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 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

递归超时，采用动态规划。

对于格点(i,j)。由于只能从上格点(i-1,j)或左格点(i,j-1)到达，并且两者路径是不重复的

因此count[i][j] = count[i-1][j]+count[i][j-1]

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

【LeetCode】Unique Paths