Dynamic Stack Using Resizable Array in DSA Javascript - Time & Space Complexity

Time Complexity: Dynamic Stack Using Resizable Array

O(1) amortized

Understanding Time Complexity

We want to understand how the time to add or remove items from a dynamic stack changes as the stack grows.

How does resizing the array affect the speed of stack operations?

Scenario Under Consideration

Analyze the time complexity of this dynamic stack push operation.

class DynamicStack {
  constructor() {
    this.array = new Array(2);
    this.size = 0;
  }

  push(value) {
    if (this.size === this.array.length) {
      this.resize();
    }
    this.array[this.size] = value;
    this.size++;
  }

  resize() {
    const newArray = new Array(this.array.length * 2);
    for (let i = 0; i < this.array.length; i++) {
      newArray[i] = this.array[i];
    }
    this.array = newArray;
  }
}
    

This code adds items to a stack. When the array is full, it doubles its size by copying items to a bigger array.

Identify Repeating Operations

Look at what repeats when pushing items.

• Primary operation: Copying all items during resize.
• How many times: Resizing happens only when the array is full, so copying happens less often as size grows.

How Execution Grows With Input

Most pushes just add an item quickly. Occasionally, resizing copies all items, which takes longer.

Input Size (n)	Approx. Operations
10	About 10 simple adds + 3 copies during resizes
100	About 100 simple adds + 7 copies during resizes
1000	About 1000 simple adds + 10 copies during resizes

Pattern observation: Most operations are quick, and copying happens rarely, so average time per push stays low.

Final Time Complexity

Time Complexity: O(1) amortized

This means each push usually takes the same short time, even though resizing sometimes takes longer.

Common Mistake

[X] Wrong: "Every push takes a long time because of resizing."

[OK] Correct: Resizing happens only occasionally, so most pushes are very fast, making the average time low.

Interview Connect

Understanding amortized time helps you explain why dynamic arrays and stacks are efficient in real programs.

Self-Check

"What if we increased the array size by only 1 each time instead of doubling? How would the time complexity change?"

Practice

1. What is the main advantage of using a dynamic stack implemented with a resizable array over a fixed-size array stack?

easy

A. It does not allow duplicate elements.

B. It uses less memory than a fixed-size array stack.

C. It always has a fixed capacity to avoid resizing overhead.

D. It can grow or shrink automatically as elements are added or removed.

Solution

1. Step 1: Understand fixed-size array stack limitation

   A fixed-size array stack has a set capacity and cannot grow beyond it, causing overflow if exceeded.

2. Step 2: Understand dynamic stack advantage

   A dynamic stack using a resizable array can increase its capacity automatically when full, allowing more elements without overflow.

3. Final Answer:

   It can grow or shrink automatically as elements are added or removed. -> Option D

4. Quick Check:

   Dynamic resizing = automatic growth/shrink [OK]

Hint: Dynamic stack resizes array automatically when full [OK]

Common Mistakes:

• Thinking dynamic stack uses less memory always
• Assuming fixed capacity avoids resizing overhead
• Believing dynamic stack disallows duplicates

2. Which of the following is the correct way to double the size of the internal array in a dynamic stack implemented in JavaScript?

easy

A. this.array = new Array(this.array.length * 2);

B. this.array = [...this.array, ...new Array(this.array.length)];

C. this.array.length = this.array.length + 1;

D. this.array.push(new Array(this.array.length));

Solution

1. Step 1: Understand array resizing in JavaScript

   JavaScript arrays are dynamic but to simulate resizing, we create a new larger array and copy elements.

2. Step 2: Analyze options for doubling size

   this.array = [...this.array, ...new Array(this.array.length)]; uses spread operator to copy existing elements and adds a new array of same length, effectively doubling size.

