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How to implement stack using priority queue or heap?

Last Updated : 23 May, 2024
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How to Implement stack using a priority queue(using min heap)? Asked In: Microsoft, Adobe. 

Solution: In the priority queue, we assign priority to the elements that are being pushed. A stack requires elements to be processed in the Last in First Out manner. The idea is to associate a count that determines when it was pushed. This count works as a key for the priority queue. So the implementation of stack uses a priority queue of pairs, with the first element serving as the key.

CPP
#include <bits/stdc++.h>
using namespace std;

int main() {
    // Creating a pair of integers (key, value)
    pair<int, int> pair = make_pair(1, 42);

    // Accessing key and value
    int key = pair.first;
    int value = pair.second;

    // Printing key and value
    cout << "Key: " << key <<endl;
    cout << "Value: " << value <<endl;

    return 0;
}
Java
import java.util.AbstractMap;
import java.util.Map;

public class Main {
    public static void main(String[] args)
    {
        // Creating a pair of integers (key, value)
        Map.Entry<Integer, Integer> pair
            = new AbstractMap.SimpleEntry<>(1, 42);

        // Accessing key and value
        int key = pair.getKey();
        int value = pair.getValue();

        // Printing key and value
        System.out.println("Key: " + key);
        System.out.println("Value: " + value);
    }
}
Python
# Creating a pair of integers (key, value)
pair = (1, 42)

# Accessing key and value
key = pair[0]
value = pair[1]

# Printing key and value
print("Key:", key)
print("Value:", value)
C#
using System;
using System.Collections.Generic;

class Program {
    static void Main(string[] args)
    {
        // Creating a list of KeyValuePairs
        List<KeyValuePair<int, int> > myList
            = new List<KeyValuePair<int, int> >();

        // Adding elements to the list
        myList.Add(new KeyValuePair<int, int>(1, 10));
        myList.Add(new KeyValuePair<int, int>(2, 20));
        myList.Add(new KeyValuePair<int, int>(3, 30));

        // Displaying the elements in the list
        Console.Write("Elements in the list: ");
        foreach(var pair in myList)
        {
            Console.Write($"({pair.Key}, {pair.Value}) ");
        }
        Console.WriteLine();

        // Accessing elements by index
        int firstElement = myList[0].Value;
        int secondElement = myList[1].Value;

        // Modifying an element
        myList[1] = new KeyValuePair<int, int>(2, 25);

        // Removing an element by value
        for (int i = 0; i < myList.Count; i++) {
            if (myList[i].Value == 30) {
                myList.RemoveAt(i);
                break;
            }
        }

        // Displaying the updated list
        Console.Write("Updated list: ");
        foreach(var pair in myList)
        {
            Console.Write($"({pair.Key}, {pair.Value}) ");
        }
        Console.WriteLine();
    }
}
Javascript
// JavaScript does not have a built-in Pair or Map.Entry class like Java,
// but we can achieve similar functionality using an object literal.

// Main function
function main() {
    // Creating a pair of integers (key, value)
    const pair = { key: 1, value: 42 };

    // Accessing key and value
    const key = pair.key;
    const value = pair.value;

    // Printing key and value
    console.log("Key: " + key);
    console.log("Value: " + value);
}

// Calling the main function
main();

Below is the implementation of the above approach:

C++
// C++ program to implement a stack using
// Priority queue(min heap)
#include<bits/stdc++.h>
using namespace std;

typedef pair<int, int> pi;

// User defined stack class
class Stack{
    
    // cnt is used to keep track of the number of
    //elements in the stack and also serves as key
    //for the priority queue.
    int cnt;
    priority_queue<pair<int, int> > pq;
public:
    Stack():cnt(0){}
    void push(int n);
    void pop();
    int top();
    bool isEmpty();
};

// push function increases cnt by 1 and
// inserts this cnt with the original value.
void Stack::push(int n){
    cnt++;
    pq.push(pi(cnt, n));
}

// pops element and reduces count.
void Stack::pop(){
    if(pq.empty()){ cout<<"Nothing to pop!!!";}
    cnt--;
    pq.pop();
}

// returns the top element in the stack using
// cnt as key to determine top(highest priority),
// default comparator for pairs works fine in this case
int Stack::top(){
    pi temp=pq.top();
    return temp.second;
}

