【Lintcode】114. Unique Paths

题目地址：

https://www.lintcode.com/problem/unique-paths/description

给定一个矩阵，从左上到右下格子一共有多少种不同走法。每次只能向右或者向下走一格，不能出界。代码如下：

import java.util.Arrays;

public class Solution {
    /**
     * @param m: positive integer (1 <= m <= 100)
     * @param n: positive integer (1 <= n <= 100)
     * @return: An integer
     */
    public int uniquePaths(int m, int n) {
        // write your code here
        int[][] dp = new int[m][n];
        Arrays.fill(dp[0], 1);
        for (int i = 0; i < m; i++) {
            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];
    }
}

时空复杂度 $O(mn)$。