LeetCode62. Unique Paths

一、题目

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:

Input: m = 3, n = 7
Output: 28
Example 2:

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

二、题解

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int>> dp(m,vector<int>(n,0));
        //初始化dp数组
        for(int row = 0;row < m;row++){
            dp[row][0] = 1;
        }
        for(int col = 0;col < n;col++){
            dp[0][col] = 1;
        }
        for(int row = 1;row < m;row++){
            for(int col = 1;col < n;col++){
                dp[row][col] = dp[row][col-1] + dp[row-1][col];
            }
        }
        return dp[m-1][n-1];
    }
};