The.Algorithm.Design.Manual.Springer-Verlag.1998

Lecture 4 - heapsort
Listen To Part 4-8
A simple sorting algorithm is selection sort.
Selection Sort
Sweep through all the elements to find the smallest item, then the smallest remaining item, etc. until the
array is sorted.
Selection-sort(A)
swap(A[i],A[j])
for i = 1 to n
for j = i+1 to n
if (A[j] < A[i]) then
It is clear this algorithm must be correct from an inductive argument, since the ith element is in its correct
position.
It is clear that this algorithm takes time.
It is clear that the analysis of this algorithm cannot be improved because there will be n/2 iterations
which will require at least n/2 comparisons each, so at least comparisons will be made. More careful
analysis doubles this.
Thus selection sort runs in time.
Listen To Part 4-9
Binary Heaps
A binary heap is defined to be a binary tree with a key in each node such that:
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