62. Unique Paths

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]
;
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];
}
}