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

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Suppose we want to make a stack that can store the maximum element in the stack. And we can get it in O(1) time. The constraint is that, it should use O(1) extra space.

We can make one user-defined stack, that will store the max value, when one operation is performed, like pop or peek, then the max will be returned. For peek operation, return the maximum of stack top and the max element, for pop operation, when the top element is larger, then print it and update max as 2*max – top_element. otherwise return top_element. For push operation update the max element as x(data to be inserted), 2*x – max.

## Example

#include <iostream>
#include <stack>
using namespace std;
class CustomStack {
stack<int> stk;
int stack_max;
public:
void getMax() {
if (stk.empty())
cout << "Stack is empty"<<endl;
else
cout << "Maximum Element in the stack is: "<< stack_max <<endl;
}
void peek() {
if (stk.empty()) {
cout << "Stack is empty ";
return;
}
int top = stk.top(); // Top element.
cout << "Top Most Element is: "<<endl;
(top > stack_max) ? cout << stack_max : cout << top;
}
void pop() {
if (stk.empty()) {
cout << "Stack is empty"<<endl;
return;
}
cout << "Top Most Element Removed: ";
int top = stk.top();
stk.pop();
if (top > stack_max) {
cout << stack_max <<endl;
stack_max = 2 * stack_max - top;
} else
cout << top <<endl;
}
void push(int element) {
if (stk.empty()) {
stack_max = element;
stk.push(element);
cout << "Element Inserted: " << element <<endl;
return;
}
if (element > stack_max) {
stk.push(2 * element - stack_max);
stack_max = element;
} else
stk.push(element);
cout << "Element Inserted: " << element <<endl;
}
};
int main() {
CustomStack stk;
stk.push(4);
stk.push(6);
stk.getMax();
stk.push(8);
stk.push(20);
stk.getMax();
stk.pop();
stk.getMax();
stk.pop();
stk.peek();
}

## Output

Element Inserted: 4
Element Inserted: 6
Maximum Element in the stack is: 6
Element Inserted: 8
Element Inserted: 20
Maximum Element in the stack is: 20
Top Most Element Removed: 20
Maximum Element in the stack is: 8
Top Most Element Removed: 8
Top Most Element is:
6