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Largest Rectangle in Histogram

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C# program to implement the LargestRectangleArea(int[] heights) function, which calculates the area of the largest rectangle in a histogram where the width of each bar is 1.

Example 1
    

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

  • Output: 10
    • 

  • Explanation:

      

    • Step 1: Analyze each bar and calculate the maximum rectangle that can extend from it.
      • 

    • Step 2: For each bar, find how far it can extend to the left and right while maintaining its height.

        

      • At position 2 (height 5), it can extend to position 3 (height 6).
        • 

      • This forms a rectangle of height 5 and width 2.
        • 

      • The area of this rectangle is 5 × 2 = 10.
        • 

      

      • 

    • Step 3: Compare all possible rectangle areas to find the maximum.
      • 

    • Step 4: Return the maximum area, which is 10.
      • 

    •
Example 2
    

  • Input: heights = [2, 4]
    • 

  • Output: 4
    • 

  • Explanation:

      

    • Step 1: Analyze each bar and calculate the maximum rectangle that can extend from it.
      • 

    • Step 2: For each bar, find how far it can extend to the left and right while maintaining its height.

        

      • At position 0 (height 2), it can extend across both bars.
        • 

      • This forms a rectangle of height 2 and width 2.
        • 

      • The area of this rectangle is 2 × 2 = 4.
        • 

      • At position 1 (height 4), it can only include itself.
        • 

      • This forms a rectangle of height 4 and width 1.
        • 

      • The area of this rectangle is 4 × 1 = 4.
        • 

      

      • 

    • Step 3: Compare all possible rectangle areas to find the maximum.
      • 

    • Step 4: Return the maximum area, which is 4.
      • 

    •
Constraints
    

  • 1 ≤ heights.length ≤ 10^5
    • 

  • 0 ≤ heights[i] ≤ 10^4
    • 

  • Time Complexity: O(n) where n is the length of the heights array
    • 

  • Space Complexity: O(n) for the stack used in the algorithm
    •
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Hint
Solution

Solution Hints

    
  
  • Use a stack to keep track of increasing heights
    • 
  
  • When a shorter bar is found, pop from the stack and calculate areas
    • 
  
  • Consider using a sentinel value at the end of the array to simplify the algorithm
    • 
  
  • For each bar, the area can be calculated as height × width
    •

Steps to solve by this approach:

 Step 1: Initialize a stack to keep track of indices of heights in ascending order.
 Step 2: Process each bar from left to right, adding a zero-height bar at the end.
 Step 3: When encountering a bar shorter than the top of the stack, pop bars from the stack.
 Step 4: For each popped bar, calculate the area extending to the left and right as far as possible while maintaining the height.
 Step 5: The width extends from the current position to the next bar on the stack (or from the beginning if the stack is empty).
 Step 6: Update the maximum area if the calculated area is larger.
 Step 7: Push the current bar's index onto the stack and continue.

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