alg0183 algorithms & data structures lecture 12 taxonomies of sorting algorithms 8/25/20091...
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ALG0183 Algorithms & Data Structures by Dr Andy Brooks
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ALG0183 Algorithms & Data Structures
Lecture 12Taxonomies of Sorting Algorithms
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taxonomy/flokkunarkerfi
Sorting Algorithms @ YouTubehttp://www.youtube.com/watch?v=INHF_5RIxTE
ALG0183 Algorithms & Data Structures by Dr Andy Brooks
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case study article
“An inverted taxonomy of sorting algorithms”Susan M. MerritCommunications of the ACM, Volume 28, Number 1, (1985), pp 96-99
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Insertion Sort
• Items are considered one at a time. Each new item is inserted into the appropriate place relative to the previously sorted items.
• Having a sorted subarray A[1 . . j -1], we insert the single element A[j] into its proper place, yielding the sorted subarray A[1 . . j].
• Insertion sort is used when sorting a hand of cards.
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Traditional Taxonomy due to D.E.Knuth
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Exchange Sort
• If two elements are out of order, they are exchanged. The process repeats until all possible comparisons have been made or until no more exchanges are possible.
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Traditional Taxonomy due to D.E.Knuth
if a[j] > a[j+1] then swap(a[j],a[j+1])
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Selection Sort
• The smallest (largest) item is located and separated from the rest. The next smallest (largest) is selected and so on.
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Traditional Taxonomy due to D.E.Knuth
In the example in the video, additional space is used to perform the sort.
Sorting can be done in-place by swapping the least remaining item with the item in the next position to be filled.
A sorting algorithm is described as in-place if the sorted items occupy the same storage as the original ones.
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The focus of Insertion Sort, Exchange Sort, and Selection Sort.
• “The focus is on an operation on an individual element or pair of elements.” Merrill
• “The method of choosing the individual element or elements is the key to the algorithm.” Merrill
• “The algorithm is built by constructing an iteration about the focal operation.” Merrill
• The focus of the traditional taxonomy is low-level and bottom-up.
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Traditional Taxonomy due to D.E.Knuth
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Merge Sort• Two already sorted lists are merged into a single,
sorted list.
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Traditional Taxonomy due to D.E.Knuth
http://www.sparknotes.com/cs/recursion/examples/section3.rhtml
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Figure 3. The Traditional Taxonomy of Sorting Algorithms©ACM
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An Inverted Taxonomytop-down rather than bottom-up
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Sorting can be viewed as a three-step process:
1. Split the set S to be sorted into parts, say S1 and S2.2. Sort each part, giving S1´ and S2´.3. Join the parts to produce the sorted set S´.
The process has a split procedure and a join procedure.
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Figure 1. A Top-Down High-Level Sort Process ©ACM
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Figure 2. Merge Sort and Quicksort ©ACM
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easy
easy
hard
hard
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Insertion Sort and Selection Sort
• What if we do not split into equal-size parts?• Suppose set S2 has only one element, then merge sort collapses
into insertion sort, and quicksort collapses into selection sort.• Knuth recognised that merging a singleton sequence with an
arbitrary sequence is essentially insertion sort.– Neverthless he went ahead and placed these sorts into different
categories.• Several authors have recognised that quicksort´s worse-case
performance occurs when it degrades into selection sort by partitioning a singleton set at each split. – Yet quicksort and selection sort are in different categories in the
traditional taxonomy.
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singleton/einstaksmengi
ALG0183 Algorithms & Data Structures by Dr Andy Brooks
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Exchange Sorts
• Sinking sort can be seen as an in-place version of insertion sort.
• Bubble sort can be seen as an in-place version of selection sort.
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Sinking Sortfrom Remarks on “A Synthesis of Serving Sorting Algorithms” by John Darlington by David R. Barstow, Acta Informatica 13, 225-227 (1980) © Springer-Verlag
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Input to the right of the ^ and output to the left of the ^.
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Bubble Sortfrom Remarks on “A Synthesis of Serving Sorting Algorithms” by John Darlington by David R. Barstow, Acta Informatica 13, 225-227 (1980) © Springer-Verlag
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Input to the left of the ^ and output to the right of the ^.
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Figure 4. Inverted Taxonomy of Sorting Algorithms©ACM
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What about distributive sorting algorithms?
• Distributive sorting algorithms do not fit into the inverted taxonomy presented in Figure 4.
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Figure 6. A logical inverted taxonomy of sorting algorithmsPresented in an article with the same title.
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