[leetcode] 62. Unique Paths

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:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input:

m = 7, n = 3

Output:

28

分析

题目的意思是：一个机器人从左上角走到右下角，有几种走法。

• 令dp[i][j]为从0，0位置到i，j位置的走法数，所以dp[i][j]=dp[i-1][j]+dp[i][j-1],即既可以从 左边的i-1,j位置走到i,j位置，也可以从i,j-1位置走到i,j位置。

代码

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];
    }
};

参考文献

​​62. Unique Paths​​