Algorithms Analysis

Eng: Mohammed Hussein1

Republic of Yemen

THAMAR UNIVERSITY

Faculty of Computer Science&

Information System

Lecturer, and Researcher at Thamar University

By Eng: Mohammed Hussein

Outlines

Analysis of running time

O(n² ):

Bubble Sort

Insertion Sort

Selection Sort

2 Eng: Mohammed Hussein

Sorting Algorithms:


There are some classes of Sorting Algorithms:

O(n² ):

Bubble Sort

Insertion Sort

Selection Sort

Shell Sort

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.


Bubble sort code


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.


Bubble sort example


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.


Insertion sort is a simple sorting

algorithm: a comparison sort in which

the sorted array (or list) is built one

entry at a time.

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

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.


Insertion sort example


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.


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).


Selection sort example


Reference

Wikipedia, the free encyclopedia

XoaX.net


Algorithms Analysis

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