技術標籤：leetcode每日一題202012leetcode動態規劃

Problem

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?

Constraints:

• 1 <= m, n <= 100
• It’s guaranteed that the answer will be less than or equal to 2 * 10^9.

Example1

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

Example2

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

Example3

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

Example4

Input: m = 3, n = 3
Output: 6

Solution

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int>> dp(m,vector<
 
int>(n,0));
        

        for(int i = 0;i<n;++i)
            dp[0][i] = 1;
        
        for(int i = 0;i<m;++i)
            dp[i][0] = 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];

    }
};