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Largest Rectangle in Histogram

Certification: Advanced Level Accuracy: 50% Submissions: 2 Points: 15

Write a Java program to find the largest rectangle area in a histogram. A histogram is represented as an array of integers where each element represents the height of the bar at that position. The width of each bar is 1.

Example 1
    
  
  • Input: heights = [2, 1, 5, 6, 2, 3]
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  • Output: 10
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  • Explanation: The maximum area can be formed by heights[2] = heights[3] = 5 with width 2. Area = 5 * 2 = 10.
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Example 2
    
  
  • Input: heights = [2, 4, 5, 3, 1]
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  • Output: 9
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  • Explanation: For heights[3] = 3, we can extend the width to 3, creating an area of 3 * 3 = 9.
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Constraints
    
  
  • 1 <= heights.length <= 10^5
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  • 0 <= heights[i] <= 10^4
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  • Time Complexity: O(n), where n is the length of the heights array
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  • Space Complexity: O(n)
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ArraysStackCapgeminiPhillips
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Hint
Solution

Solution Hints

    
  
  • Use a stack to keep track of increasing heights in the histogram
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  • When you find a bar shorter than the top of the stack, you've found a right boundary
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  • Pop from the stack to get the height of the rectangle
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  • The width will be the current position minus the new top of the stack minus 1
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  • For each popped element, calculate the area and keep track of the maximum area
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  • Process a sentinel value at the end to handle remaining elements in the stack
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  • Take special care with empty stack cases
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Steps to solve by this approach:

 Step 1: Initialize an empty stack and a variable to track the maximum area.

 Step 2: Iterate through each bar in the histogram, including a sentinel bar of height 0 at the end.

 Step 3: For each bar, while the current bar's height is less than the bar at the top of the stack, we've found a right boundary.

 Step 4: Pop the top bar from the stack, calculate its height, and determine its width based on the current position and the new top of the stack.

 Step 5: Calculate the area of the rectangle and update the maximum area if necessary.

 Step 6: Push the current bar's index onto the stack.

 Step 7: Return the maximum area after processing all bars.

Submitted Code :