[leetcode]Unique Paths

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.

题意：一个机器人在m X n的矩阵的左上角， 且每次只能向下或向右移动。问如果要移动最右下角有多少种方案？

解题思路：动态规划， 状态转移方程 dp[i][j] = dp[i + 1][j] + dp[i][j + 1]， 数组最右边一列，及数组最下边一行初始化为1.

class Solution {
public:
    int uniquePaths(int m, int n) {
    	// Note: The Solution object is instantiated only once and is reused by each test case.
    	//动态规划
    	//一个机器人在m*n的格子左上角要到右下角去，只能向右或是向下移动，列出所有可走的路线数
    	//定义一个二维数组，用容器vector模拟，数组最下及最右一排为一，然后从右下方做叠加到左上方
    	vector<vector<int> > v;
    	vector<int> tmp(n, 1);
    	
    	for (int i = 0; i < m; i++){
    		v.push_back(tmp);
    	}
    	//处理非最右及最下的数据项
    	for (int i = m - 2; i >= 0; i--)
    	{
    		for (int j = n - 2; j >= 0; j--)
    		{
    		    //当前数据 等于 右面与下面数据之和
    			v[i][j] = v[i + 1][j] + v[i][j + 1];
    		}
    	}
        //返回总路径数
    	return v[0][0];
    }
};