Data Structures | Heap | Question 1

What is the time complexity of Build Heap operation. Build Heap is used to build a max(or min) binary heap from a given array. Build Heap is used in Heap Sort as a first step for sorting.
(A) O(nLogn)
(B) O(n^2)
(C) O(Logn)
(D) O(n)

Answer: (D)

Explanation: Following is algorithm for building a Heap of an input array A.

    heapsize := size(A); 
    for i := floor(heapsize/2) downto 1 
        do HEAPIFY(A, i); 
    end for 

Although the worst case complexity looks like O(nLogn), upper bound of time complexity is O(n). See following links for the proof of time complexity.

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