题目描述:

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.

经典的动态规划题目, 由于每一个格子只能从上面的格子和左面的格子到达, 所以到达每个格子的路线数量等于到达上面格子的路线数量+到达左面格子的路线数量.

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