Largest Rectangle in Histogram Using Stack in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the stack for indices.

DSA Rust

let mut stack: Vec<usize> = [1];

Drag options to blanks, or click blank then click option'

AVec::with_capacity(10)

Bvec![0]

CVec::new()

Dvec![]

Attempts:

3 left

💡 Hint

Common Mistakes

Using vec![0] initializes stack with one element which is incorrect.

Using Vec::with_capacity(10) reserves space unnecessarily for an empty stack.

We initialize an empty vector to use as a stack for indices.

2fill in blank

medium

Complete the code to push the current index i onto the stack.

DSA Rust

stack.[1](i);

Drag options to blanks, or click blank then click option'

Ainsert

Bpush

Cappend

Dadd

Attempts:

3 left

💡 Hint

Common Mistakes

Using insert requires an index and is not typical for stack push.

append is for concatenating vectors, not pushing single elements.

The push method adds an element to the end of the vector, acting like a stack push.

3fill in blank

hard

Fix the error in the condition to pop from stack when current height is less than height at stack top.

DSA Rust

while !stack.is_empty() && heights[i] [1] heights[*stack.last().unwrap()] {

Drag options to blanks, or click blank then click option'

A<

B>

C>=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' or '>=' causes incorrect popping behavior.

Using '<=' pops too early or late, breaking logic.

We pop when current height is less than the height at the top of the stack to find smaller boundaries.

4fill in blank

hard

Fill both blanks to calculate width and update max_area correctly.

DSA Rust

let width = if stack.is_empty() { i } else { i [1] *stack.last().unwrap() [2] 1 };
max_area = max_area.max(height * width);

Drag options to blanks, or click blank then click option'

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '-' for width calculation causes wrong width.

Using '*' or '/' are incorrect for index arithmetic.

Width is calculated by subtracting the index at stack top from current index and subtracting 1 to get the correct width.

5fill in blank

hard

Fill all three blanks to complete the loop that processes remaining stack elements after main iteration.

DSA Rust

while !stack.is_empty() {
    let height = heights[stack.pop().unwrap()];
    let width = if stack.is_empty() { [1] } else { [2] - *stack.last().unwrap() [3] 1 };
    max_area = max_area.max(height * width);
}

Drag options to blanks, or click blank then click option'

Aheights.len()

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using heights.len() for both blanks is correct; mixing with other values causes errors.

Using '+' instead of '-' in last blank causes wrong width.

Width is calculated using the total length minus the last index in stack minus one for correct width after popping.

Practice

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

easy

A. To store the maximum area found so far

B. To sort the histogram bars by height

C. To reverse the order of histogram bars

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

Solution

1. Step 1: Understand stack usage in the problem

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

2. Step 2: Explain why this helps

   This allows quick calculation of largest rectangle areas when a smaller height bar is found.

3. Final Answer:

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

4. Quick Check:

   Stack tracks indices with increasing heights = C [OK]

Hint: Stack holds indices of increasing heights for area calculation [OK]

Common Mistakes:

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

2. Which of the following Rust code snippets correctly initializes an empty stack to store indices for the histogram bars?

easy

A. let mut stack: Vec<usize> = Vec::new();

B. let stack = Vec::with_capacity(0);

C. let stack: Vec<i32> = Vec::new();

D. let mut stack: Vec<i32> = Vec::new();

Solution

1. Step 1: Identify correct stack type for indices

   Indices are usize type, so stack must be Vec<usize>.

2. Step 2: Check mutability and initialization

   Stack must be mutable and initialized empty with Vec::new().

3. Final Answer:

   let mut stack: Vec<usize> = Vec::new(); -> Option A

4. Quick Check:

   Mutable Vec of usize initialized empty = B [OK]

Hint: Use mutable Vec<usize> for indices stack [OK]

Common Mistakes:

• Using wrong type like i32 for indices
• Not making stack mutable
• Using Vec::with_capacity(0) without mut

3. What is the output of the following Rust code that calculates the largest rectangle area in the histogram heights = [2, 1, 5, 6, 2, 3]?

fn largest_rectangle_area(heights: Vec<i32>) -> i32 {
    let mut stack: Vec<usize> = Vec::new();
    let mut max_area = 0;
    let mut i = 0;
    while i <= heights.len() {
        let h = if i == heights.len() { 0 } else { heights[i] };
        if stack.is_empty() || h >= heights[*stack.last().unwrap()] {
            stack.push(i);
            i += 1;
        } else {
            let top = stack.pop().unwrap();
            let width = if stack.is_empty() { i } else { i - stack.last().unwrap() - 1 };
            max_area = max_area.max(heights[top] * width as i32);
        }
    }
    max_area
}

fn main() {
    println!("{}", largest_rectangle_area(vec![2, 1, 5, 6, 2, 3]));
}

medium

A. 12

B. 10

C. 9

D. 8

Solution

1. Step 1: Trace stack and area calculation

   For heights [2,1,5,6,2,3], largest rectangle area is 10 (from bars 5 and 6 with width 2).

2. Step 2: Confirm max_area value

   Code correctly calculates max_area as 10 after processing all bars.

3. Final Answer:

   10 -> Option B

4. Quick Check:

   Largest rectangle area = 10 [OK]

Hint: Largest rectangle area for example histogram is 10 [OK]

Common Mistakes:

• Confusing max area with sum of heights
• Miscomputing width when popping stack
• Forgetting to add sentinel zero height

4. Identify the bug in this Rust code snippet for Largest Rectangle in Histogram and select the fix:

fn largest_rectangle_area(heights: Vec<i32>) -> i32 {
    let mut stack: Vec<usize> = Vec::new();
    let mut max_area = 0;
    let mut i = 0;
    while i < heights.len() {
        if stack.is_empty() || heights[i] >= heights[*stack.last().unwrap()] {
            stack.push(i);
            i += 1;
        } else {
            let top = stack.pop().unwrap();
            let width = if stack.is_empty() { i } else { i - stack.last().unwrap() - 1 };
            max_area = max_area.max(heights[top] * width as i32);
        }
    }
    max_area
}

medium

A. Subtract 1 from width calculation: i - stack.last().unwrap() - 1

B. Change while condition to i <= heights.len() and use 0 height sentinel

C. Make stack mutable by adding 'mut' keyword

D. Initialize max_area with i32::MIN instead of 0

Solution

1. Step 1: Identify width calculation error

   Width should be i - stack.last().unwrap() - 1 to exclude the popped bar's index.

2. Step 2: Explain fix impact

   Without subtracting 1, width is overcounted, causing wrong area calculation.

3. Final Answer:

   Subtract 1 from width calculation: i - stack.last().unwrap() - 1 -> Option A

4. Quick Check:

   Correct width calculation subtracts 1 [OK]

Hint: Width = i - previous index - 1 when popping stack [OK]

Common Mistakes:

• Missing -1 in width calculation
• Not handling sentinel zero height
• Incorrect while loop condition

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

hard

A. 8

B. 10

C. 12

D. 15

Solution

1. Step 1: Use stack to track indices with increasing heights

   Push indices while heights increase; pop when current height is less to calculate areas.

2. Step 2: Calculate largest rectangle area

   Largest rectangle area is 12 (from bars at indices 2,3,4 with min height 4 and width 3).

3. Final Answer:

   12 -> Option C

4. Quick Check:

   Stack helps find max area 12 [OK]

Hint: Stack finds max area 12 by tracking increasing heights [OK]

Common Mistakes:

• Calculating area without considering width correctly
• Ignoring bars after popping stack
• Not using sentinel zero height to flush stack