<prompt> Hlalosa hore na ke hobaneng ha ho le bohlokoa ho sebelisa dynamic programming ho e-na le naive recursive algorithm.nan  <response>: Instruction in English: Explain why it is important to use dynamic programming instead of naive recursive algorithm. . Response in English: Dynamic programming is an optimization technique that can be used to improve the time complexity of certain computational problems, particularly those that can be broken down into smaller subproblems with overlapping substructures. In contrast, a naive recursive algorithm can quickly become very inefficient for large problems, as it will repeatedly recalculate the same subproblems multiple times, leading to an exponential increase in the amount of processing time required.The primary advantage of using dynamic programming instead of a naive recursive algorithm lies in its ability to store and reuse the results of previously computed subproblems. This can help to avoid unnecessary calculations and reduce the overall time complexity of the algorithm. Rather than recalculating the same subproblems over and over again, dynamic programming algorithms can simply refer to the stored results of those subproblems and use this information to solve the larger problem more efficiently.Moreover, dynamic programming can also help to improve the space complexity of an algorithm, as it makes it possible to implement solutions with an iterative, bottom-up approach rather than a recursive, top-down approach. This can help to reduce the amount of memory used by the algorithm, as it does not require the use of a call stack to solve the problem.Overall, dynamic programming is an important tool for solving complex computational problems in an efficient and effective manner. By avoiding the repetitive calculations of a naive recursive algorithm, dynamic programming can help to save both time and space, making it an essential technique for many different types of problems. . Response in Sesotho: Lenaneo la matla ke mokhoa oa ho ntlafatsa o ka sebelisoang ho ntlafatsa ho rarahana ha nako ea mathata a itseng a khomphutha, haholo a ka aroloang ka mathata a manyane a nang le likaroloana tse tsamaisanang. Ka lehlakoreng le leng, algorithm ea naive recursive algorithm e ka potlakela ho se sebetse hantle bakeng sa mathata a maholo, kaha e tla pheta khafetsa mathata a tšoanang ka makhetlo a mangata, e leng se lebisang keketsehong e kholo ea nako ea tsebetso e hlokahalang. Monyetla o ka sehloohong oa ho sebelisa dynamic programming ho fapana le naive recursive algorithm ke bokhoni ba eona ba ho boloka le ho sebelisa hape liphetho tsa mathata a neng a entsoe computed nakong e fetileng. Sena se ka thusa ho qoba lipalo tse sa hlokahaleng le ho fokotsa ho rarahana ha nako ka kakaretso ea algorithm. Ho e-na le ho pheta-pheta li-subproblems tse tšoanang khafetsa, li-algorithms tsa dynamic programming li ka bolela feela liphetho tse bolokiloeng tsa li-subproblems tseo le ho sebelisa boitsebiso bona ho rarolla bothata bo boholo ka katleho. Ho feta moo, lenaneo le matla le ka boela la thusa ho ntlafatsa ho rarahana ha sebaka sa algorithm, kaha e etsa hore ho khonehe ho kenya tsebetsong tharollo ka mokhoa oa ho pheta-pheta, ho ea holimo ho e-na le mokhoa oa ho pheta-pheta, o holimo-tlaase. Sena se ka thusa ho fokotsa palo ea mohopolo o sebelisoang ke algorithm, kaha ha e hloke tšebeliso ea mohala oa mohala ho rarolla bothata. Ka kakaretso, mananeo a matla ke sesebelisoa sa bohlokoa sa ho rarolla mathata a rarahaneng a khomphutha ka mokhoa o sebetsang hantle le o sebetsang. Ka ho qoba lipalo tse pheta-phetoang tsa algorithm ea naive recursive, lenaneo le matla le ka thusa ho boloka nako le sebaka, ho e etsa mokhoa oa bohlokoa bakeng sa mefuta e mengata e fapaneng ea mathata. 