Heaps

Question

Why do we need a Build Heap procedure ?

if we want to build a heap, we will call max_heapify on root node and we will form a heap in O(log N) TC.

if we use build heap, it will take O(N) TC, what is the use im not getting ?

please explain.

Comments

without build heap , time complexity of heap sort is $O(nlogn)$

but with build heap TC= $O(n)$

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are we not able to build heap in one go, if we call max_heapify on root node which leads to O(log N) TC

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heapify and heap sort is different

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yes mam, im asking about max_heapify and build_heap

we are using max_heapify in build_heap. i want to know : by only using max_heapify(), are we not able to form a heap which satisfies heapify property ?

we will call max_heapify on root, and in one go we can form a heap in O(log N) rather than O(N) if build_heap is used ?