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(n)

(D)

O(logn)

Answer: (C)
Explanation:

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

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

Although the worst-case complexity looks like O(N log N), upper bound of time complexity is O(n). See following links for the proof of time complexity. Time Complexity of building a heap.

Hence Option(C) is the correct answer.

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