April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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418 Design and Analysis of Algorithms
time complexity of heapsort is T(n) ∈ O(n log(n)). The algorithm is optimal, since the lower bound of any
sorting algorithm based on comparison and exchange is attained.
Suppose we use such a heap for a priority queue. Then extracting the head of the queue will be very fast,
just take the root node. This will result in an increase of potential, because several nodes need realocation.
The number of relocations will be limited to the height of the tree and thus we can use the height as the
potential function.
Implementation
A complete binary tree with n vertices and vertex labeling can be stored effi ciently in an array. The C language
program is available as fi le
heapsort.c. Note that in the C implementation, ...
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