Dynamic Stack Using Resizable Array in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a dynamic stack using a resizable array?

A dynamic stack using a resizable array is a stack data structure that can grow or shrink its storage array automatically when elements are pushed or popped, allowing flexible size without fixed limits.

beginner

How does the stack resize when it becomes full?

When the stack's underlying array is full, it creates a new larger array (usually double the size), copies all elements to the new array, and then continues to add new elements.

intermediate

What happens when elements are popped and the array is mostly empty?

If the number of elements becomes much smaller than the array size (commonly less than a quarter), the array size can be reduced to save memory by copying elements to a smaller array.

beginner

Why use a dynamic stack instead of a fixed-size stack?

A dynamic stack avoids overflow errors by resizing automatically, making it flexible for unknown or changing data sizes, unlike fixed-size stacks which have a limited capacity.

intermediate

What is the time complexity of push and pop operations in a dynamic stack using a resizable array?

Push and pop operations are generally O(1) on average. Occasionally, resizing takes O(n) time, but amortized analysis shows average operations remain O(1).

What triggers the resizing of the array in a dynamic stack?

A When the array is full during a push operation

B When the array is empty

C When popping an element

D When the stack size is even

The array resizes when it is full and a new element needs to be pushed.

What is the usual factor by which the array size increases during resizing?

A No change

B 0.5 times

C 2 times

D 10 times

The array size usually doubles to reduce the number of resizes.

What is the main advantage of using a dynamic stack over a fixed-size stack?

A It never needs resizing

B It uses less memory always

C It is faster for all operations

D It can grow and shrink automatically

Dynamic stacks adjust their size automatically to fit the number of elements.

What happens to the array size when many elements are popped and the stack is mostly empty?

A The array size can shrink to save memory

B The array size doubles

C The array size stays the same

D The stack throws an error

Shrinking the array helps save memory when the stack has fewer elements.

What is the average time complexity of push and pop in a dynamic stack?

A O(n)

B O(1)

C O(log n)

D O(n^2)

Amortized analysis shows push and pop are O(1) on average despite occasional resizing.

Explain how a dynamic stack using a resizable array manages its size during push and pop operations.

Think about what happens when the stack is full or almost empty.

Describe the benefits and trade-offs of using a dynamic stack with a resizable array compared to a fixed-size stack.

Consider flexibility, performance, and memory.

Practice

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

easy

A. It can grow or shrink automatically as elements are pushed or popped.

B. It uses less memory than a linked list stack.

C. It does not require any resizing operations.

D. It always has a fixed maximum size.

Solution

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

   A fixed-size array stack has a maximum capacity that cannot change, so it can overflow if too many elements are pushed.

2. Step 2: Understand dynamic stack resizing

   A dynamic stack using a resizable array can increase or decrease its size automatically when needed, avoiding overflow and wasting less memory.

3. Final Answer:

   It can grow or shrink automatically as elements are pushed or popped. -> Option A

4. Quick Check:

   Dynamic resizing = automatic growth/shrink [OK]

Hint: Dynamic stack resizes array automatically on overflow or underflow [OK]

Common Mistakes:

• Thinking dynamic stack never resizes
• Confusing dynamic stack with linked list stack
• Assuming fixed size means dynamic resizing

2. Which of the following Java code snippets correctly doubles the size of the internal array when the stack is full?

easy

A. if (top == arr.length) { arr = Arrays.copyOf(arr, arr.length * 2); }

B. if (top > arr.length) { arr = Arrays.copyOf(arr, arr.length / 2); }

C. if (top == arr.length) { arr = Arrays.copyOf(arr, arr.length / 2); }

D. if (top < arr.length) { arr = Arrays.copyOf(arr, arr.length * 2); }

Solution

1. Step 1: Check condition for resizing

   The array should resize when the stack is full, i.e., when top equals array length.

2. Step 2: Check resizing operation

   The array size should double to accommodate more elements, so new size is arr.length * 2.

