Maximal Rectangle — Algorithm Visualization & Coding Challenge

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Understanding Maximal Rectangle

Detailed explanation and reference materials

Problem Overview

🧱 Maximal Rectangle

Difficulty: 🔴 Hard
Topics: Dynamic Programming, Stack, Matrix
Goal: Find the largest rectangle made of only 1s in a binary matrix and return its area.

📌 Problem Statement (One Line)

Given a binary matrix, return the area of the largest rectangle containing only 1's.

🧪 Examples

✅ Example 1

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

Output: 6

📦 The largest rectangle of 1s has area = 6.

❌ Example 2

Input: [["0"]]
Output: 0

✅ Example 3

Input: [["1"]]
Output: 1

import java.util.Stack;

public class Main {

public static void main(String[] args) {

    int[][] matrix = {
        {1, 0, 1, 0, 0},
        {1, 0, 1, 1, 1},
        {1, 1, 1, 1, 1},
        {1, 0, 0, 1, 0}
    };

    System.out.println(maximalRectangle(matrix)); // Output: 6
}

public static int maximalRectangle(int[][] matrix) {
    if (matrix.length == 0) return 0;

    int cols = matrix[0].length;
    int[] heights = new int[cols];
    int maxArea = 0;

    for (int[] row : matrix) {
        // Build histogram heights
        for (int j = 0; j < cols; j++) {
            heights[j] = row[j] == 1 ? heights[j] + 1 : 0;
        }

        // Calculate max rectangle area for current histogram
        maxArea = Math.max(maxArea, area(heights));
    }

    return maxArea;
}

// Function to calculate largest rectangle area in histogram
public static int area(int[] heights) {
    Stack<Integer> stack = new Stack<>();
    int maxArea = 0;

    for (int i = 0; i <= heights.length; i++) {
        int currentHeight = (i == heights.length) ? 0 : heights[i];

        while (!stack.isEmpty() && currentHeight < heights[stack.peek()]) {
            int height = heights[stack.pop()];
            int width = stack.isEmpty() ? i : i - stack.peek() - 1;
            maxArea = Math.max(maxArea, height * width);
        }
        stack.push(i);
    }

    return maxArea;
}

}

— Written by Saurabh Patil • B.Tech CSE • Software Developer

Reference Link

https://leetcode.com/problems/maximal-rectangle/

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Java

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