LeetCode – Maximal Rectangle (Java)

 

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

Analysis

This problem can be converted to the "Largest Rectangle in Histogram" problem.

Java Solution

public int maximalRectangle(char[][] matrix) {
	int m = matrix.length;
	int n = m == 0 ? 0 : matrix[0].length;
	int[][] height = new int[m][n + 1];
 
	int maxArea = 0;
	for (int i = 0; i < m; i++) {
		for (int j = 0; j < n; j++) {
			if (matrix[i][j] == '0') {
				height[i][j] = 0;
			} else {
				height[i][j] = i == 0 ? 1 : height[i - 1][j] + 1;
			}
		}
	}
 
	for (int i = 0; i < m; i++) {
		int area = maxAreaInHist(height[i]);
		if (area > maxArea) {
			maxArea = area;
		}
	}
 
	return maxArea;
}
 
private int maxAreaInHist(int[] height) {
	Stack<Integer> stack = new Stack<Integer>();
 
	int i = 0;
	int max = 0;
 
	while (i < height.length) {
		if (stack.isEmpty() || height[stack.peek()] <= height[i]) {
			stack.push(i++);
		} else {
			int t = stack.pop();
			max = Math.max(max, height[t]
					* (stack.isEmpty() ? i : i - stack.peek() - 1));
		}
	}
 
	return max;
}

Related posts:

  1. LeetCode – Maximal Square (Java)
  2. LeetCode – Rectangle Area (Java)
  3. LeetCode – Largest Rectangle in Histogram (Java)
  4. LeetCode – Max Sum of Rectangle No Larger Than K (Java)
Category >> Algorithms >> Interview  
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  1. Guangyu Wang on 2015-8-23

    Hi, I have a question about the maxAreaInHist() method: if the heights are in ascending order, the max will remain zero all the time. This is a bug right?

  2. Kyle on 2015-9-26

    It will not. Because height[] has one additional element at the end which is 0 ( int[][] height = new int[m][n + 1];) . So even if the elements are in increasing order, zero will be at the end, so non increasing. 🙂

  3. Kyle on 2015-9-26

    It’s very cool that you converted a problem to another. Brilliant!!

  4. Simon on 2015-12-1

    I have a more elegant implement about it.

  5. Yinglei Zhang on 2016-1-24

    This is pretty awesome. Finding connections between different problems is better than solving the problem itself.

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