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- [Leetcode]
- [Python]
- [medium]

- [💡]

- Math
- Dynamic Programming
- Combinatorics

cover: /img/cover/leetcode.jpg
categories: Leetcode

Problem

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to 2 * 109.

Example 1:

!https://assets.leetcode.com/uploads/2018/10/22/robot_maze.png

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

Example 2:

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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 -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Constraints:

  • 1 <= m, n <= 100

Solve

x-1 , y-1 x , y-1
x-1 , y x , y

應該是國中數學吧

右下角的為，上方 + 左邊 的方法次數

使用dp，memo

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class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        dp = {}
        
        dp[(0,0)] = 1

        for i in range(m):
            dp[(i,0)] = 1
        
        for j in range(n):
            dp[(0,j)] = 1

        for i in range(1,m):
            for j in range(1,n):
                dp[(i,j)] = dp[(i-1,j)] + dp[(i,j-1)]

        return dp[(m-1,n-1)]