Min Stack Design in DSA C - Time & Space Complexity

Time Complexity: Min Stack Design

O(1)

Understanding Time Complexity

We want to understand how fast the Min Stack operations run as the number of elements grows.

Specifically, how does the time to push, pop, or get the minimum change with more items?

Scenario Under Consideration

Analyze the time complexity of the following Min Stack code snippet.

typedef struct {
    int *stack;
    int *minStack;
    int top;
    int capacity;
} MinStack;

void push(MinStack* obj, int val) {
    obj->stack[++obj->top] = val;
    int minVal = obj->top == 0 ? val : (val < obj->minStack[obj->top - 1] ? val : obj->minStack[obj->top - 1]);
    obj->minStack[obj->top] = minVal;
}

void pop(MinStack* obj) {
    if (obj->top >= 0) obj->top--;
}

int getMin(MinStack* obj) {
    return obj->minStack[obj->top];
}
    

This code keeps track of the minimum value at each stack level to allow quick minimum retrieval.

Identify Repeating Operations

Look for loops or repeated steps inside each operation.

• Primary operation: Each push, pop, and getMin runs a fixed number of steps without loops.
• How many times: Each operation runs once per call, no matter how many elements are in the stack.

How Execution Grows With Input

Each operation does a constant amount of work regardless of stack size.

Input Size (n)	Approx. Operations per push/pop/getMin
10	5-6 steps
100	5-6 steps
1000	5-6 steps

Pattern observation: The number of steps stays the same no matter how many elements are in the stack.

Final Time Complexity

Time Complexity: O(1)

This means each operation takes the same short time no matter how big the stack is.

Common Mistake

[X] Wrong: "Finding the minimum must scan all elements, so it takes longer as stack grows."

[OK] Correct: The min stack stores the minimum at each step, so getMin just reads one value instantly.

Interview Connect

Knowing how to keep track of minimum values efficiently shows your skill in designing smart data structures.

Self-Check

"What if we used only one stack and searched for the minimum each time getMin is called? How would the time complexity change?"

Practice

1. What is the main purpose of a Min Stack data structure?

easy

A. To reverse the order of elements

B. To retrieve the minimum element in constant time

C. To store elements in a queue fashion

D. To sort elements in ascending order

Solution

1. Step 1: Understand Min Stack functionality

   A Min Stack is designed to allow retrieval of the minimum element quickly, usually in constant time.

2. Step 2: Compare with other options

   Sorting or queue behavior is not the main goal of a Min Stack; it focuses on minimum element retrieval.

3. Final Answer:

   To retrieve the minimum element in constant time -> Option B

4. Quick Check:

   Min Stack = fast minimum retrieval [OK]

Hint: Min Stack always tracks minimum element fast [OK]

Common Mistakes:

• Confusing Min Stack with sorting algorithms
• Thinking it behaves like a queue
• Assuming it reverses elements

2. Which of the following is the correct way to declare a stack node structure for a Min Stack in C?

easy

A. typedef struct Node { int value; struct Node* next; int min; } Node;

B. typedef struct Node { int value; int min; } Node;

C. typedef struct Node { int value; struct Node* prev; } Node;

D. typedef struct Node { int value; struct Node* next; } Node;

Solution

1. Step 1: Identify required fields for Min Stack node

   A Min Stack node needs to store the value, a pointer to the next node, and the minimum value at that node.

2. Step 2: Match with options

   typedef struct Node { int value; struct Node* next; int min; } Node; includes value, next pointer, and min field, which is correct for Min Stack implementation.

3. Final Answer:

   typedef struct Node { int value; struct Node* next; int min; } Node; -> Option A

4. Quick Check:

   Node stores value, next, and min [OK]

Hint: Min Stack node needs value, next pointer, and min [OK]

Common Mistakes:

• Omitting the min field in node
• Using prev pointer instead of next
• Not using struct pointer for next

3. Consider the following C code snippet for a Min Stack push operation:

void push(Node** top, int x) {
    Node* newNode = malloc(sizeof(Node));
    newNode->value = x;
    if (*top == NULL) {
        newNode->min = x;
    } else {
        newNode->min = (x < (*top)->min) ? x : (*top)->min;
    }
    newNode->next = *top;
    *top = newNode;
}

What will be the minimum value after pushing elements 3, 5, 2 in this order on an empty stack?

medium

A. 2

B. 3

C. 5

D. Error

Solution

1. Step 1: Push 3 on empty stack

   Stack top is NULL, so min = 3.

2. Step 2: Push 5

   Compare 5 with current min 3; min remains 3.

3. Step 3: Push 2

   Compare 2 with current min 3; min updates to 2.

4. Final Answer:

   2 -> Option A

5. Quick Check:

   Minimum after pushes = 2 [OK]

Hint: Min updates only if new value is smaller [OK]

Common Mistakes:

• Not updating min on push
• Confusing min with last pushed value
• Assuming min resets on each push

4. The following C function is intended to pop an element from a Min Stack. Identify the error:

int pop(Node** top) {
    if (*top == NULL) return -1;
    int val = (*top)->value;
    free(*top);
    *top = (*top)->next;
    return val;
}

medium

A. Not checking if stack is empty

B. Returning value before freeing node

C. Accessing (*top)->next after freeing *top

D. Missing return statement

Solution

1. Step 1: Analyze order of operations

   The code frees *top, then accesses (*top)->next, which is invalid after free.

2. Step 2: Correct order

   Should save next pointer before freeing current node to avoid invalid access.

3. Final Answer:

   Accessing (*top)->next after freeing *top -> Option C

4. Quick Check:

   Free before next access causes error [OK]

Hint: Save next pointer before freeing node [OK]

Common Mistakes:

• Freeing node before accessing next
• Ignoring NULL check
• Returning value after free without saving

5. You want to design a Min Stack that supports push, pop, and getMin all in O(1) time using two stacks. Which approach correctly implements getMin?

hard

A. Use a queue to track minimum values

B. Sort the main stack on every push to keep minimum on top

C. Traverse the main stack on every getMin call to find minimum

D. Maintain a second stack that stores the minimum values; push new min or duplicate current min on push

Solution

1. Step 1: Understand two-stack Min Stack design

   One stack stores all values; the second stack keeps track of minimums for O(1) retrieval.

2. Step 2: Evaluate options

   Maintain a second stack that stores the minimum values; push new min or duplicate current min on push correctly describes pushing new minimum or current minimum duplicate onto second stack.

3. Final Answer:

   Maintain a second stack that stores the minimum values; push new min or duplicate current min on push -> Option D

4. Quick Check:

   Two stacks: one for values, one for mins [OK]

Hint: Use second stack to track mins for O(1) getMin [OK]

Common Mistakes:

• Sorting stack on every push (slow)
• Searching stack on getMin (not O(1))
• Using queue instead of stack