[Thomas_H._Cormen]_Algorithms_unlocked(BookZZ.org)

Chapter 3: Algorithms for Sorting and Searching 33
whose name comes first alphabetically. Now go through the bookshelf,
left to right, starting with the book in slot 2 to find the book in slots 2
through n whose author name comes earliest in the alphabet. Suppose
that it’s by Jane Austen. Swap the location of this book with the book
in slot 2, so that now slots 1 and 2 have the first and second books in the
overall alphabetical ordering. Then do the same for slot 3, and so on.
Once we have put the correct book into slot n 1 (perhaps it’s by H. G.
Wells), we are done, because there’s only one book left (say, a book by
Oscar Wilde), and it’s in slot n where it belongs.
To turn this approach into a computer algorithm, change the bookshelf
to an array and the books to array elements. Here’s the result:
Procedure SELECTION-SORT.A; n/
Inputs:
A: an array.
n: the number of elements in A to sort.
Result: The elements of A are sorted into nondecreasing order.
1. For i D 1 to n 1:
A. Set smallest to the index of the smallest element in the
subarray AŒi : : n.
B. Swap AŒi with AŒsmallest.
Finding the smallest element in AŒi : : n is a variant on linear search.
First declare AŒi to be the smallest element seen in the subarray so far,
and then go through the rest of the subarray, updating the index of the
smallest element every time we find an element less than the current
smallest. Here’s the refined procedure:
Procedure SELECTION-SORT.A; n/
Inputs and Result: Same as before.
1. For i D 1 to n 1:
A. Set smallest to i.
B. For j D i C 1 to n:
i. If AŒj < AŒsmallest, then set smallest to j .
C. Swap AŒi with AŒsmallest.