*Unique Paths

Posted 2021-03-14 hujianglang

Unique Paths

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

 

class Solution{
public:
    int uniquePaths(int m, int n){
        if(m == 1 || n == 1) return 1;
        vector<vector<int>> memo(m,vector<int>(n));
        for(int i = 0; i < m; i++)
            memo[i][0] = 1;
        for(int j = 0; j < n; j++)
            memo[0][j] = 1;
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                memo[i][j] = memo[i-1][j] + memo[i][j-1];
            }
        }
        return memo[m-1][n-1];
    }
};

 

 

参考：

1，https://blog.csdn.net/u013250416/article/details/80558542