procedure heapify(arr, n, i):

    largest = i

    left = 2 * i + 1

    right = 2 * i + 2

​

    if left < n and arr[left] > arr[largest]:

        largest = left

​

    if right < n and arr[right] > arr[largest]:

        largest = right

​

    if largest != i:

        swap(arr[i], arr[largest])

        heapify(arr, n, largest)

​

procedure heapSort(arr):

    n = length(arr)

​

    // Build a max-heap by heapifying each non-leaf node

    for i from n/2 - 1 down to 0:

        heapify(arr, n, i)

​

    // Extract elements from the heap one by one

    for i from n - 1 down to 1:

        swap(arr[0], arr[i])

        heapify(arr, i, 0)