Priority Queue in C++ Standard Template Library (STL)

A C++ priority queue is a type of container adapter, specifically designed such that the first element of the queue is either the greatest or the smallest of all elements in the queue, and elements are in non-increasing or non-decreasing order (hence we can see that each element of the queue has a priority {fixed order}).

In C++ STL, the top element is always the greatest by default. We can also change it to the smallest element at the top. Priority queues are built on the top of the max heap and use an array or vector as an internal structure. In simple terms, STL Priority Queue is the implementation of Heap Data Structure.

Syntax:

std::priority_queue<int> pq;

Example:

C++

// C++ program to demonstrate the use of priority_queue
#include <iostream>
#include <queue>
using namespace std;

// driver code
int main()
{
    int arr[6] = { 10, 2, 4, 8, 6, 9 };

    // defining priority queue
    priority_queue<int> pq;

    // printing array
    cout << "Array: ";
    for (auto i : arr) {
        cout << i << ' ';
    }
    cout << endl;
    // pushing array sequentially one by one
    for (int i = 0; i < 6; i++) {
        pq.push(arr[i]);
    }

    // printing priority queue
    cout << "Priority Queue: ";
    while (!pq.empty()) {
        cout << pq.top() << ' ';
        pq.pop();
    }

    return 0;
}

Output

Array: 10 2 4 8 6 9 
Priority Queue: 10 9 8 6 4 2 

Max Heap Priority Queue (default scheme)

How to create a min heap for the priority queue?

As we saw earlier, a priority queue is implemented as max heap by default in C++ but, it also provides us an option to change it to min heap by passing another parameter while creating a priority queue.

Syntax:

priority_queue <int, vector<int>, greater<int>> gq;

Example:

C++

// C++ program to demonstrate
// min heap for priority queue
#include <iostream>
#include <queue>
using namespace std;

void showpq(
    priority_queue<int, vector<int>, greater<int> > gq)
{
    priority_queue<int, vector<int>, greater<int> > g = gq;
    while (!g.empty()) {
        cout << ' ' << g.top();
        g.pop();
    }
    cout << '\n';
}

void showArray(int* arr, int n)
{
    for (int i = 0; i < n; i++) {
        cout << arr[i] << ' ';
    }
    cout << endl;
}

// Driver Code
int main()
{
    int arr[6] = { 10, 2, 4, 8, 6, 9 };
    priority_queue<int, vector<int>, greater<int> > gquiz(
        arr, arr + 5);

    cout << "Array: ";
      showArray(arr, 6);

    cout << "Priority Queue : ";
    showpq(gquiz);

    return 0;
}

Output

The priority queue gquiz is :     2    4    6    8    9    10

gquiz.size() : 6
gquiz.top() : 2
gquiz.pop() :     4    6    8    9    10

Min Heap Priority Queue

Note: The above syntax may be difficult to remember, so in case of numeric values, we can multiply the values with -1 and use max heap to get the effect of min heap. Not only that we can use custom sorting method by replacing greater with custom comparator function.

Methods of Priority Queue

Following list of all the methods of std::priority_queue class:

Method	Definition
priority_queue::empty()	Returns whether the queue is empty.
priority_queue::size()	Returns the size of the queue.
priority_queue::top()	Returns a reference to the topmost element of the queue.
priority_queue::push()	Adds the element ‘g’ at the end of the queue.
priority_queue::pop()	Deletes the first element of the queue.
priority_queue::swap()	Used to swap the contents of two queues provided the queues must be of the same type, although sizes may differ.
priority_queue::emplace()	Used to insert a new element into the priority queue container.
priority_queue value_type	Represents the type of object stored as an element in a priority_queue. It acts as a synonym for the template parameter.

Operations on Priority Queue in C++

1. Inserting and Removing Elements of a Priority Queue

The push() method is used to insert an element into the priority queue. To remove an element from the priority queue the pop() method is used because this removes the element with the highest priority.

