[LeetCode]62. Unique Paths&&动态规划

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?

采用动态规划对于格点(i,j)。由于只能从上格点(i-1,j)或左格点(i,j-1)到达，并且两者路径是不重复的

因此a[i][j] = ai-1][j]+a[i][j-1]

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