Analysis of running time O(n²): Bubble Sort Insertion Sort Selection Sort

1. Eng: Mohammed Hussein1
Republic of Yemen
THAMAR UNIVERSITY
Faculty of Computer Science&
Information System
Lecturer, and Researcher atThamar University
By Eng: Mohammed Hussein

2. Outlines
Analysis of running time
 O(n² ):
 Bubble Sort
 Insertion Sort
 Selection Sort
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3. Sorting Algorithms:
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 There are some classes of Sorting Algorithms:
 O(n² ):
 Bubble Sort
 Insertion Sort
 Selection Sort
 Shell Sort

4. Bubble sort
 Bubble sort, is a simple sorting algorithm that works by repeatedly stepping through the
list to be sorted, comparing each pair of adjacent items and swapping them if they are in
the wrong order.
 The pass through the list is repeated until no swaps are needed, which indicates that the list
is sorted.
 The algorithm gets its name from the way smaller elements "bubble" to the top of the list.
Because it only uses comparisons to operate on elements, it is a comparison sort.Although
the algorithm is simple, some other algorithms are more efficient for sorting large lists.
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5. Bubble sort code
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6. Bubble sort
 Sorting is one of the most common operations in programming;
 it is used everywhere from email programs to databases, wherever
there is a list of data.
 The bubble sort algorithm applied to this list of four names can be
illustrated graphically in a sequence like this:
 The dark gray represents a comparison and the white represents a
swap.
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7. Bubble sort example
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8. Insertion sort
 The insertion sort provides several advantages:
1. Simple implementation.
2. Efficient for small data sets.
3. Adaptive for data sets that are already substantially sorted: the time complexity
is O(n + d), where d is the number of inversions.
4. More efficient in practice than most other simple quadratic (i.e., O(n2))
algorithms such as selection sort or bubble sort;
5. Stable; i.e., does not change the relative order of elements with equal keys.
6. In-place; i.e., only requires a constant amount O(1) of additional memory
space.
7. Online; i.e., can sort a list as it receives it.
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Insertion sort is a simple sorting
algorithm: a comparison sort in which
the sorted array (or list) is built one
entry at a time.

9. Insertion sort code
 The first four elements have already
been sorted.The fifth element, 7, is
being inserted into the sorted list.
After the next comparison and
swap, the array looks like this.
 Continuing with the insertion of
this element.We make comparisons
with each of the elements in front
of the 7 and swap them if they are
out of order. In this particular
insertion, the 7 moves all the way
to the front of the array. if the 7 were larger than some of the other
elements we would make fewer comparisons and
swaps; that is how the insertion sort gains a speed
advantage over the bubble sort.9 Eng: Mohammed Hussein

10. Insertion sort
 It requires fewer comparisons than bubble sort, unless the list is backward.
 If the array is already sorted, it only requires one comparison per element
for a presorted list, so we only need n comparison.
 The convenient concept of this algorithm, we can insert new elements at
any time with a sorted array, which make this algorithm used in practice.
 The insertion sort compares adjacent elements and swaps them if they are
out of order. However, the insertion sort gains some added efficiency by
maintaining a sorted list that we insert elements into.
 So, it is much less efficient on large lists than more advanced algorithms
such as quick sort, heap sort, or merge sort.
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11. Insertion sort example
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12. Selection sort
 In computer science, a Selection sort is a sorting algorithm,
specifically an in-place comparison sort.
 It has O(n2) time complexity, making it inefficient on large lists, and
generally performs worse than the similar insertion sort.
 Selection sort is noted for its simplicity, and also has performance
advantages over more complicated algorithms in certain situations,
particularly where auxiliary memory is limited.
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13. Selection sort code
 The algorithm works as follows:
 Find the minimum value in the list
 Swap it with the value in the first
position.
 Repeat the steps above for the
remainder of the list (starting at the
second position and advancing each
time).
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14. Selection sort example
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15. Reference
 Wikipedia, the free encyclopedia
 XoaX.net
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