LeetCode85 Maximal Rectangle 最大矩阵 C++

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

Example:

Input:
[
  ["1","0","1","0","0"],
  ["1","0","1","1","1"],
  ["1","1","1","1","1"],
  ["1","0","0","1","0"]
]
Output: 6

题源： here；完整实现： here

思路：

这道题可以转换为求解直方图中的最大矩阵（即第84题）来解决，我们将按行将原矩阵投影为直方图，然后记录每一行所对应的直方图的最大矩阵。代码如下：

int largestRectangleArea(vector<int>& heights){
	stack<int> records; int maxRec = 0;
	heights.push_back(0);
	for (int i = 0; i < heights.size(); i++){
		if (records.size() == 0 || heights[records.top()] <= heights[i]){
			records.push(i); continue;
		}

		int top = records.top(); records.pop();
		int rec = records.size() ? (i - records.top() - 1)*heights[top] : i*heights[top];
		maxRec = max(maxRec, rec);
		i--;
	}

	return maxRec;
}

int maximalRectangle(vector<vector<char>>& matrix) {
	if (matrix.size() == 0) return 0;
	vector<int> heights(matrix[0].size(), 0);
	int maxRec = 0;
	for (int i = 0; i < matrix.size(); i++){
		for (int j = 0; j < matrix[0].size(); j++){
			if (matrix[i][j] == '1'){
				heights[j] += 1;
			}
			else heights[j] = 0;
		}
		int rec = largestRectangleArea(heights);
		maxRec = max(maxRec, rec);
	}
	return maxRec;
}