Leetcode 62. Unique Paths

-题目

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?

Note: m and n will be at most 100.

题目的意思就是说一个m*n的网格从左上角走到右下角有多少条路径，要求只能走向右边或者下边。

-思路

其实这道题的状态和状态转移方程都非常好定义，因为已经限制只能往右或者往下走。那么对一个中间结点k，到达结点k的总方式为到达结点左边和节点上边的方式之和。

-代码

class Solution {
public:
int uniquePaths(int m, int n) {
//以点k为中介，从左上角的点到点k然后再到最右下角
vector<vector<int> > path(m);
for(int i = 0; i < m; i++) {
path[i].resize(n);
path[i][0] = 1;
}
for(int i = 0; i < n; i++) path[0][i] = 1;
for(int i = 1; i < m; i++) {
for(int j = 1; j < n; j++) {
//只能从左边或者从上面下来
path[i][j] = path[i][j-1] + path[i-1][j];
}
}
return path[m-1][n-1];
}
};