Algorithm Day71 - Min Stack

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🧩 Problem Description

Design a stack that supports push, pop, top, and retrieving the minimum element in constant time.

Implement the MinStack class:

  • MinStack() initializes the stack object.
  • void push(int val) pushes the element val onto the stack.
  • void pop() removes the element on the top of the stack.
  • int top() gets the top element of the stack.
  • int getMin() retrieves the minimum element in the stack.

You must implement all the functions of the stack such that each function works in O(1) time complexity.

💬 Examples

Example 1

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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

💡 Intuition

We need a stack that can return the minimum element in constant time.

  • Use two stacks:
    1. One for storing all values.
    2. Another for storing the current minimum at each level.
  • When pushing, also update the min stack with the smaller value between new element and current min.
  • When popping, remove from both stacks.

🔢 Java Code (Two Stacks)

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import java.util.*;

class MinStack {
    private Stack<Integer> stack;
    private Stack<Integer> minStack;

    public MinStack() {
        stack = new Stack<>();
        minStack = new Stack<>();
    }
    
    public void push(int val) {
        stack.push(val);
        if (minStack.isEmpty() || val <= minStack.peek()) {
            minStack.push(val);
        } else {
            minStack.push(minStack.peek());
        }
    }
    
    public void pop() {
        stack.pop();
        minStack.pop();
    }
    
    public int top() {
        return stack.peek();
    }
    
    public int getMin() {
        return minStack.peek();
    }
}

⏱ Complexity Analysis

  • Time: O(1) for all operations (push, pop, top, getMin).
  • Space: O(n) — extra stack to track minimums.

✍️ Summary

  • Maintain a parallel min stack to track current minimum.
  • Ensures constant time retrieval of min element.

Related problems

  • lc-716 — Max Stack
  • lc-20 — Valid Parentheses