Unique Paths

 

题目：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.

思路：动态规划

使用动态规划，此时刻的数值等于左边的数值加上上边的数值。

公式到，编程自然迎刃而解。

代码：

 

class Solution {
public:
//https://leetcode.com/problems/unique-paths/
    int uniquePaths(int m, int n) {
        if(m==0||n==0){
            return 0;
        }
        int sum[m][n];
        for(int i=0;i<m;i++){
            sum[i][0]=1;//一直往下走只有一条路
        }
        for(int i=0;i<n;i++){
            sum[0][i]=1;//一直往右走只有一条路
        }
        
        for(int i=1;i<m;i++){
            for(int j=1;j<n;j++){
                sum[i][j]=sum[i-1][j]+sum[i][j-1];
            }
        }
        return sum[m-1][n-1];
    }
};