LeetCode 221. Maximal Square

原题链接在这里：https://leetcode.com/problems/maximal-square/

题目：

Given a 2D binary matrix filled with 0's and 1's, find the largest square containing only 1's and return its area.

For example, given the following matrix:

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

Return 4.

题解：

DP, 状态: 以当前点为右下角的最大都包含1的square边长.

转移方程 如果当前点为1, dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1])+1.

初始化dp[m+1][n+1], 多一行一列方便处理边界.

res 一直取maintain dp的最大值.

优化dp成一行, 因为只需要左, 上, 和左斜上三个值. prev 来保存左斜上.

Time Complexity: O(m*n). m = matrix.length, n = matrix[0].length.

Space: O(n).

AC Java:

public class Solution {
    public int maximalSquare(char[][] matrix) {
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0){
            return 0;
        }
        
        int res = 0;
        int m = matrix.length;
        int n = matrix[0].length;
        int [] dp = new int[n+1];
        int prev = 0;
        
        for(int i = 1; i<=m; i++){
            for(int j = 1; j<=n; j++){
                int temp = dp[j];
                if(matrix[i-1][j-1] == '1'){
                    dp[j] = Math.min(Math.min(dp[j], dp[j-1]), prev) + 1;
                }else{
                    dp[j] = 0;
                }
                prev = temp;
                res = Math.max(res, dp[j]);
            }
        }
        return res*res;
    }
}

跟上Maximal Rectangle.