[LintCode] Maximal Square 最大正方形

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

Have you met this question in a real interview?

Example

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.

LeetCode上的原题，请参见我之前的博客Maximal Square。

解法一：

class Solution {
public:
    /**
     * @param matrix: a matrix of 0 and 1
     * @return: an integer
     */
    int maxSquare(vector<vector<int> > &matrix) {
        if (matrix.empty() || matrix[0].empty()) return 0;
        int m = matrix.size(), n = matrix[0].size(), res = 0;
        vector<vector<int>> sum = matrix;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                int t = sum[i][j];
                if (i > 0) t += sum[i - 1][j];
                if (j > 0) t += sum[i][j - 1];
                if (i > 0 && j > 0) t -= sum[i - 1][j - 1];
                sum[i][j] = t;
                int cnt = 1;
                for (int k = min(i, j); k >= 0; --k) {
                    int d = sum[i][j];
                    if (i - cnt >= 0) d -= sum[i - cnt][j];
                    if (j - cnt >= 0) d -= sum[i][j - cnt];
                    if (i - cnt >= 0 && j - cnt >= 0) d += sum[i - cnt][j - cnt];
                    if (d == cnt * cnt) res = max(res, d);
                    ++cnt;
                }
            }
        }
        return res;
    }
};