Largest Rectangle in Histogram Using Stack in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Largest Rectangle Calculation

What is the output of the following TypeScript code that calculates the largest rectangle area in a histogram?

DSA Typescript

function largestRectangleArea(heights: number[]): number {
  const stack: number[] = [];
  let maxArea = 0;
  heights.push(0);
  for (let i = 0; i < heights.length; i++) {
    while (stack.length && heights[i] < heights[stack[stack.length - 1]]) {
      const height = heights[stack.pop()!];
      const width = stack.length === 0 ? i : i - stack[stack.length - 1] - 1;
      maxArea = Math.max(maxArea, height * width);
    }
    stack.push(i);
  }
  return maxArea;
}

console.log(largestRectangleArea([2,1,5,6,2,3]));

A 9

B 10

C 8

D 12

💡 Hint

Think about the largest rectangle that can be formed by consecutive bars.

The largest rectangle area in the histogram [2,1,5,6,2,3] is 10, formed by bars with heights 5 and 6 (width 2).

🧠 Conceptual

intermediate

Understanding Stack Usage in Histogram Problem

Why does the algorithm use a stack to solve the Largest Rectangle in Histogram problem?

A To store the heights of bars in sorted order

B To count the total number of bars in the histogram

C To reverse the histogram array for easier processing

D To keep track of indices of bars in increasing height order for area calculation

💡 Hint

Think about how the stack helps find the width of rectangles.

The stack stores indices of bars in increasing height order. When a smaller bar is found, it calculates areas using bars popped from the stack.

🔧 Debug

advanced

Identify the Error in Stack Implementation

What error will occur when running this modified code snippet for largest rectangle area?

DSA Typescript

function largestRectangleArea(heights: number[]): number {
  const stack: number[] = [];
  let maxArea = 0;
  for (let i = 0; i <= heights.length; i++) {
    while (stack.length && (i === heights.length || heights[i] < heights[stack[stack.length - 1]])) {
      const height = heights[stack.pop()!];
      const width = stack.length === 0 ? i : i - stack[stack.length - 1] - 1;
      maxArea = Math.max(maxArea, height * width);
    }
    stack.push(i);
  }
  return maxArea;
}

console.log(largestRectangleArea([2,1,5,6,2,3]));

A The output is 15 (incorrect area)

B Runtime error: undefined index access

C The output is 10 (correct area)

D SyntaxError due to missing brackets

💡 Hint

Check how width is calculated when the stack is not empty.

The width calculation is off by 1, causing an incorrect larger area 15 instead of 10.

📝 Syntax

advanced

Syntax Error in Stack-Based Histogram Code

Which option contains a syntax error in the TypeScript code for largest rectangle in histogram?

DSA Typescript

function largestRectangleArea(heights: number[]): number {
  const stack: number[] = [];
  let maxArea = 0;
  heights.push(0);
  for (let i = 0; i < heights.length; i++) {
    while (stack.length && heights[i] < heights[stack[stack.length - 1]]) {
      const height = heights[stack.pop()!];
      const width = stack.length === 0 ? i : i - stack[stack.length - 1] - 1;
      maxArea = Math.max(maxArea, height * width);
    }
    stack.push(i);
  }
  return maxArea;
}

A Missing closing parenthesis in while condition

B Missing exclamation mark after pop()

C Missing semicolon after stack declaration

D Missing curly braces for for loop

💡 Hint

Check line endings carefully.

The line 'const stack: number[] = []' is missing a semicolon, causing a syntax error in TypeScript.

🚀 Application

expert

Maximum Rectangle Area for Large Histogram

Given a histogram with heights [6, 2, 5, 4, 5, 1, 6], what is the largest rectangle area calculated by the stack-based algorithm?

A 12

B 10

C 15

D 9

💡 Hint

Consider rectangles spanning multiple bars with minimum height.

The largest rectangle area is 12, formed by bars at indices 2,3,4 with heights 5,4,5 (min height 4 * width 3 = 12).

Practice

1. What is the main purpose of using a stack in the Largest Rectangle in Histogram problem?

easy

A. To reverse the order of histogram bars

B. To keep track of bars' indices with increasing heights

C. To store the maximum area found so far

D. To sort the histogram bars by height

Solution

1. Step 1: Understand the stack's role

   The stack stores indices of bars in increasing height order to find boundaries for rectangles.

2. Step 2: Why increasing heights?

   This helps identify when a bar is lower than the previous, signaling to calculate area for taller bars.

