[LeetCode-Algorithms-62] "Unique Paths" (2017.11.21-WEEK12)

题目链接：Unique Paths

• 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.

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(1)思路：动态规划，对于点(i， j)，只能从上边的点(i-1,j)或者左边的点(i,j-1)到达，且两者路径是不重复的，因此path[i][j] = path[i-1][j]+path[i][j-1]。

(2)代码：

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

(3)提交结果：