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最新推荐文章于 2024-05-18 21:10:45 发布

martin_liang

最新推荐文章于 2024-05-18 21:10:45 发布

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本文介绍了一个算法问题：在一个由0和1填充的二维矩阵中找到包含全1的最大正方形，并返回其面积。通过动态规划的方法解决该问题，利用辅助矩阵记录中间结果，最终找出最大正方形边长。

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

For example, given the following matrix:

Return 4.

Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.

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class Solution {
public:
    int maximalSquare(vector<vector<char>>& matrix) {
        
        if (matrix.empty() || matrix[0].empty()) return 0;
        int M = matrix.size(), N = matrix[0].size(), res = 0;
        vector<vector<int>> dp(M, vector<int>(N, 0));
        for (int i = 0; i < M; ++i) if (matrix[i][0] == '1') {
            dp[i][0] = 1; res = 1;
        }
        for (int j = 0; j < N; ++j) if (matrix[0][j] == '1') {
            dp[0][j] = 1; res = 1;
        }
        for (int i = 1; i < M; ++i) {
            for (int j = 1; j < N; ++j) {
                if (matrix[i][j] == '1') 
                    dp[i][j] = min(dp[i-1][j-1], min(dp[i-1][j], dp[i][j-1])) + 1;
                res = max(res, dp[i][j]);
            }
        }
        return res * res;
    }
};