Min Stack Design in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Min Stack?

A Min Stack is a special stack that supports push, pop, and retrieving the minimum element in constant time.

intermediate

How does a Min Stack keep track of the minimum element efficiently?

It keeps an extra stack that stores the minimum values at each level, so the current minimum is always on top of this extra stack.

beginner

What operations must a Min Stack support?

Push (add element), Pop (remove element), Top (get top element), and GetMin (get minimum element) all in constant time.

beginner

Why can't we just scan the stack to find the minimum each time?

Scanning the stack each time would take linear time, which is slow. Min Stack design keeps minimum retrieval in constant time.

intermediate

What happens to the minimum stack when we pop the main stack?

We also pop the minimum stack if the popped element is the current minimum, keeping both stacks in sync.

What extra data structure is commonly used in Min Stack design to track minimum values?

A Linked list

B Queue

C Hash map

D Another stack

A second stack is used to keep track of minimum values at each push.

What is the time complexity to get the minimum element in a Min Stack?

A O(n)

B O(log n)

C O(1)

D O(n^2)

Min Stack retrieves the minimum element in constant time O(1).

When pushing a new element, when do we push it onto the minimum stack?

A Never

B Only if it is smaller or equal to the current minimum

C Always

D Only if it is larger than the current minimum

We push onto the minimum stack only if the new element is smaller or equal to the current minimum.

What happens to the minimum stack when the top element is popped from the main stack and it equals the current minimum?

A Pop from the minimum stack as well

B Do nothing

C Push a new minimum

D Clear the minimum stack

We pop from the minimum stack to keep it in sync with the main stack.

Which of these is NOT a required operation for a Min Stack?

A Sort

B Pop

C GetMin

D Push

Sorting is not required; Min Stack only needs push, pop, top, and getMin.

Explain how a Min Stack maintains the minimum element during push and pop operations.

Think about syncing two stacks to track minimum.

Describe the time complexity of each operation in a Min Stack and why it is efficient.

Focus on how the extra stack helps avoid slow searches.

Practice

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

easy

A. To store only the minimum elements pushed so far

B. To sort elements in ascending order automatically

C. To retrieve the minimum element in constant time along with stack operations

D. To reverse the order of elements pushed into the stack

Solution

1. Step 1: Understand the Min Stack concept

   A Min Stack is designed to support normal stack operations and also return the minimum element quickly.

2. Step 2: Identify the key feature

   The key feature is retrieving the minimum element in constant time, not sorting or reversing.

3. Final Answer:

   To retrieve the minimum element in constant time along with stack operations -> Option C

4. Quick Check:

   Min Stack = fast minimum retrieval [OK]

Hint: Min Stack always tracks minimum for O(1) retrieval [OK]

Common Mistakes:

• Thinking Min Stack sorts elements
• Assuming it stores only minimum elements
• Confusing with reversing stack order

2. Which of the following is the correct way to initialize a Min Stack class in Python?

easy

A. class MinStack:
def __init__(self):
stack = []
min_stack = []

B. class MinStack:
def __init__(self):
self = []

C. class MinStack:
def __init__(self):
self.stack = None
self.min_stack = None

D. class MinStack:
def __init__(self):
self.stack = []
self.min_stack = []

Solution

1. Step 1: Check correct attribute initialization

   Attributes must be initialized with self to be instance variables.

2. Step 2: Verify list initialization

   Both stack and min_stack should be empty lists initialized with self.

3. Final Answer:

   class MinStack:\n def __init__(self):\n self.stack = []\n self.min_stack = [] -> Option D

4. Quick Check:

   Use self for instance variables [OK]

Hint: Always use self to define instance variables in __init__ [OK]

Common Mistakes:

• Not using self for attributes
• Initializing attributes as None instead of lists
• Assigning self to a list directly

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

min_stack = MinStack()
min_stack.push(3)
min_stack.push(5)
min_stack.push(2)
min_stack.push(1)
min_stack.pop()
print(min_stack.get_min())

medium

A. 2

B. 1

C. 3

D. 5

Solution

1. Step 1: Trace push operations and min tracking

   Push 3 (min=3), push 5 (min=3), push 2 (min=2), push 1 (min=1).

2. Step 2: Pop removes 1, min updates to 2

   After popping 1, the minimum is the next smallest, which is 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Pop removes min 1, next min = 2 [OK]

Hint: Pop min, next min is previous min in min stack [OK]

Common Mistakes:

• Assuming min stays 1 after pop
• Confusing push order with min updates
• Ignoring min stack updates on pop

4. Identify the bug in this Min Stack pop method and choose the correct fix:

def pop(self):
    if self.stack:
        self.stack.pop()
        self.min_stack.pop()

medium

A. No bug; code is correct

B. Pop from min_stack only if popped element equals current min

C. Pop from min_stack before popping from stack

D. Check if min_stack is empty before popping it

Solution

1. Step 1: Understand pop logic in Min Stack

   Pop from min_stack only if the popped element is the current minimum to keep min_stack accurate.

2. Step 2: Identify bug and fix

   Current code always pops min_stack, which can cause errors if min_stack is out of sync.

3. Final Answer:

   Pop from min_stack only if popped element equals current min -> Option B

4. Quick Check:

   Pop min_stack conditionally to keep min correct [OK]

Hint: Pop min_stack only if popped value equals current min [OK]

Common Mistakes:

• Always popping min_stack without condition
• Not checking min_stack emptiness
• Changing pop order incorrectly

5. You want to design a Min Stack that supports push, pop, top, and get_min all in O(1) time. Which approach is best?

hard

A. Use two stacks: one for all elements, one for current minimums

B. Use a queue to store elements and a variable for min

C. Use one stack and scan all elements to find min on get_min

D. Use a linked list and traverse to find min on each get_min

Solution

1. Step 1: Analyze time complexity requirements

   All operations must be O(1), so scanning or traversing is not allowed.

2. Step 2: Choose data structure approach

   Using two stacks, one for elements and one for minimums, allows constant time min retrieval.

3. Final Answer:

   Use two stacks: one for all elements, one for current minimums -> Option A

4. Quick Check:

   Two stacks = O(1) min retrieval [OK]

Hint: Two stacks track elements and minimums for O(1) min [OK]

Common Mistakes:

• Using scanning which is O(n)
• Using queue which doesn't support stack operations
• Using linked list traversal for min