Peek Top Element of Stack in DSA C - Time & Space Complexity

Time Complexity: Peek Top Element of Stack

O(1)

Understanding Time Complexity

We want to understand how long it takes to look at the top item of a stack.

The question is: How does the time to peek change as the stack grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Peek top element of stack
int peek(int stack[], int top) {
    if (top == -1) {
        return -1; // stack empty
    }
    return stack[top];
}
    

This code returns the top element of the stack without removing it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing the element at the top index.
• How many times: Exactly once per peek call.

How Execution Grows With Input

Looking at the top element takes the same time no matter how big the stack is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The time stays constant as the stack size grows.

Final Time Complexity

Time Complexity: O(1)

This means peeking the top element takes the same short time no matter how many items are in the stack.

Common Mistake

[X] Wrong: "Peeking takes longer if the stack is bigger because it has more items to check."

[OK] Correct: Peeking only looks at one position, the top, so it does not depend on stack size.

Interview Connect

Knowing that peek is a constant time operation helps you explain stack efficiency clearly and confidently.

Self-Check

"What if the stack was implemented as a linked list instead of an array? How would the time complexity of peek change?"

Practice

1. What does the peek operation do in a stack?

easy

A. Removes the top element from the stack

B. Returns the top element without removing it

C. Adds a new element to the top of the stack

D. Checks if the stack is empty

Solution

1. Step 1: Understand the peek operation

   The peek operation looks at the top element of the stack without changing the stack.

2. Step 2: Compare with other stack operations

   Pop removes the top element, push adds an element, and isEmpty checks if stack is empty.

3. Final Answer:

   Returns the top element without removing it -> Option B

4. Quick Check:

   Peek = top element without removal [OK]

Hint: Peek shows top without removing it [OK]

Common Mistakes:

• Confusing peek with pop operation
• Thinking peek removes the element
• Mixing peek with push or isEmpty

2. Which of the following is the correct syntax to peek the top element of a stack named stack in C if top is the index of the top element and arr is the array storing stack elements?

easy

A. int x = arr[top - 1];

B. int x = arr[top + 1];

C. int x = arr[0];

D. int x = arr[top];

Solution

1. Step 1: Understand stack top indexing

   Top points to the current top element index in the array.

2. Step 2: Access the top element

   Accessing arr[top] gives the top element. Using top+1 or top-1 is incorrect as it points to wrong positions.

3. Final Answer:

   int x = arr[top]; -> Option D

4. Quick Check:

   Top index points to top element [OK]

Hint: Use arr[top] to peek top element [OK]

Common Mistakes:

• Using top+1 or top-1 instead of top
• Accessing arr[0] assuming stack bottom is top
• Confusing top index with element value

3. What will be the output of the following C code snippet?

int stack[3] = {10, 20, 30};
int top = 2;
printf("%d", stack[top]);

medium

A. 10

B. 20

C. 30

D. Runtime error

Solution

1. Step 1: Identify the top element index and stack contents

   Stack array has elements 10 at index 0, 20 at 1, and 30 at 2. Top is 2.

2. Step 2: Access and print the top element

   stack[top] = stack[2] = 30, so printf prints 30.

3. Final Answer:

   30 -> Option C

4. Quick Check:

   stack[top] = 30 [OK]

Hint: Print stack[top] to get top element [OK]

Common Mistakes:

• Confusing index 0 as top
• Assuming top is out of range
• Expecting pop removes element but code only prints

4. Find the error in this C code snippet that tries to peek the top element of a stack:

int stack[5] = {1, 2, 3, 4, 5};
int top = 4;
int peek() {
  return stack[top + 1];
}

medium

A. Accessing stack[top + 1] causes out-of-bounds error

B. top should be initialized to -1

C. Function should return void, not int

D. Stack array size is too small

Solution

1. Step 1: Analyze the peek function access

   Peek returns stack[top + 1], which is stack[5] here (top=4), exceeding array size 5 (0-4).

2. Step 2: Understand correct top indexing

   Top points to current top element, so peek should return stack[top], not stack[top + 1].

3. Final Answer:

   Accessing stack[top + 1] causes out-of-bounds error -> Option A

4. Quick Check:

   Index out of bounds error [OK]

Hint: Peek uses stack[top], not stack[top+1] [OK]

Common Mistakes:

• Using top+1 instead of top for peek
• Ignoring array bounds causing runtime error
• Incorrect top initialization assumptions

5. Given a stack implemented using an array stack[5] and a variable top initialized to -1, which sequence of operations correctly peeks the top element after pushing 3 elements (10, 20, 30)?

hard

A. stack[++top] = 10; stack[++top] = 20; stack[++top] = 30; int x = stack[top];

B. stack[top] = 10; top = top + 1; stack[top] = 20; top = top + 1; stack[top] = 30; top = top + 1; int x = stack[top];

C. stack[top++] = 10; stack[top++] = 20; stack[top++] = 30; int x = stack[top];

D. top = 0; stack[top] = 10; top = 1; stack[top] = 20; top = 2; stack[top] = 30; int x = stack[top + 1];

Solution

1. Step 1: Understand push operation with top

   Using stack[++top] = value increments top first, then assigns value, correctly pushing elements.

2. Step 2: Peek top element after pushes

   After pushing 3 elements, top points to last pushed element. Accessing stack[top] gives top element.

3. Final Answer:

   stack[++top] = 10; stack[++top] = 20; stack[++top] = 30; int x = stack[top]; -> Option A

4. Quick Check:

   Push increments top, peek uses stack[top] [OK]

Hint: Use stack[++top] to push, stack[top] to peek [OK]

Common Mistakes:

• Using post-increment top++ causing wrong indexing
• Accessing stack[top + 1] for peek
• Not initializing top to -1 before push