// return true if stack is empty
bool Stack::isEmpty(){
    return pq.empty();
}

// Driver code
int main()
{
    Stack* s=new Stack();
    s->push(1);
    s->push(2);
    s->push(3);
    while(!s->isEmpty()){
        cout<<s->top()<<endl;
        s->pop();
    }
}
Java
// Java program to implement a stack using
// Priority queue(min heap)
import java.util.PriorityQueue;

class Stack 
{

  // cnt is used to keep track of the number of
  //elements in the stack and also serves as key
  //for the priority queue.
  int cnt;
  PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[0] - b[0]);

  public Stack() {
    cnt = 0;
  }

  public void push(int n) {
    cnt++;
    pq.offer(new int[]{cnt, n});
  }

  public void pop() {
    if (pq.isEmpty()) {
      System.out.println("Nothing to pop!!!");
      return;
    }
    cnt--;
    pq.poll();
  }

  public int top() {
    int[] temp = pq.peek();
    return temp[1];
  }

  public boolean isEmpty() {
    return pq.isEmpty();
  }

  public static void main(String[] args) {
    Stack s = new Stack();
    s.push(3);
    s.push(2);
    s.push(1);
    while (!s.isEmpty()) {
      System.out.println(s.top());
      s.pop();
    }
  }
}

// This code is contributed by adityamaharshi21
Python
import heapq

# User defined stack class
class Stack:
    # cnt is used to keep track of the number of
    # elements in the stack and also serves as key
    # for the priority queue.
    def __init__(self):
        self.cnt = 0
        self.pq = []

    def push(self, n):
        # push function increases cnt by 1 and
        # inserts this cnt with the original value.
        self.cnt += 1
        heapq.heappush(self.pq, (-self.cnt, n))

    def pop(self):
        # pops element and reduces count.
        if not self.pq:
            print("Nothing to pop!!!")
        self.cnt -= 1
        return heapq.heappop(self.pq)[1]

    def top(self):
        # returns the top element in the stack using
        # cnt as key to determine top(highest priority),
        # default comparator for pairs works fine in this case
        return self.pq[0][1]

    def isEmpty(self):
        # return true if stack is empty
        return not bool(self.pq)

# Driver code
s = Stack()
s.push(1)
s.push(2)
s.push(3)
while not s.isEmpty():
    print(s.top())
    s.pop()
C#
// C# program to implement a stack using
// Priority queue(min heap)
using System;
using System.Collections.Generic;

class Stack
{
    // cnt is used to keep track of the number of
   //elements in the stack and also serves as key
  //for the priority queue.
    List<int> stack = new List<int>();

    public void Push(int n)
    {
        stack.Add(n);
    }

    public int Pop()
    {
        if (stack.Count == 0)
        {
            Console.WriteLine("Nothing to pop!!!");
            return -1;
        }
        int lastIndex = stack.Count - 1;
        int last = stack[lastIndex];
        stack.RemoveAt(lastIndex);
        return last;
    }

    public int Top()
    {
        if (stack.Count == 0)
        {
            Console.WriteLine("Nothing to get the top!!!");
            return -1;
        }
        return stack[stack.Count - 1];
    }

    public bool IsEmpty()
    {
        return stack.Count == 0;
    }
}

class Program
{
    static void Main(string[] args)
    {
        Stack s = new Stack();
        s.Push(1);
        s.Push(2);
        s.Push(3);
        while (!s.IsEmpty())
        {
            Console.WriteLine(s.Top());
            s.Pop();
        }
    }
}
Javascript
class Stack {
    constructor() {
        this.stack = [];
    }

    push(n) {
        this.stack.push(n);
    }

    pop() {
        if (this.stack.length === 0) {
            console.log("Nothing to pop!!!");
        }
        return this.stack.pop();
    }

    top() {
        return this.stack[this.stack.length - 1];
    }

    isEmpty() {
        return this.stack.length === 0;
    }
}

// Driver code
let s = new Stack();
s.push(1);
s.push(2);
s.push(3);
while (!s.isEmpty()) {
    console.log(s.top());
    s.pop();
}

Output
3
2
1

Time Complexity: O(log n), Now, as we can see this implementation takes O(log n) time for both push and pop operations. This can be slightly optimized by using fibonacci heap implementation of priority queue which would give us O(1) time complexity for push operation, but pop still requires O(log n) time. 
Auxiliary Space: O(n) where n is size of priority queue



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