[Leetcode]62. Unique Paths

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本文探讨了机器人在m×n网格中从左上角到右下角的不同路径数量问题，提供了递归与非递归两种解决方案，并分析了各自的时间与空间复杂度。

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62. Unique Paths

本题难度: Easy
Topic: Dynamic Programming

Description

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:

Right -> Right -> Down
Right -> Down -> Right
Down -> Right -> Right
Example 2:

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

我的代码

recursion

class Solution:
    def uniquePaths(self, m: 'int', n: 'int') -> 'int':
        if m < 0 or n<0:
            return 0
        if m==1 and n==1:
            return 1
        return self.uniquePaths(m-1,n)+self.uniquePaths(m,n-1)

no recursion

class Solution:
    def uniquePaths(self, m: 'int', n: 'int') -> 'int':
        res = [[0 for _ in range(m+1)] for _ in range(n+1)]
        res[1][1] = 1
        for i in range(1,n+1):
            for j in range(1,m+1):
                if j==1 and i==1:
                    continue
                res[i][j] = res[i-1][j]+res[i][j-1]
        return res[n][m]