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题目内容

[引自] https://leetcode.com/problems/unique-paths/description/

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.

伪代码

核心: uniquePaths(i,j)=uniquePaths(i-1,j)+uniquePaths(i,j-1)
states数组保存状态值 states[i][j]表示到达i,j位置的不同路径数
边界值:初始边界为(0,x)和 (x,0)
初始化: states[0][0]=0,states[0][x]=0,states[x][0]=0
(1,1)表示初始位置,states[1][1]=0,states[1][2]=1,states[2][1]=1

算法

int uniquePaths(int m, int n)int[][] states =new int[101][101]states[1][1]=1for  i=1 to m+1for j=1 to n+1if(i==1 and j==1)continue;states[i][j]=states[i-1][j]+states[i][j-1]states[1][1]=0return states[m][n]

java 代码实现

    public int uniquePaths(int m, int n) {int[][] states =new int[101][101];states[1][1]=1;for(int i=1;i<m+1;i++){for(int j=1;j<n+1;j++){if(i==1&&j==1){continue;}states[i][j]=states[i-1][j]+states[i][j-1];}}states[1][1]=0;return states[m][n];}

转载于:https://my.oschina.net/u/3706181/blog/1605610

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动态规划练习1--Unique Paths

题目内容

伪代码

算法

java 代码实现

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