How to Solve Min Stack

The Min Stack problem requires designing a stack that supports push, pop, top, and retrieving the minimum element in constant time. The challenge is ensuring O(1) time complexity for each function. The key idea involves stack-based state management, where each stack node stores a minimum value.

Problem Statement

You are tasked with designing a stack that supports four key operations: push, pop, top, and getMin. The twist is that all these operations must run in constant time, O(1). Implement a class, MinStack, that allows efficient access to the minimum element while maintaining stack integrity.

To achieve this, the solution must incorporate stack-based state management, where each node in the stack will track the minimum element at that point in time. Consider edge cases like maintaining correct values after pops and handling getMin calls during stack mutations.

Examples

Example 1

Input: See original problem statement.

Output: See original problem statement.

Input ["MinStack","push","push","push","getMin","pop","top","getMin"] [[],[-2],[0],[-3],[],[],[],[]]

Output [null,null,null,null,-3,null,0,-2]

Explanation MinStack minStack = new MinStack(); minStack.push(-2); minStack.push(0); minStack.push(-3); minStack.getMin(); // return -3 minStack.pop(); minStack.top(); // return 0 minStack.getMin(); // return -2

Constraints

• -231 <= val <= 231 - 1
• Methods pop, top and getMin operations will always be called on non-empty stacks.
• At most 3 * 104 calls will be made to push, pop, top, and getMin.

Solution Approach

MinStack Design

The solution can involve maintaining two stacks: one for the actual values and another for tracking the minimum value at each point. Each time a new element is pushed, compare it with the current minimum and store the new minimum in the second stack. This ensures that getMin can retrieve the minimum in constant time.

Push and Pop Operations

For each push operation, push the value onto the main stack and the minimum onto the auxiliary stack. For pop, remove elements from both stacks to maintain synchronization, ensuring that the minimum stack always has the correct value for getMin.

Top and getMin Operations

The top operation returns the value from the main stack. The getMin operation returns the top value from the auxiliary stack, which always stores the minimum value for the corresponding state of the main stack.

Complexity Analysis

Both time and space complexities are O(1) for all operations (push, pop, top, getMin). The auxiliary stack ensures that every operation can be performed in constant time. The space complexity depends on the size of the stack, but it remains linear in terms of the number of elements.

What Interviewers Usually Probe

• Looking for efficient O(1) time complexity for all operations.
• Check if the candidate handles the edge cases when the stack becomes empty.
• Evaluate if the solution maintains stack synchronization properly, particularly with respect to the minimum tracking.

Common Pitfalls or Variants

Common pitfalls

• Incorrect handling of stack underflow, especially for pop and getMin operations.
• Failure to maintain the correct minimum values when elements are popped.
• Confusion about how to manage two stacks or how to update the minimum value stack.

Follow-up variants

• Implementing a stack that supports additional operations like peek.
• Designing a thread-safe version of the MinStack for concurrent operations.
• Optimizing space by reducing auxiliary stack usage while maintaining O(1) time complexity.

How GhostInterview Helps

• GhostInterview helps you solve this problem step-by-step, ensuring you understand the critical concepts of stack-based state management.
• It walks you through the best practices of maintaining two stacks and the intricacies of ensuring constant time for every operation.
• Our solution explanations provide detailed insights into handling edge cases, preparing you for the interview environment.

Topic Pages

• Stack
• Design

Related GhostInterview Pages

• LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
• Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
• How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.

FAQ

What is the main challenge in solving the Min Stack problem?

The main challenge is ensuring that all operations—push, pop, top, and getMin—run in constant time, O(1), while maintaining correct tracking of the minimum value.

How can we efficiently track the minimum element in a stack?

You can use a secondary stack to track the minimum value. Every time a new value is pushed, compare it with the current minimum and store the smaller of the two in the secondary stack.

What is the time complexity of the Min Stack problem?

The time complexity for each operation (push, pop, top, getMin) is O(1), making the solution highly efficient.

Can the Min Stack problem be solved with just one stack?

While it's possible, using two stacks is the most straightforward and efficient approach to ensure constant-time operations for both min tracking and stack management.

How do you handle edge cases like empty stacks in the Min Stack problem?

Edge cases, such as popping from an empty stack or calling getMin on an empty stack, are managed by checking if the stack is empty before performing operations.