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public class Solution {
    public int maximalSquare(char[][] matrix) {
        if (matrix == null || matrix.length < 1 || matrix[0].length < 1) return 0;
        int m = matrix.length;
        int n = matrix[0].length;
        int[][] dp = new int[m + 1][n + 1]; 
        // dp(i, j) represents the length of the square whose lower-right corner is located at (i, j)
        // dp(i, j) = min{ dp(i-1, j-1), dp(i-1, j), dp(i, j-1) }
        int res = 0;
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (matrix[i - 1][j - 1] == '0') continue;
                
                dp[i][j] = Math.min(dp[i - 1][j - 1], Math.min(dp[i - 1][j], dp[i][j - 1])) + 1;
                res = Math.max(res, dp[i][j]);
            }
        }
        return res * res;
    }
}

int maximalSquare(vector<vector<char>>& matrix) {
    if (matrix.empty()) return 0;
    int m = matrix.size(), n = matrix[0].size();
    vector<int> dp(m + 1, 0);
    int maxsize = 0, pre = 0;
    for (int j = 0; j < n; j++) {
        for (int i = 1; i <= m; i++) {
            int temp = dp[i];
            if (matrix[i - 1][j] == '1') {
                dp[i] = min(dp[i], min(dp[i - 1], pre)) + 1;
                maxsize = max(maxsize, dp[i]);
            }
            else dp[i] = 0; 
            pre = temp;
        }
    }
    return maxsize * maxsize;
}