Content

Given an m x n binary matrix filled with 0's and 1's, find the largest square containing only 1's and return its area.

Example 1:

Input: matrix = [["1","0","1","0","0"],["1","0","1","1","1"],["1","1","1","1","1"],["1","0","0","1","0"]]
Output: 4

Example 2:

Input: matrix = [["0","1"],["1","0"]]
Output: 1

Example 3:

Input: matrix = [["0"]]
Output: 0

Constraints:

• m == matrix.length
• n == matrix[i].length
• 1 <= m, n <= 300
• matrix[i][j] is '0' or '1'.

Solution

1. 动态规划

Java

class Solution {
    public int maximalSquare(char[][] matrix) {
        // m == matrix.length
        // n == matrix[i].length
        // 1 <= m, n <= 300
        // matrix[i][j] is '0' or '1'.
        int m = matrix.length;
        int n = matrix[0].length;
        // dp[i][j][0]表示以[i,j]为右端点，水平方向连续'1'的最长长度
        // dp[i][j][1]表示以[i,j]为下端点，垂直方向连续'1'的最大高度
        int[][][] dp = new int[m][n][2];
        dp[0][0][0] = matrix[0][0] == '1' ? 1 : 0;
        dp[0][0][1] = dp[0][0][0];
        int max = dp[0][0][0];
        for (int j = 1; j < n; j++) {
            dp[0][j][0] = matrix[0][j] == '1' ? dp[0][j - 1][0] + 1 : 0;
            dp[0][j][1] = matrix[0][j] == '1' ? 1 : 0;
            max = Math.max(max, dp[0][j][1]);
        }
        for (int i = 1; i < m; i++) {
            dp[i][0][0] = matrix[i][0] == '1' ? 1 : 0;
            dp[i][0][1] = matrix[i][0] == '1' ? dp[i - 1][0][1] + 1 : 0;
            max = Math.max(max, dp[i][0][0]);
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j][0] = matrix[i][j] == '1' ? dp[i][j - 1][0] + 1 : 0;
                dp[i][j][1] = matrix[i][j] == '1' ? dp[i - 1][j][1] + 1 : 0;
                int y = 1;
                int x = dp[i][j][0];
                while (y <= dp[i][j][1]) {
                    x = Math.min(x, dp[i - y + 1][j][0]);
                    if (x < y) {
                        break;
                    }
                    max = Math.max(max, y * y);
                    y++;
                }
            }
        }
        return max;
    }
}

2. 动态规划（优化）

Java

class Solution {
    static final char ONE = '1';
    public int maximalSquare(char[][] matrix) {
        // m == matrix.length
        // n == matrix[i].length
        // 1 <= m, n <= 300
        // matrix[i][j] is '0' or '1'.
        int m = matrix.length;
        int n = matrix[0].length;
        // dp[i][j][0]表示以[i,j]为右端点，水平方向连续'1'的最长长度
        // dp[i][j][1]表示以[i,j]为下端点，垂直方向连续'1'的最大高度
        // dp[i][j][2]表示以[i,j]为右下端点，只包含'1'的最大正方形的边长
        int[][][] dp = new int[m][n][3];
        dp[0][0][0] = matrix[0][0] == ONE ? 1 : 0;
        dp[0][0][1] = dp[0][0][0];
        dp[0][0][2] = dp[0][0][0];
        int maxSide = dp[0][0][2];
        for (int j = 1; j < n; j++) {
            if (matrix[0][j] == ONE) {
                dp[0][j][0] = dp[0][j - 1][0] + 1;
                dp[0][j][1] = 1;
            }
            dp[0][j][2] = dp[0][j][1];
            maxSide = Math.max(maxSide, dp[0][j][2]);
        }
        for (int i = 1; i < m; i++) {
            if (matrix[i][0] == ONE) {
                dp[i][0][0] = 1;
                dp[i][0][1] = dp[i - 1][0][1] + 1;
            }
            dp[i][0][2] = dp[i][0][0];
            maxSide = Math.max(maxSide, dp[i][0][2]);
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                if (matrix[i][j] == ONE) {
                    dp[i][j][0] = dp[i][j - 1][0] + 1;
                    dp[i][j][1] = dp[i - 1][j][1] + 1;
                    dp[i][j][2] = Math.min(
                            dp[i - 1][j - 1][2] + 1,
                            Math.min(dp[i][j][0], dp[i][j][1])
                    );
                    maxSide = Math.max(maxSide, dp[i][j][2]);
                }
            }
        }
        return maxSide * maxSide;
    }
}