Unique Paths ——LeetCode

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.

题目大意：给定一个棋盘，从左上走到右下，一步走一个格，只能往右或往下走，问有多少种不同的走法。

解题思路：简单的动规，递推公式F(i,j)=F(i-1,j)+F(i,j-1),初始值F(0,0)=1。

public class Solution {
    public int uniquePaths(int m, int n) {
        int[][] cnt = new int[m][n];
        cnt[0][0]=1;
        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                if(i==0&&j==0)
                    continue;
                if(i==0&&j!=0){
                    cnt[i][j]=cnt[i][j-1];
                }
                else if(j==0&&i!=0){
                    cnt[i][j]=cnt[i-1][j];
                } else {
                    cnt[i][j]=cnt[i-1][j]+cnt[i][j-1];
                }
            }
        }
        return cnt[m-1][n-1];
    }
}