62. 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.

解题思路：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path[i][j] = path[i-1][j]+path[i][j-1]

源码：

import java.util.Scanner;public class _62UniquePaths {public static void main(String[] args) {Scanner sc = new Scanner(System.in);int m = sc.nextInt();int n = sc.nextInt();if(m>100||n>100)return;int result = uniquePaths(m,n);System.out.println(result);}public static int uniquePaths(int m, int n) {int a [][] = new int[m][n];a[0][0] = 1;for(int i=1;i<n;i++){a[0][i] = 1;}for(int i=1;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];    }}