Leetcode NO.62 Unique Paths

本题题目要求如下：

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.

本题我第一次做并没有依靠dynamic programming的思想。。。这段时间老用dp做题，对dp有了一定的理解，下面说明解法：

声明并初始化一个二维数组dp[m][n],

dp[i][j]表示某一点(i,j)到(0,0)原点的possible unique paths数目

dp[i][j]其实就等于dp[i-1][j]+dp[i][j-1]，这是因为只允许向0->m,-0->n单方向移动。

构建模型后，写代码就很简单了。。代码如下：

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