Sorting Programs -

Fruit flies of algorithm analysis

Min (or max) selection sort

Simple insertion sort

Bubble sort

Quicksort

Heapsort

Mergesort

Bucket sort

Radix sort

O(N²)

In-place

(Insertion or bubble sort are equivalent.)

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Other Sorting Options...

Note:

We discuss sorting as if we were just sorting numbers.

Often the numbers are just a part (called the "key") of a more complex object or "record".

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Some Ways to Speed Up

- Divide & Conquer

(cleave rather than whittle)

- Data Structuring

(tree rather than list)

- "Digital" Representations

exploit linear addressing princ.

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Bucket Sort

Use when applicable:

Small range of integer values (or equivalent).

O(N) time to sort N items

Extra space is required ("buckets")

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Radix Sort

An alternated to bucket sort for larger (but not too large) range of integers.

Effectively a multi-pass bucket sort

O(N) time

Extra space is required

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Quicksort

Prototypical divide & conquer

In-place (no extra space)

O(N logN) "average" time

O(N²) worst case time

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Quicksort Operation

O(N logN) "best" case

O(N²) worst case

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HeapSort

O(N logN) without qualification

In-Place

Use tree to great advantage

Non-recursive

Based on "Peter Principle"

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2 meanings of "heap" in CS:

• Heap for storage allocation (dynamic)
• Heap for sorting, a form of "priority queue"

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Heap for Storage Allocation (Digression)

Typical memory layout

Calls to new find free space large enough.

C++: delete releases space

Java: space released when not accessible