[LeetCode] 048: 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.

[Solution]

class Solution {
public:
	// get the size of the maximal rectangle
	int maximalRectangle(int height[], int len){
		if(len == 0)return 0;

		// set the leftH
		int leftH[len];
		for(int i = 0; i < len; ++i){
			if(i == 0 || height[i] > height[i-1]){
				leftH[i] = i;
			}
			else{
				int j = leftH[i-1];
				while(true){
					if(j != leftH[j]){
						j = leftH[j];
					}
					else if(j > 0 && height[j-1] >= height[i]){
						j--;
					}
					else{
						break;
					}
				}
				leftH[i] = j;
			}
		}

		// set the rightH
		int rightH[len];
		for(int i = len-1; i >= 0; --i){
			if(i == len-1 || height[i] > height[i+1]){
				rightH[i] = i;
			}
			else{
				int j = rightH[i+1];
				while(true){
					if(j != rightH[j]){
						j = rightH[j];
					}
					else if(j < len-1 && height[j+1] >= height[i]){
						j++;
					}
					else{
						break;
					}
				}
				rightH[i] = j;
			}
		}

		// get the maximal rectangle
		int res = 0, area = 0;
		for(int i = 0; i < len; ++i){
			area = height[i] * (rightH[i] - leftH[i] + 1);
			res = max(res, area);
		}
		return res;
	}
	// get the maximal rectangle in the matrix
	int maximalRectangle(vector<vector<char> > &matrix) {
		// Start typing your C/C++ solution below
		// DO NOT write int main() function

		// empty matrix
		if(matrix.size() == 0 || matrix[0].size() == 0)return 0;

		// init height
		int **height = new int*[matrix.size()];
		for(int i = 0; i < matrix.size(); ++i){
			height[i] = new int[matrix[i].size()];
			for(int j = 0; j < matrix[i].size(); ++j){
				// the height is 0
				if(matrix[i][j] == '0'){
					height[i][j] = 0;
				}
				else{
					// the height is the previous row's height +1
					if(i > 0){
						height[i][j] = height[i-1][j] + 1;
					}
					else{
						height[i][j] = 1;
					}
				}
			}
		}

		// get result
		int res = 0;
		for(int i = 0; i < matrix.size(); ++i){
			res = max(res, maximalRectangle(height[i], matrix[i].size()));
		}
		return res;
	}
};

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