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.
分两种情况讨论，每次只有往下走或者往右走，那么f(m,n)=f(m-1.n)+f(m,n-1).一开始直接使用递归，超时了。 应该存在数组里。
1 public class Solution { 2 public int uniquePaths(int m, int n) { 3 int[][] f = new int[m][n]; 4 for (int i = 0; i < n; i++) { 5 f[0][i]=1; 6 } 7 8 for (int i = 0; i < m; i++) { 9 f[i][0]=1; 10 } 11 12 for (int i = 1; i < m; i++) { 13 for (int j = 1; j < n; j++) { 14 f[i][j]=f[i-1][j]+f[i][j-1]; 15 } 16 } 17 return f[m-1][n-1]; 18 } 19 }
原文：http://www.cnblogs.com/birdhack/p/4025473.html