[LeetCode] Maximal Rectangle

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

[Analysis]
和  Largest Rectangle in Histogram  的方法比较相似，对于矩阵的每一个点，确定该点能够向上达到的最大高度，然后按照 Largest Rectangle in Histogram 的方法，确定每个点上能够达到的最大矩形，最后选择最大的。

[Solution]

class Solution {
public:
    // Definition for Grid
    struct Grid{
        int left, right, top, height;
        int area;
        Grid(int _left, int _right, int _top, int _height, int _area) : left(_left), right(_right), top(_top), height(_height), area(_area) {}
    };
   
    // maximal rectangle
    int maximalRectangle(vector<vector<char> > &matrix) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
       
        // get number of rows
        int m = matrix.size();
        if(m == 0){
            return 0;
        }
   
        // get number of columns
        int n = matrix[0].size();
   
        // init mark
        vector<vector<Grid> > mark;
        for(int i = 0; i < m; ++i){
            vector<Grid> row;
            for(int j = 0; j < n; ++j){
                row.push_back(Grid(-1, -1, -1, 0, 0));
            }
            mark.push_back(row);
        }
   
        // set top
        for(int i = 0; i < m; ++i){
            for(int j = 0; j < n; ++j){
                if(matrix[i][j] == '1'){
                    if(i > 0 && matrix[i-1][j] == '1'){
                        mark[i][j].top = mark[i-1][j].top;
                        mark[i][j].height = i - mark[i][j].top + 1;
                    }
                    else{
                        mark[i][j].top = i;
                        mark[i][j].height = 1;
                    }
                }
            }
        }
   
        // set left
        for(int i = 0; i < m; ++i){
            for(int j = 0; j < n; ++j){
                if(matrix[i][j] == '1'){
                    mark[i][j].left = j;
                    while(mark[i][j].left >= 1 && mark[i][mark[i][j].left - 1].height >= mark[i][j].height){
                        mark[i][j].left = mark[i][mark[i][j].left - 1].left;
                    }
                }
            }
        }
   
        // set right
        for(int i = 0; i < m; ++i){
            for(int j = n-1; j >= 0; --j){
                if(matrix[i][j] == '1'){
                    mark[i][j].right = j;
                    while(mark[i][j].right <= n-2 && mark[i][mark[i][j].right + 1].height >= mark[i][j].height){
                        mark[i][j].right = mark[i][mark[i][j].right + 1].right;
                    }
                }
            }
        }
   
        // set area
        for(int i = 0; i < m; ++i){
            for(int j = 0; j < n; ++j){
                if(matrix[i][j] == '1'){
                    mark[i][j].area = (mark[i][j].right - mark[i][j].left + 1) * mark[i][j].height;
                }
            }
        }
   
        // get result
        int res = 0;
        for(int i = 0; i < m; ++i){
            for(int j = 0; j < n; ++j){
                res = max(res, mark[i][j].area);
            }
        }
        return res;
    }
};

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