3. Final Answer:

   this.array = [...this.array, ...new Array(this.array.length)]; -> Option B

4. Quick Check:

   Spread operator copies + new array doubles size [OK]

Hint: Use spread operator to copy and extend array [OK]

Common Mistakes:

• Setting length to length + 1 only increases size by 1, not doubling
• Using push with array adds nested array, not size
• Creating new array without copying loses data

3. Consider the following JavaScript code for a dynamic stack push operation:

class DynamicStack {
  constructor() {
    this.array = [];
    this.top = -1;
  }
  push(value) {
    if (this.top + 1 === this.array.length) {
      this.array = [...this.array, ...new Array(this.array.length || 1)];
    }
    this.top++;
    this.array[this.top] = value;
  }
}
const stack = new DynamicStack();
stack.push(10);
stack.push(20);
stack.push(30);
console.log(stack.array.slice(0, stack.top + 1));

What is the output?

medium

A. [10, 20, 30, undefined, undefined]

B. [10, 20]

C. [10, 20, 30]

D. Error: Cannot read property 'slice' of undefined

Solution

1. Step 1: Trace push operations and resizing

   Initially array is empty. First push adds 10, array resizes to length 1 (from 0), then 10 stored at index 0. Second push resizes array from length 1 to 2, adds 20 at index 1. Third push resizes from 2 to 4, adds 30 at index 2.

2. Step 2: Slice array up to top index + 1

   top is 2 after three pushes, so slice(0, 3) returns [10, 20, 30]. Extra undefined elements are beyond slice range.

3. Final Answer:

   [10, 20, 30] -> Option C

4. Quick Check:

   Slice array to top+1 = [10, 20, 30] [OK]

Hint: Slice array up to top+1 to get valid stack elements [OK]

Common Mistakes:

• Expecting undefined elements in output
• Confusing array length with number of elements
• Not updating top index correctly

4. The following code attempts to implement pop operation for a dynamic stack but has a bug:

pop() {
  if (this.top === -1) {
    return null;
  }
  const value = this.array[this.top];
  this.array[this.top] = undefined;
  this.top--;
  if (this.top < this.array.length / 4) {
    this.array.length = Math.floor(this.array.length / 2);
  }
  return value;
}

What is the bug in this pop method?

medium

A. Reducing array length directly may remove elements still in use.

B. It does not check if stack is empty before popping.

C. It does not update the top index after popping.

D. It never shrinks the array size.

Solution

1. Step 1: Understand array shrinking logic

   The code shrinks the array length when top is less than quarter of array length.

2. Step 2: Identify problem with direct length reduction

   Reducing array length directly truncates elements beyond new length, which may include valid stack elements if top is not updated properly.

3. Final Answer:

   Reducing array length directly may remove elements still in use. -> Option A

4. Quick Check:

   Direct length cut risks losing valid elements [OK]

Hint: Avoid direct length cut; copy elements to smaller array instead [OK]

Common Mistakes:

• Ignoring empty stack check
• Not decrementing top index
• Assuming array never shrinks

5. You want to implement a dynamic stack that doubles its array size when full and halves it when the number of elements falls below one-fourth of the capacity. Which approach below correctly handles resizing without losing stack elements?

hard

A. Create a new array of the new size and copy existing elements before replacing the old array.

B. Directly set the array length property to new size to resize the array.

C. Use array.push() to add undefined elements to increase size and pop() to reduce size.

D. Do not resize the array; just keep track of top index.

Solution

1. Step 1: Understand resizing requirements

   Doubling and halving array size requires creating new arrays to avoid losing elements.

2. Step 2: Analyze resizing methods

   Create a new array of the new size and copy existing elements before replacing the old array. copies elements to a new array of correct size, preserving stack data safely.

3. Step 3: Why other options fail

   Directly set the array length property to new size to resize the array. truncates or extends array without copying, losing data. Use array.push() to add undefined elements to increase size and pop() to reduce size. misuses push/pop for resizing. Do not resize the array; just keep track of top index. ignores resizing.

4. Final Answer:

   Create a new array of the new size and copy existing elements before replacing the old array. -> Option A

5. Quick Check:

   Copy elements to new array for safe resizing [OK]

Hint: Always copy elements to new array when resizing [OK]

Common Mistakes:

• Setting length property directly to resize
• Using push/pop to resize array
• Ignoring resizing and risking overflow