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?

解题报告：动态规划的基础题，用一个数组存储到各个点的有多少条路。

                  如果数组没被存入数字，那就存储，这条路前一点的数字。如果已被存入数字，那就加入这条路前一点的数字。

class Solution {
public:
   int uniquePaths(int m, int n)  {
        int temp[m][n];
        for (size_t i = 0; i != m; i++)
            for(size_t j = 0; j != n; j++)
            temp[i][j] = -1;

        temp[0][0] = 1;
        for (size_t i = 0; i != m; i++) {
            for(size_t j = 0; j != n; j++) {
              if(j != n-1) {
                if(temp[i][j+1] != -1)
                   temp[i][j+1] += temp[i][j];
                else
                    temp[i][j+1] = temp[i][j];
              }
              if(i != m-1) {
                if(temp[i+1][j] != -1)
                    temp[i+1][j] += temp[i][j];
                else
                    temp[i+1][j] = temp[i][j] ;
              }
            }
         }
         return temp[m-1][n-1];
    }
};

Note: m and n will be at most 100.

LeetCode-Unique Paths