MediumStacks

Min Stack

Explanation & Solution

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

You must implement a solution with O(1) time complexity for each function.

Examples

Example 1:

Input:

`

["MinStack","push","push","push","getMin","pop","top","getMin"]

[[],[-2],[0],[-3],[],[],[],[]]

`

Output:[null,null,null,null,-3,null,0,-2]
0
null
1
null
2
null
3
null
4
-3
5
null
6
0
7
-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

  • -2^31 <= val <= 2^31 - 1
  • Methods pop, top and getMin operations will always be called on non-empty stacks
  • At most 3 * 10^4 calls will be made to push, pop, top, and getMin

Approach

Stacks pattern

1. Two Stacks Approach

  • Maintain two stacks: a main stack for values and a min stack that tracks the minimum at each level

2. Push Operation

  • Push the value onto the main stack
  • Push min(val, current minimum) onto the min stack
  • This ensures the min stack always has the current minimum at its top

3. Pop Operation

  • Pop from both stacks simultaneously
  • The min stack stays synchronized with the main stack

4. Top and GetMin

  • top() returns the top of the main stack
  • getMin() returns the top of the min stack
  • Both are O(1) operations

Key Insight

  • By maintaining a parallel min stack, we trade O(n) extra space for O(1) getMin time
  • Each position in the min stack stores the minimum of all elements from that position down to the bottom of the stack

Solution Code