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In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order.
• Computational complexity
• Memory usage
Evaluation of the algorithm:
• Quicksort• Heapsort• Shell sort• Bubble sort• Merge sort• Insertion sort• Selection sort
……
many algorithms
Quicksort was invented by Sir Charles Antony Richard Hoare in 1962.
4 8 1 6 5
PIVOT
We have an unsorted array of five elements.
Left pointer Right pointer
4
4 8 1 6 5
PIVOT
We choose one element, pivot element. Let it be most left element.
8 1 6 5
4Now we go to the right pointer. It’s expected that the element must be higher the pivot and it is, so the right pointer move left.
8 1 6 5
4It’s expected that the element must be higher than the pivot element and it is, so the right pointer move one position left.
1 8 1 6 5
4Again, It’s expected that the element must be higher than the pivot element but it’s not, 4 higher than 1, so that element move to the left pointer.
Left pointer moves one position right.
1 8 8 6 5
4Now it’s expected that the element must be lower than the pivot, but it’s not, 8>4, so the element move to the position of the right pointer.
Right pointer moves left.
PIVOT
1 4 8 6 5
4The position where pointers match is the position the pivot element.
PIVOT
1 4 8 6 5
III
Now we have two groups. If a group consist of less than two elements it’s taught sorted (on it’s right place).
1
PIVOT
1 4 8 6 5
Then we start the same procedure for the rest groups.
1
8PIVO
T
1 4 8 6 5
We choose pivot element, let it be most left element. Then we move to the right pointer.
1
8
1 4 5 6 5
It’s is expected that the element must be higher than the pivot, but it is not, so the element move to the left pointer.
1
left pointer moves right.
8
1 4 5 6
Now it is expected that the elemenet must be lower than the pivot and it is, so the left pointer moves right.
1
PIVOT8
1 4 5 6 8
We found the position of our pivot as the pointers matched.
1
PIVOT8
1 4 5 6 8
We found the position of our pivot as the pointers matched. “8” on it’s right place!
1
PIVOT
1 4 5 6 8
We have a group of two elements, so we have to run the same procedure once again.
1
5PIVO
T
1 4 5 6 8
Let’s watch it without comments.
1
PIVOT5
1 4 5 6 81
1 4 5 6 81
The array has been sorted!
Donald L. Shell is a retired American computer scientist who designed the Shell sort sorting algorithm.
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3 6 7 9 8 4
We have an unsorted array of seven elements.
7 div 2 = 3
Array’s length
These elements will be compared.
1
1319
First pass
3 6 79 8 41
First pass
1 6 7 3 8 4 9
Has been finished!
7 div 2 = 3 div 2 = 1
Second pass
1 6 7 3 8 4 9
These elements will be compared.
467448
63
73
1673849
Second pass
1 3 4 6 7 8 9
has been finished!
The array has been sorted!
Heapsort is a comparison-based sorting algorithm to create a sorted array (or list), and is part of the selection sort family.
4 8 1 6 5 0 74
8
488
4 1
64
6
46
5 0 71
7
17
8
6 7
4 5 0 1
8 6 7 4 5 0 11
81
1
70
70
0
6
5
0
0 65 00
605
04
0
5 0040
507 1060504 04
0
1000
411
6 7
8
1
7
05
6
04
514 04
0
The array has been sorted!
A bubble sort, a sorting algorithm that continuously steps through a list, swapping items until they appear in the correct order.
Bubble sort
Literature:
• Thimas H. Cormen; Charles E. Leiserson; Ronald L. Rivest; Clifford Stein. Introduction to Algorithms (2nd ed.) The MIT Press. ISBN 0-07-013151-1.• Shell D.L.. A high-speed sorting procedure// Communications of the ACM. — 2. — (1959) (7): 30–32. DOI:10.1145/368370.368387.• http://en.wikipedia.org/wiki/Sorting_algorithm• http://en.wikipedia.org/wiki/Heapsort• http://en.wikipedia.org/wiki/Bubble_sort• http://en.wikipedia.org/wiki/Quicksort• http://en.wikipedia.org/wiki/Shell_sort• www.zutopedia.com
Yaroslav [email protected]