Below is the C++ program for various functions in the priority queue:

C++

// C++ Program to demonstrate various
//  method/function in Priority Queue
#include <iostream>
#include <queue>
using namespace std;

// Implementation of priority queue
void showpq(priority_queue<int> gq)
{
    priority_queue<int> g = gq;
    while (!g.empty()) {
        cout << ' ' << g.top();
        g.pop();
    }
    cout << '\n';
}

// Driver Code
int main()
{
    priority_queue<int> gquiz;
    // used in inserting the element
    gquiz.push(10);
    gquiz.push(30);
    gquiz.push(20);
    gquiz.push(5);
    gquiz.push(1);

    cout << "The priority queue gquiz is : ";

    // used for highlighting the element
    showpq(gquiz);

    // used for identifying the size
    // of the priority queue
    cout << "\ngquiz.size() : " <<
             gquiz.size();
    // used for telling the top element
    // in priority queue
    cout << "\ngquiz.top() : " <<
             gquiz.top();

    // used for popping the element
    // from a priority queue
    cout << "\ngquiz.pop() : ";
    gquiz.pop();
    showpq(gquiz);

    return 0;
}

Output

The priority queue gquiz is :  30 20 10 5 1

gquiz.size() : 5
gquiz.top() : 30
gquiz.pop() :  20 10 5 1

Refer end for complexity analysis.

Note: Above shown is one of the methods of priority queue initialization. To know more about efficient initialization of priority queue, click here.

2. To Access the Top Element of the Priority Queue 

The top element of the Priority Queue could be accessed using the top() method.

C++

// C++ program to access the top
// element of priority queue
#include <iostream>
#include <queue>
using namespace std;

// Driver code
int main()
{
  // create a priority queue of int
  priority_queue<int> numbers;

  // add items to priority_queue
  numbers.push(1);
  numbers.push(20);
  numbers.push(7);

  // get the element at the top
  cout << "Top element: " <<
           numbers.top();
  return 0;
}

Output

Top element: 20

Refer end for complexity analysis.

Note: We can only access the top element in the priority queue.

3. To Check whether the Priority Queue is Empty or Not:

We use the empty() method to check if the priority_queue is empty. This method returns:

• True – It is returned when the priority queue is empty and is represented by 1 
• False – It is produced when the priority queue is not empty or False and is characterized by 0

Example:

C++

// C++ program to demonstrate
// Implementation of empty() function
#include <iostream>
#include <queue>
using namespace std;

// Driver code
int main()
{
  priority_queue<int> pqueueGFG;
  pqueueGFG.push(1);

  // Priority Queue becomes 1
  // check if it is empty or not
  if (pqueueGFG.empty())
  {
    cout << "Empty or true";
  }
  else
  {
    cout << "Contains element or False";
  }
  return 0;
}

Output

Contains element or False

Refer end for complexity analysis.

4. To Get/Check the Size of the Priority Queue

It determines the size of a priority queue. In simple terms, the size() method is used to get the number of elements present in the Priority Queue.

Below is the C++ program to check the size of the priority queue:

C++

// C++ program to demonstrate the
// size() method of priority queue
#include <iostream>
#include <queue>
using namespace std;

// Driver code
int main()
{
  // create a priority queue of string
  priority_queue<string> pqueue;

  // add items to priority_queue
  pqueue.push("Geeks");
  pqueue.push("for");
  pqueue.push("Geeks");
  pqueue.push("C++");

  // get the size of queue
  int size = pqueue.size();
  cout << "Size of the queue: " << size;

  return 0;
}

Output

Size of the queue: 4

Refer end for complexity analysis.

5. To Swap Contents of a Priority Queue with Another of Similar Type

Swap() function is used to swap the contents of one priority queue with another priority queue of same type and same or different size.

