LeetCode 155. MinStack

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

Example 1:

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.

Idea:

Stack by default supports push(), pop(), top() in O(1) time complexity. But getting the minimum value in O(1) is not default operation of stack data structure.

Lets take the example [“MinStack”,”push”,”push”,”push”,”getMin”,”pop”,”top”,”getMin”]
[[],[-2],[0],[-3],[],[],[],[]]

Here after 3 push() operations, how can we get the minimum value from the stack? Naïve way would be look at every single element of the stack to get the minimum which is O(N) operation.

[-2] whats the minimum at this point? -2

[-2,0] ==> min value : 0

[-2,0,-3] ==> min value = -3

How about keeping a single variable to keep track of the minimum value? No it wont work why?

Because for example if you pop() from [-2,0,-3] , that would be [-2,0] and correct answer of new getMin() should be at this point: -2. How can we keep the min value at every element?

So what we need is two stacks : (1) Stack for keeping track of elements pushed into the stack (2) MinStack to store “minimum so far” for each element added to the stack.