# 8-Heaps - Heaps Definition Two methods of construction...

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Heaps Definition Two methods of construction O(nlog n) and O(n) O(n) proof: A node at depth i can move down at most d-i levels before reaching the bottom in a tree of depth d. There are at most 2 i-1 nodes at depth i. So the total number of comparisons (and exchanges) cannot exceed ∑ 2 i-1 (d-i) i=1,d-1 which is ∑ 2 d-j-1 j where j=d-i or 2 d-1 ∑ (1/2) j j j=1,d-1
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Unformatted text preview: j=1,d-1 Now, ∑ (1/2) j j < ∑ (1/2) j j which is less than 2. j=1,m j=1,∞ So, the total time is less than 2 d but 2 d-1 < n < 2 d-1, so 2 d < 2 n. Heapsort Sequential representation of binary trees versus linked - dependence on shape and operations Priority Queues . Heaps versus arrays or linked lists sorted and unsorted. ....
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• Fall '16
• James Korsh
• Binary heap, Heaps Definition

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