LeetCode062. Unique Paths

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本文探讨了一个经典的动态规划问题：在m x n的网格中，从左上角开始，机器人只能向右或向下移动，到达右下角有多少种不同的路径。通过建立矩阵并逐步计算，给出了详细的解答过程。

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?

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

一道动态规划的题.这样的题先建立一个矩阵,然后逐步进行计算.

因为只能向右向下走,所以到达每个格子的可能就是到这个格子上方和格子左方这两个格子的方法的和.

class Solution(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        dp = [[1 for _ in range(m)] for _ in range(n)]
        for i in range(1,n):
            for j in range(1,m):
                dp[i][j]=dp[i-1][j]+dp[i][j-1]
        return dp[-1][-1]