LeetCode OJ 62. Unique Paths

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

Note: m and n will be at most 100.

解题思路

机器人每次只能向右或者向下移动，因此对于到达[i, j]网格的路径数等于从左网格过来的路径数加上从上过来的路径数。所以得到状态方程dp[i, j] = dp[i-1, j] + dp[i, j+1]。但是要注意dp数组初始化为1。

代码

个人github代码链接

class Solution {public:    int uniquePaths(int m, int n) {        vector<vector<int> > dp(m, vector<int>(n, 1));        for(int i = 1; i < m; i ++){            for(int j = 1; j < n; j ++)                dp[i][j] = dp[i-1][j] + dp[i][j-1];        }        return dp[m-1][n-1];    }};