[leetcode]Unique Paths

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.

算法思路：

典型的二维DP，dp[i][j]表示从左上角(0,0)到(i,j)的paths。状态转移方程：dp[i][j] = dp[i - 1][j] + dp[i][j - 1];

代码如下：

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