Sorting Algorithms

Sorting Algorithms

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  Eng: Mohammed Hussein1 Republicof Yemen THAMAR UNIVERSITY Faculty of Computer Science& Information System
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  Outlines: Eng: Mohammed Hussein2 There are some classes of Sorting Algorithms:  O(n² ):  Bubble Sort  Insertion Sort  Selection Sort
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  Bubble sort  Bubblesort, 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. 3 Eng: Mohammed Hussein
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  Bubble sort code Eng:Mohammed Hussein4
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  Bubble sort  Sortingis 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. 5 Eng: Mohammed Hussein
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  Bubble sort example 6Eng: Mohammed Hussein
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  Insertion sort  Theinsertion 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. 7 Eng: Mohammed Hussein Insertion sort is a simple sorting algorithm: a comparison sort in which the sorted array (or list) is built one entry at a time.
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  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.8 Eng: Mohammed Hussein
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  Insertion sort  Itrequires 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. 9 Eng: Mohammed Hussein
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  Insertion sort example 10Eng: Mohammed Hussein
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  Selection sort  Incomputer 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. 11 Eng: Mohammed Hussein
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  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). 12 Eng: Mohammed Hussein
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  Selection sort example 13Eng: Mohammed Hussein
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  Reference  Wikipedia, thefree encyclopedia  XoaX.net 14 Eng: Mohammed Hussein