How to implement Min Heap using STL?

In C++ STL, there is priority_queue that can directly be used to implement Max Heap. In order to fully understand the code, make sure you are familiar with following concepts in C++ 

• Container Adaptors in STL
• Functors

See below example:

C++

// C++ program to show that priority_queue is by
// default a Max Heap
#include <bits/stdc++.h>
using namespace std;

// Driver code
int main ()
{
    // Creates a max heap
    priority_queue <int> pq;
    pq.push(5);
    pq.push(1);
    pq.push(10);
    pq.push(30);
    pq.push(20);

    // One by one extract items from max heap
    while (pq.empty() == false)
    {
        cout << pq.top() << " ";
        pq.pop();
    }

    return 0;
}

Output

30 20 10 5 1 

Since elements are printed in descending order, we have a max heap by default.

How to implement Min Heap?
priority_queue supports a constructor that requires two extra arguments to make it min-heap. 

priority_queue <Type, vector<Type>, ComparisonType > min_heap;

`The third parameter, ‘Comparison Type’ can either be a function or functor (aka function object) that must have bool as return-type and must have 2 arguments.

Below is an example for integers.

C++

// C++ program to use priority_queue to implement min heap
#include <bits/stdc++.h>
using namespace std;

// Driver code
int main ()
{
    // Creates a min heap
    priority_queue <int, vector<int>, greater<int> > pq;
    pq.push(5);
    pq.push(1);
    pq.push(10);
    pq.push(30);
    pq.push(20);

    // One by one extract items from min heap
    while (pq.empty() == false)
    {
        cout << pq.top() << " ";
        pq.pop();
    }

    return 0;
}

Output: 

1 5 10 20 30 

Another method for making min-heap using default priority_queue:

This is frequently used in Competitive Programming. We first multiply all elements with (-1). Then we create a max heap (max heap is the default for priority queue). When we access the data and want to print it we simply multiply those elements with (-1) again.

Below is the implementation of the above idea:

C++

// C++ Program to implement min heap
// using default priority_queue(max-heap)

#include <iostream>
#include <queue>
using namespace std;

int main()
{
    // data
    int arr[] = { 25, 7, 9, 15, 20, 36, 50 };

      // default priority_queue using max-heap
    priority_queue<int> pq;

      // size of the array
    int n = sizeof(arr) / sizeof(arr[0]);

    // multiply -1 with all elements while
    // inserting
    for (int i = 0; i < n; i++) {
        pq.push((-1) * arr[i]);
    }

    // multiply all elements with -1 while
    // retrieve the elements
    while (!pq.empty()) {
        cout << (pq.top()) * (-1) << " ";
        pq.pop();
    }

    return 0;
}

Output

7 9 15 20 25 36 50 

How to make a min-heap of user-defined class?

Let us consider below example where we build a min-heap of 2 D points ordered by X-axis.

C++

// C++ program to use priority_queue to implement Min Heap
// for user defined class
#include <bits/stdc++.h>
using namespace std;

// User defined class, Point
class Point
{
   int x;
   int y;
public:
   Point(int x, int y)
   {
      this->x = x;
      this->y = y;
   }
   int getX() const { return x; }
   int getY() const { return y; }
};

// To compare two points
class myComparator
{
public:
    int operator() (const Point& p1, const Point& p2)
    {
        return p1.getX() > p2.getX();
    }
};

// Driver code
int main ()
{
    // Creates a Min heap of points (order by x coordinate)
    priority_queue <Point, vector<Point>, myComparator > pq;

    // Insert points into the min heap
    pq.push(Point(10, 2));
    pq.push(Point(2, 1));
    pq.push(Point(1, 5));

    // One by one extract items from min heap
    while (pq.empty() == false)
    {
        Point p = pq.top();
        cout << "(" << p.getX() << ", " << p.getY() << ")";
        cout << endl;
        pq.pop();
    }

    return 0;
}

Output: 

(1, 5)
(2, 1)
(10, 2)

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