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Analysis of running time

O(n²):

Bubble Sort

Insertion Sort

Selection Sort

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- 1. Eng: Mohammed Hussein1Republic of YemenTHAMAR UNIVERSITYFaculty of Computer Science&Information SystemLecturer, and Researcher atThamar UniversityBy Eng: Mohammed Hussein
- 2. OutlinesAnalysis of running time O(n² ): Bubble Sort Insertion Sort Selection Sort2 Eng: Mohammed Hussein
- 3. Sorting Algorithms:Eng: Mohammed Hussein3 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 thelist to be sorted, comparing each pair of adjacent items and swapping them if they are inthe wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the listis 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.Althoughthe algorithm is simple, some other algorithms are more efficient for sorting large lists.4 Eng: Mohammed Hussein
- 5. Bubble sort codeEng: Mohammed Hussein5
- 6. Bubble sort Sorting is one of the most common operations in programming; it is used everywhere from email programs to databases, whereverthere is a list of data. The bubble sort algorithm applied to this list of four names can beillustrated graphically in a sequence like this: The dark gray represents a comparison and the white represents aswap.6 Eng: Mohammed Hussein
- 7. Bubble sort example7 Eng: Mohammed Hussein
- 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 complexityis 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 memoryspace.7. Online; i.e., can sort a list as it receives it.8 Eng: Mohammed HusseinInsertion sort is a simple sortingalgorithm: a comparison sort in whichthe sorted array (or list) is built oneentry at a time.
- 9. Insertion sort code The first four elements have alreadybeen sorted.The fifth element, 7, isbeing inserted into the sorted list.After the next comparison andswap, the array looks like this. Continuing with the insertion ofthis element.We make comparisonswith each of the elements in frontof the 7 and swap them if they areout of order. In this particularinsertion, the 7 moves all the wayto the front of the array. if the 7 were larger than some of the otherelements we would make fewer comparisons andswaps; that is how the insertion sort gains a speedadvantage 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 elementfor a presorted list, so we only need n comparison. The convenient concept of this algorithm, we can insert new elements atany time with a sorted array, which make this algorithm used in practice. The insertion sort compares adjacent elements and swaps them if they areout of order. However, the insertion sort gains some added efficiency bymaintaining a sorted list that we insert elements into. So, it is much less efficient on large lists than more advanced algorithmssuch as quick sort, heap sort, or merge sort.10 Eng: Mohammed Hussein
- 11. Insertion sort example11 Eng: Mohammed Hussein
- 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, andgenerally performs worse than the similar insertion sort. Selection sort is noted for its simplicity, and also has performanceadvantages over more complicated algorithms in certain situations,particularly where auxiliary memory is limited.12 Eng: Mohammed Hussein
- 13. Selection sort code The algorithm works as follows: Find the minimum value in the list Swap it with the value in the firstposition. Repeat the steps above for theremainder of the list (starting at thesecond position and advancing eachtime).13 Eng: Mohammed Hussein
- 14. Selection sort example14 Eng: Mohammed Hussein
- 15. Reference Wikipedia, the free encyclopedia XoaX.net15 Eng: Mohammed Hussein

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