparison of a real world tree hierarchy and also our logical tree. But so far what we've seen is a very general tree. When I say general, it is not a variation or a special type of tree.


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[Assistant] Now we'll see what is a special type of tree which is called as a binary tree. And as the name suggests, a binary tree is nothing but a tree


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[Assistant] Where each node or where every node can have maximum of two children. Okay, so that is the only specific definition for a binary tree compared to a general tree. That is in a binary tree, every node can have only maximum of two children. So over here you can see node two has three children.


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[Assistant] So that is not valid in a binary tree. So let's remove out one node and let's see how a binary tree would look like.