[Leetcode] Maximal Rectangle

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

給定一個矩陣中，只有0和1，求出這個矩陣的一個最大的子矩陣，其中只包含1.

例如

01101

11010

01110

11110

11111

00000

其實這個問題可以轉化為Largest Rectangle in Histogram，先將上面的矩陣轉化為：

01101

12010

03110

14210

25321

00000

然后對每一行求直方圖的最大面積。

class Solution {
public:
    int maxArea(vector<int> &line) {
        if (line.size() < 1) return 0;
        stack<int> S;
        line.push_back(0);
        int sum = 0;
        for (int i = 0; i < line.size(); i++) {
            if (S.empty() || line[i] > line[S.top()]) S.push(i);
            else {
                int tmp = S.top();
                S.pop();
                sum = max(sum, line[tmp]*(S.empty()? i : i-S.top()-1));
                i--;
            }
        }
        return sum;
    }
    
    int maximalRectangle(vector<vector<char> > &matrix) {
        if (matrix.size() < 1) return 0;
        int n = matrix.size();
        if (n == 0) return 0;
        int m = matrix[0].size();
        if (m == 0) return 0;
        vector<vector<int> > lines(n, vector<int>(m, 0));
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                if (i == 0) {
                    lines[i][j] = ((matrix[i][j] == '1') ? 1 : 0);
                } else {
                    lines[i][j] += ((matrix[i][j] == '1') ? lines[i-1][j] + 1 : 0);
                }
            }
        }
        int maxRec = 0, tmpRec;
        for (int i = 0; i < n; ++i) {
            tmpRec = maxArea(lines[i]);
            maxRec = (maxRec > tmpRec) ? maxRec : tmpRec;
        }
        return maxRec;
    }
};