3. Final Answer:

   To keep track of bars' indices with increasing heights -> Option B

4. Quick Check:

   Stack tracks increasing bars = To keep track of bars' indices with increasing heights [OK]

Hint: Stack holds indices of increasing bars to find rectangle widths [OK]

Common Mistakes:

• Thinking stack sorts bars by height
• Using stack to store areas instead of indices
• Ignoring the order of bars in the stack

2. Which of the following TypeScript code snippets correctly initializes an empty stack for indices in the Largest Rectangle problem?

easy

A. const stack = new Stack<number>();

B. const stack: string[] = [];

C. const stack: number[] = [];

D. const stack = []; stack.push('index');

Solution

1. Step 1: Identify correct stack type

   We need a stack of numbers (indices), so number[] is correct.

2. Step 2: Check other options

   const stack: string[] = []; uses string[], wrong type. const stack = new Stack<number>(); uses a Stack class which is not standard in TypeScript. const stack = []; stack.push('index'); pushes a string 'index', wrong type.

3. Final Answer:

   const stack: number[] = []; -> Option C

4. Quick Check:

   Stack of numbers = const stack: number[] = []; [OK]

Hint: Use number[] for stack of indices in TypeScript [OK]

Common Mistakes:

• Using string[] instead of number[]
• Assuming Stack class exists by default
• Pushing wrong data types into stack

3. What is the output of the following TypeScript code snippet for histogram heights [2, 1, 5, 6, 2, 3]?

function largestRectangleArea(heights: number[]): number {
  const stack: number[] = [];
  let maxArea = 0;
  heights.push(0);
  for (let i = 0; i < heights.length; i++) {
    while (stack.length && heights[i] < heights[stack[stack.length - 1]]) {
      const height = heights[stack.pop()!];
      const width = stack.length ? i - stack[stack.length - 1] - 1 : i;
      maxArea = Math.max(maxArea, height * width);
    }
    stack.push(i);
  }
  return maxArea;
}

console.log(largestRectangleArea([2, 1, 5, 6, 2, 3]));

medium

A. 10

B. 12

C. 8

D. 6

Solution

1. Step 1: Add sentinel and iterate

   Heights become [2,1,5,6,2,3,0]. We use stack to track indices of increasing bars.

2. Step 2: Calculate max area during pops

   Pop bars when current height is less, calculate area: max area found is 10 (from bars 5 and 6 with width 2).

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Max rectangle area = 10 [OK]

Hint: Add 0 height at end to flush stack and find max area [OK]

Common Mistakes:

• Not adding sentinel 0 at end
• Wrong width calculation after popping
• Ignoring last bars in stack

4. Identify the bug in this TypeScript code snippet for Largest Rectangle in Histogram:

function largestRectangleArea(heights: number[]): number {
  const stack: number[] = [];
  let maxArea = 0;
  for (let i = 0; i <= heights.length; i++) {
    while (stack.length && heights[i] < heights[stack[stack.length - 1]]) {
      const height = heights[stack.pop()!];
      const width = stack.length ? i - stack[stack.length - 1] - 1 : i;
      maxArea = Math.max(maxArea, height * width);
    }
    stack.push(i);
  }
  return maxArea;
}

medium

A. maxArea is not updated inside the loop

B. Stack is not initialized properly

C. Width calculation is incorrect

D. Loop goes out of bounds accessing heights[i] when i == heights.length

Solution

1. Step 1: Check loop boundary

   The loop runs i from 0 to heights.length inclusive, so heights[i] is accessed when i == heights.length, causing out-of-bounds error.

2. Step 2: Fix by adding sentinel or changing loop

   Adding a 0 height at end or changing loop to i < heights.length fixes this.

3. Final Answer:

   Loop goes out of bounds accessing heights[i] when i == heights.length -> Option D

4. Quick Check:

   Out-of-bounds access = Loop goes out of bounds accessing heights[i] when i == heights.length [OK]

Hint: Avoid accessing heights[i] when i equals length without sentinel [OK]

Common Mistakes:

• Ignoring loop boundary causing runtime error
• Assuming stack initialization is wrong
• Misreading width calculation

5. Given a histogram with heights [6, 2, 5, 4, 5, 1, 6], what is the largest rectangle area using the stack approach? Explain why the rectangle with area 12 is the largest.

hard

A. 12

B. 10

C. 15

D. 8

Solution

1. Step 1: Use stack to find max area

   Push indices while heights increase. When a lower bar appears, pop and calculate area. For this histogram, max area is 12 from bars at indices 2,3,4 (heights 5,4,5) width 3.

2. Step 2: Why area 12 is largest

   The rectangle covers bars with heights >=4 over width 3, area = 4*3=12. No other rectangle covers more area.

3. Final Answer:

   12 -> Option A

4. Quick Check:

   Max rectangle area = 12 [OK]

Hint: Pop stack on lower bar, calculate area with width between indices [OK]

Common Mistakes:

• Calculating area only for single bars
• Ignoring width when popping multiple bars
• Missing the largest rectangle spanning multiple bars