3. Final Answer:

   if (top == arr.length) { arr = Arrays.copyOf(arr, arr.length * 2); } -> Option A

4. Quick Check:

   Resize when full, double size [OK]

Hint: Resize when top == length, double array size [OK]

Common Mistakes:

• Resizing when top > length (impossible)
• Shrinking array instead of doubling
• Resizing when array not full

3. Consider the following Java code for a dynamic stack using a resizable array:

DynamicStack stack = new DynamicStack();
stack.push(10);
stack.push(20);
stack.push(30);
stack.pop();
stack.push(40);
stack.push(50);
System.out.println(stack);

What will be the printed output if the stack's toString method prints elements from bottom to top separated by ' -> ' and ends with ' -> null'?

medium

A. 50 -> 40 -> 20 -> 10 -> null

B. 10 -> 20 -> 30 -> 40 -> 50 -> null

C. 10 -> 20 -> null

D. 10 -> 20 -> 40 -> 50 -> null

Solution

1. Step 1: Trace push and pop operations

   Push 10, 20, 30: stack = [10, 20, 30]
   Pop removes 30: stack = [10, 20]
   Push 40, 50: stack = [10, 20, 40, 50]

2. Step 2: Understand toString output

   Prints from bottom to top separated by ' -> ' ending with ' -> null'. So output is "10 -> 20 -> 40 -> 50 -> null".

3. Final Answer:

   10 -> 20 -> 40 -> 50 -> null -> Option D

4. Quick Check:

   Stack after operations = 10,20,40,50 [OK]

Hint: Track push/pop stepwise, print bottom to top [OK]

Common Mistakes:

• Forgetting pop removes last pushed element
• Printing top to bottom instead of bottom to top
• Including popped element in output

4. The following Java method is part of a dynamic stack implementation. It is supposed to pop an element and shrink the array size by half when the number of elements is less than a quarter of the array length. Identify the bug:

public int pop() {
    if (top == 0) throw new EmptyStackException();
    int val = arr[--top];
    if (top < arr.length / 4) {
        arr = Arrays.copyOf(arr, arr.length / 2);
    }
    return val;
}

medium

A. The pop method does not decrement top before accessing arr.

B. Shrinking array without checking minimum size can cause array size zero.

C. The condition should be top > arr.length / 4 to shrink.

D. The method should double the array size instead of halving it.

Solution

1. Step 1: Analyze shrinking condition and operation

   The array shrinks when top < arr.length / 4 by halving the array size.

2. Step 2: Identify potential bug

   If array size is small (like 1 or 2), halving repeatedly can reduce array size to zero, causing errors on next push/pop.

3. Final Answer:

   Shrinking array without checking minimum size can cause array size zero. -> Option B

4. Quick Check:

   Check minimum array size before shrinking [OK]

Hint: Always check minimum array size before shrinking [OK]

Common Mistakes:

• Not checking for empty stack before pop
• Wrong condition for shrinking
• Shrinking array too small causing errors

5. You want to implement a dynamic stack using a resizable array that doubles its size when full and halves its size when the number of elements falls below one-fourth of the array length, but never shrinks below a minimum capacity of 4. Which of the following code snippets correctly implements the pop method with this behavior?

public int pop() {
    if (top == 0) throw new EmptyStackException();
    int val = arr[--top];
    if (top < arr.length / 4 && arr.length > 4) {
        arr = Arrays.copyOf(arr, Math.max(arr.length / 2, 4));
    }
    return val;
}

hard

A. Does not shrink array at all.

B. Shrinks array below size 4 causing errors.

C. Correctly shrinks array but never below size 4.

D. Doubles array size on pop instead of shrinking.

Solution

1. Step 1: Check shrinking condition and minimum size

   The code shrinks array only if top < arr.length / 4 and arr.length > 4, ensuring minimum size 4.

2. Step 2: Verify shrinking operation

   Uses Math.max(arr.length / 2, 4) to avoid shrinking below 4, preventing errors.

3. Final Answer:

   Correctly shrinks array but never below size 4. -> Option C

4. Quick Check:

   Shrink with minimum size check = correct pop method [OK]

Hint: Use Math.max to enforce minimum array size when shrinking [OK]

Common Mistakes:

• Shrinking array below minimum size
• Not shrinking array when needed
• Incorrect condition for shrinking