Find maximum in a stack in O(1) time and O(1) extra space

Given a stack of integers. The task is to design a special stack such that maximum element can be found in O(1) time and O(1) extra space.


Given Stack :
64   --> Maximum

So Output must be 64 when getMax() is called.

Below are the different functions designed to push and pop elements from the stack.
Push(x) : Inserts x at the top of stack.

  • If stack is empty, insert x into the stack and make maxEle equal to x.
  • If stack is not empty, compare x with maxEle. Two cases arise:
    • If x is less than or equal to maxEle, simply insert x.
    • If x is greater than maxEle, insert (2*x – maxEle) into the stack and make maxEle equal to x. For example, let previous maxEle was 3. Now we want to insert 4. We update maxEle as 4 and insert 2*4 – 3 = 5 into the stack.

Pop() : Removes an element from top of stack.

  • Remove element from top. Let the removed element be y. Two cases arise:
    • If y is less than or equal to maxEle, the maximum element in the stack is still maxEle.
    • If y is greater than maxEle, the maximum element now becomes (2*maxEle – y), so update (maxEle = 2*maxEle – y). This is where we retrieve previous maximum from current maximum and its value in stack. For example, let the element to be removed be 5 and maxEle be 4. We remove 5 and update maxEle as 2*4 – 5 = 3.

Important Points:

  • Stack doesn’t hold actual value of an element if it is maximum so far.
  • Actual maximum element is always stored in maxEle



  • Number to be Inserted: 3, Stack is empty, so insert 3 into stack and maxEle = 3.
  • Number to be Inserted: 5, Stack is not empty, 5> maxEle, insert (2*5-3) into stack and maxEle = 5.
  • Number to be Inserted: 2, Stack is not empty, 2< maxEle, insert 2 into stack and maxEle = 5.
  • Number to be Inserted: 1, Stack is not empty, 1< maxEle, insert 1 into stack and maxEle = 5.


  • Initially the maximum element maxEle in the stack is 5.
  • Number removed: 1, Since 1 is less than maxEle just pop 1. maxEle=5.
  • Number removed: 2, 2<maxEle, so number removed is 2 and maxEle is still equal to 5.
  • Number removed: 7, 7> maxEle, original number is maxEle which is 5 and new maxEle = 2*5 – 7 = 3.




// C++ program to implement a stack that supports
// getMaximum() in O(1) time and O(1) extra space.
#include <bits/stdc++.h>
using namespace std;
// A user defined stack that supports getMax() in
// addition to push() and pop()
struct MyStack {
    stack<int> s;
    int maxEle;
    // Prints maximum element of MyStack
    void getMax()
        if (s.empty())
            cout << "Stack is empty\n";
        // variable maxEle stores the maximum element
        // in the stack.
            cout << "Maximum Element in the stack is: "
                 << maxEle << "\n";
    // Prints top element of MyStack
    void peek()
        if (s.empty()) {
            cout << "Stack is empty ";
        int t =; // Top element.
        cout << "Top Most Element is: ";
        // If t < maxEle means maxEle stores
        // value of t.
        (t > maxEle) ? cout << maxEle : cout << t;
    // Remove the top element from MyStack
    void pop()
        if (s.empty()) {
            cout << "Stack is empty\n";
        cout << "Top Most Element Removed: ";
        int t =;
        // Maximum will change as the maximum element
        // of the stack is being removed.
        if (t > maxEle) {
            cout << maxEle << "\n";
            maxEle = 2 * maxEle - t;
            cout << t << "\n";
    // Removes top element from MyStack
    void push(int x)
        // Insert new number into the stack
        if (s.empty()) {
            maxEle = x;
            cout << "Number Inserted: " << x << "\n";
        // If new number is less than maxEle
        if (x > maxEle) {
            s.push(2 * x - maxEle);
            maxEle = x;
        cout << "Number Inserted: " << x << "\n";
// Driver Code
int main()
    MyStack s;
    return 0;



Number Inserted: 3
Number Inserted: 5
Maximum Element in the stack is: 5
Number Inserted: 7
Number Inserted: 19
Maximum Element in the stack is: 19
Top Most Element Removed: 19
Maximum Element in the stack is: 7
Top Most Element Removed: 7
Top Most Element is: 5

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