Maximal Rectangle

最新推荐文章于 2021-10-17 09:55:57 发布

原创最新推荐文章于 2021-10-17 09:55:57 发布 · 764 阅读

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本文介绍了一种寻找二维二进制矩阵中包含全部1的最大矩形的方法，并提供了详细的C++实现代码。通过遍历矩阵并计算不同起始点所能构成的最大矩形面积，最终找出整个矩阵中的最大值。

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

class Solution {
public:
    int maximalRectangle(vector<vector<char> > &matrix) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int size = matrix.size();
        if (size == 0) {
            return 0;
        }

        int max_area = 0;
        int area = 0;
        int max_width = 0;
        int max_height = 0;
        for (int i = 0; i < size; ++i) {
            max_height = size - i;
            if (max_height * matrix[i].size() <= max_area) {
                break;
            }
            for (int j = 0 ; j < matrix[i].size(); ++j) {
                max_width = matrix[i].size() - j;
                if (max_width * max_height <= max_area) {
                    break;
                }
                if (matrix[i][j] == '1') {
                    area = findMaxArea(i, j, matrix);
                    max_area = max_area > area ? max_area : area;
                }
            }
        }
        return max_area;
    }
    
private:
    int findMaxArea(int a, int b, vector<vector<char> > &m) {
        int size = m.size();
        int max_width_bound = m[a].size();
        int area = 0;
        int max_area = 0;

        for (int i = a; i < size; ++i) {
            for (int j = b; j < max_width_bound; ++j) {
                if (m[i][j] == '0') {
                    max_width_bound = j;
                    break;
                }
            }
            area = (i - a + 1) * (max_width_bound - b);
            max_area = max_area > area ? max_area : area;
        }
        return max_area;
    }
};