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Largest Rectangle in Histogram

Certification: Advanced Level Accuracy: 40% Submissions: 5 Points: 12

Write a C++ program to find the largest rectangle in a histogram. Given an array of integers heights representing the histogram's bar heights where the width of each bar is 1, return the area of the largest rectangle in the histogram.

Example 1
    

  • Input: heights = [2, 1, 5, 6, 2, 3]
    • 

  • Output: 10
    • 

  • Explanation: 
      

    • Step 1: Iterate through each bar in the histogram.
      • 

    • Step 2: For each bar, calculate the largest rectangle that can include this bar.
      • 

    • Step 3: The largest rectangle has an area of 10 units, formed by bars at indices 2-3 with height 5.
      • 

    • Step 4: Return the maximum area found.
      • 

    •
Example 2
    

  • Input: heights = [2, 4, 5, 3, 1]
    • 

  • Output: 9
    • 

  • Explanation: 
      

    • Step 1: Iterate through each bar in the histogram.
      • 

    • Step 2: For each bar, calculate the largest rectangle that can include this bar.
      • 

    • Step 3: The largest rectangle has an area of 9 units, formed by bars at indices 1-3 with height 3.
      • 

    • Step 4: Return the maximum area found.
      • 

    •
Constraints
    

  • 1 ≤ heights.length ≤ 10^5
    • 

  • 0 ≤ heights[i] ≤ 10^4
    • 

  • Time Complexity: O(n) where n is the number of bars
    • 

  • Space Complexity: O(n)
    •
ArraysStackGoogleTCS (Tata Consultancy Services)
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Hint
Solution

Solution Hints

    
  
  • Use a stack to keep track of indices of bars in non-decreasing order of height
    • 
  
  • When you find a bar shorter than the one at the top of the stack, you can calculate areas
    • 
  
  • The width of the rectangle is determined by the distance between the current bar and the bar just before the popped bar
    • 
  
  • Continue popping bars and calculating areas until you find a shorter bar or the stack is empty
    • 
  
  • Remember to process remaining bars in the stack after scanning the entire array
    •

Steps to solve by this approach:

 Step 1: Initialize an empty stack to keep track of indices of bars in non-decreasing order of height
 Step 2: Iterate through each bar in the histogram (including a sentinel value at the end)
 Step 3: While the current bar is shorter than the bar at the top of the stack, pop the top element
 Step 4: Calculate the area of rectangle with the popped bar as the shortest bar
 Step 5: The width is determined by the current index and the index of the element below the popped element
 Step 6: Update the maximum area if the calculated area is larger
 Step 7: Push the current index onto the stack and continue

Submitted Code :