leetcode : 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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

tag: 典型的动态规划，跟tiangle 数字三角形思路类似

状态方程：  dp[i][j] = dp[i-1][j] + dp[i][j-1];

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