Below is the C++ program to swap contents of a priority queue with another of similar type:

C++

// CPP program to illustrate
// Implementation of swap() function

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

// Print elements of priority queue
void print(priority_queue<int> pq)
{
    while (!pq.empty()) {
        cout << pq.top() << " ";
        pq.pop();
    }
    cout << endl;
}

int main()
{
    // priority_queue container declaration
    priority_queue<int> pq1;
    priority_queue<int> pq2;

    // pushing elements into the 1st priority queue
    pq1.push(1);
    pq1.push(2);
    pq1.push(3);
    pq1.push(4);

    // pushing elements into the 2nd priority queue
    pq2.push(3);
    pq2.push(5);
    pq2.push(7);
    pq2.push(9);

    cout << "Before swapping:-" << endl;
    cout << "Priority Queue 1 = ";
    print(pq1);
    cout << "Priority Queue 2 = ";
    print(pq2);

    // using swap() function to swap elements of priority
    // queues
    pq1.swap(pq2);

    cout << endl << "After swapping:-" << endl;
    cout << "Priority Queue 1 = ";
    print(pq1);
    cout << "Priority Queue 2 = ";
    print(pq2);
    return 0;
}

// This code is contributed by Susobhan Akhuli

Output

Before swapping:-
Priority Queue 1 = 4 3 2 1 
Priority Queue 2 = 9 7 5 3 

After swapping:-
Priority Queue 1 = 9 7 5 3 
Priority Queue 2 = 4 3 2 1 

Refer end for complexity analysis.

5. To emplace a new element into the priority queue container

Emplace() function is used to insert a new element into the priority queue container, the new element is added to the priority queue according to its priority. It is similar to push operation. The difference is that emplace() operation saves unnecessary copy of the object.

Below is the C++ program to emplace a new element into the priority queue container:

C++

// CPP program to illustrate
// Implementation of emplace() function

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

int main()
{
    priority_queue<int> pq;
    pq.emplace(1);
    pq.emplace(2);
    pq.emplace(3);
    pq.emplace(4);
    pq.emplace(5);
    pq.emplace(6);
    // Priority queue becomes 1, 2, 3, 4, 5, 6

    // Printing the priority queue
    cout << "Priority Queue = ";
    while (!pq.empty()) {
        cout << pq.top() << " ";
        pq.pop();
    }

    return 0;
}

// This code is contributed by Susobhan Akhuli

Output

Priority Queue = 6 5 4 3 2 1 

Refer end for complexity analysis.

6. To represent the type of object stored as an element in a priority_queue

The priority_queue :: value_type method is a built-in function in C++ STL which represents the type of object stored as an element in a priority_queue. It acts as a synonym for the template parameter.

Syntax: 

priority_queue::value_type variable_name

Below is the C++ program to represent the type of object stored as an element in a priority_queue:

C++

// C++ program to illustrate the
// priority_queue :: value_type function

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

// Driver code
int main()
{
    // declare integer value_type for priority queue
    priority_queue<int>::value_type AnInt;

    // declare string value_type for priority queue
    priority_queue<string>::value_type AString;

    // Declares priority_queues
    priority_queue<int> q1;
    priority_queue<string> q2;

    // Here AnInt acts as a variable of int data type
    AnInt = 20;
    cout << "The value_type is AnInt = " << AnInt << endl;
    q1.push(AnInt);
    AnInt = 30;
    q1.push(AnInt);
    cout << "Top element of the integer priority_queue is: "
         << q1.top() << endl;

    // here AString acts as a variable of string data type
    AString = "geek";
    cout << endl
         << "The value_type is AString = " << AString
         << endl;
    q2.push(AString);
    AString = "for";
    q2.push(AString);
    AString = "geeks";
    q2.push(AString);

    cout << "Top element of the string priority_queue is: "
         << q2.top() << endl;

    return 0;
}

// This code is contributed by Susobhan Akhuli

Output

The value_type is AnInt = 20
Top element of the integer priority_queue is: 30

The value_type is AString = geek
Top element of the string priority_queue is: geeks

Refer end for complexity analysis.

Complexities Of All The Operations:

Methods	Time Complexity	Auxiliary Space
priority_queue::empty()	O(1)	O(1)
priority_queue::size()	O(1)	O(1)
priority_queue::top()	O(1)	O(1)
priority_queue::push()	O(logN)	O(1)
priority_queue::pop()	O(logN)	O(1)
priority_queue::swap()	O(1)	O(N)
priority_queue::emplace()	O(logN)	O(1)
priority_queue value_type	O(1)	O(1)