leetcode_62题——Unique Paths （动态规划）

Unique Paths

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Question  Solution 

 

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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  Array Dynamic Programming

 

      这道题比较简单，就是采用动态规划的做法，需要维护一个路径个数的数组，从靠近终点的点开始往前算起就好了

#include<iostream>

#include <vector>

using namespace std;

#define MAXSIZE 110

int uniquePaths(int m, int n) {

	int ary1[MAXSIZE][MAXSIZE];

	ary1[m][n]=1;

	for(int i=m;i>=1;i--)

		for(int j=n;j>=1;j--)

		{

			if(i==m||j==n)

				ary1[i][j]=1;

			else

				ary1[i][j]=ary1[i+1][j]+ary1[i][j+1];

		}

		return ary1[1][1];

}



int main()

{

}