<reponame>yxun/Notebook
#%%
"""
- Unique paths
- https://leetcode.com/problems/unique-paths
- Medium

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?


Above is a 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28
"""

#%%
class S1:
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        import math
        return math.factorial(m+n-2) // (math.factorial(m-1) * math.factorial(n-1))

#%%
# DP
class S2:
    def uniquePaths(self, m, n):
        if m < 1 or n < 1:
            return 0
        dp = [0] * n
        dp[0] = 1
        for i in range(0, m):
            for j in range(1, n):
                dp[j] += dp[j-1]
        
        return dp[n-1]
        
#%%
"""
- Unique paths
- https://leetcode.com/problems/unique-paths
- Medium

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?


Above is a 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28
"""

#%%
class S1:
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        import math
        return math.factorial(m+n-2) // (math.factorial(m-1) * math.factorial(n-1))

#%%
# DP
class S2:
    def uniquePaths(self, m, n):
        if m < 1 or n < 1:
            return 0
        dp = [0] * n
        dp[0] = 1
        for i in range(0, m):
            for j in range(1, n):
                dp[j] += dp[j-1]
        
        return dp[n-1]
#%% - Unique paths - https://leetcode.com/problems/unique-paths - Medium  A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).  The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).  How many possible unique paths are there?   Above is a 7 x 3 grid. How many possible unique paths are there?  Note: m and n will be at most 100.  Example 1:  Input: m = 3, n = 2 Output: 3 Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner: 1. Right -> Right -> Down 2. Right -> Down -> Right 3. Down -> Right -> Right Example 2:  Input: m = 7, n = 3 Output: 28 #%% :type m: int         :type n: int         :rtype: int #%% # DP