Heap sort is a comparison based sorting technique based on Binary Heap data structure. It is similar to selection sort where we first find the maximum element and place the maximum element at the end. We repeat the same process for remaining element.

algorithm:

1. Build a max heap from the input data.
2. now the largest element is at the root of the heap. Replace it with the last item of the heap followed by reducing the size of heap by 1. Finally, heapify the root of tree.
3. Repeat above steps while size of heap is greater than 1.

`// To heapify a subtree rooted with node i which is// an index in arr[]. n is size of heapvoid heapify( arr[], n, i){    largest = i // Initialize largest as root    l = 2*i + 1 // left = 2*i + 1    r = 2*i + 2 // right = 2*i + 2    // If left child is larger than root    if (l < n && arr[l] > arr[largest])        largest = l    // If right child is larger than largest so far    if (r < n && arr[r] > arr[largest])        largest = r    // If largest is not root    if (largest != i)    {        swap(arr[i], arr[largest])        // Recursively heapify the affected sub-tree        heapify(arr, n, largest)    }}// main function to do heap sortvoid heapSort( arr[], n){    // Build heap (rearrange array)    for (int i = n / 2 - 1; i >= 0; i--)        heapify(arr, n, i)    // One by one extract an element from heap    for (int i=n-1; i>=0; i--)    {        // Move current root to end        swap(arr[0], arr[i])        // call max heapify on the reduced heap        heapify(arr, i, 0)    }}`

we can even using priority queues:

1)take a min heap insert all the elements in the heap

2)now just keep poping the top elements from the heap

```void heapSort( arr[], n)
{
priority_queue< int, vector<int>, greater<int> > pq(arr,arr+k); //min heap

while(!pq.empty())
{
cout<<pq.top();
pq.pop();
}

}
```

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