221. Maximal Square

• Difficulty: Medium

• Topics: Dynamic Programming

• Similar Questions:

  • Maximal Rectangle

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Problem:

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

Example:

Input: 

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

Output: 4 </pre>

Solutions:

class Solution {
public:
    int maximalSquare(vector<vector<char>>& matrix) {
        int m = matrix.size();
        if (m == 0) return 0;
        int n = matrix[0].size();
        if (n == 0) return 0;

        vector<vector<int>> dp(m, vector<int> (n, 0));

        for (int i = 0; i < m; ++i) {
            dp[i][0] = matrix[i][0] - '0';
        }

        for (int j = 0; j < n; ++j) {
            dp[0][j] = matrix[0][j] - '0';
        }

        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                if (matrix[i][j] != '0') {
                    dp[i][j] = 1 + min(dp[i-1][j-1], min(dp[i-1][j], dp[i][j-1]));
                }
            }
        }

        int ret = 0;

        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                ret = max(ret, dp[i][j]);
            }
        }

        return ret * ret;
    }
};