GATE | GATE-CS-2015 (Set 2) | Question 27

Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is
(A) Ω(logn)
(B) Ω(n)
(C) Ω(nlogn)
(D) Ω(n²)

Answer: (A)
Explanation: The answer to this question is simply max-heapify function. Time complexity of max-heapify is O(Log n) as it recurses at most through height of heap.

// A recursive method to heapify a subtree with root at given index
// This method assumes that the subtrees are already heapified
void MinHeap::MaxHeapify(int i)
{
    int l = left(i);
    int r = right(i);
    int largest = i;
    if (l < heap_size && harr[l] < harr[i])
        largest = l;
    if (r < heap_size && harr[r] < harr[smallest])
        largest = r;
    if (largest != i)
    {
        swap(&harr[i], &harr[largest]);
        MinHeapify(largest);
    }
}

See Binary Heap for details.
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