Question

Consider an ordinary stack of integers that implements the usual push () and pop () operations in constant time. Describe an algorithm that implements an auxiliary stack alongside the ordinary stack such that the push () and pop () operations occur in constant time, but also keep track of the element currently in the ordinary stack with the minimum value in constant time. That is, design the auxiliary stack with these operations such that a user can push (), pop (), and findMin() any number of times and still perform these operations in constant time

Answer 1

CODE

// C++ program to implement a stack that supports
// findMin() in O(1) time and O(1) extra space.
#include <bits/stdc++.h>
using namespace std;

// A user defined stack that supports findMin() in
// addition to push() and pop()
struct MyStack
{
   stack<int> s;
   int minEle;

   // Prints minimum element of MyStack
   void findMin()
   {
       if (s.empty())
           cout << "Stack is empty\n";

       // variable minEle stores the minimum element
       // in the stack.
       else
           cout <<"Minimum Element in the stack is: "
               << minEle << "\n";
   }

   // Prints top element of MyStack
   void peek()
   {
       if (s.empty())
       {
           cout << "Stack is empty ";
           return;
       }

       int t = s.top(); // Top element.

       cout << "Top Most Element is: ";

       // If t < minEle means minEle stores
       // value of t.
       (t < minEle)? cout << minEle: cout << t;
   }

   // Remove the top element from MyStack
   void pop()
   {
       if (s.empty())
       {
           cout << "Stack is empty\n";
           return;
       }

       cout << "Top Most Element Removed: ";
       int t = s.top();
       s.pop();

       // Minimum will change as the minimum element
       // of the stack is being removed.
       if (t < minEle)
       {
           cout << minEle << "\n";
           minEle = 2*minEle - t;
       }

       else
           cout << t << "\n";
   }

   // Removes top element from MyStack
   void push(int x)
   {
       // Insert new number into the stack
       if (s.empty())
       {
           minEle = x;
           s.push(x);
           cout << "Number Inserted: " << x << "\n";
           return;
       }

       // If new number is less than minEle
       if (x < minEle)
       {
           s.push(2*x - minEle);
           minEle = x;
       }

       else
       s.push(x);

       cout << "Number Inserted: " << x << "\n";
   }
};

// Driver Code
int main()
{
   MyStack s;
   s.push(3);
   s.push(5);
   s.findMin();
   s.push(2);
   s.push(1);
   s.findMin();
   s.pop();
   s.findMin();
   s.pop();
   s.peek();

   return 0;
}