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enhancement of sorting algorithm
- 1. An Enhancement of Major Sorting Algorithms Group 7 Roll No Akber Ali 1406 Assad Ali 1407 Qasim Ali 1425 Touseef Khadim 1427
- 2. Discuss Enhanced selection sort Enhanced bubble sort Selection sort Bubble sort Number of swaps Time complexity.
- 3. Enhanced Selection Sort Inserting an array of elements and sorting these elements in the same array (in-place) by finding the maximum element and exchanging it with the last element, and then decreasing the size of the array by one for next call. In fact, the Enhanced Selection Sort (ESS) algorithm is an enhancement to the SS algorithm in decreasing number of swap operations, making the algorithm to be data dependent, and in making it stable.
- 4. Procedures Inserting all elements of the array. Calling the “Enhanced Selection Sort” function with passing the array and its size as parameters. Finding the maximum element in the array. And swapping it with the last index of the same array. Decreasing the size of the array by one. Calling the “Enhanced Selection Sort” function recursively. The size of the array is decremented by one after each call of the “Enhanced Selection Sort” function. Operationally, the (size) after the first call became (size-1), and after the second call became (size-2), and so on
- 5. Pseudo code 1- If size > 1 then 2- var index, temp, max 3- index := size-1 4- max := array(index) 5- for a:= 0 to size-2 do 6- if array(a) ≥ max then 7- max := array(a) 8- index := a 9- end if 10- end for 11- if index ≠ size-1 then 12- temp := array(size-1) 13- array(size-1) := max 14- array(index) := temp 15- end if 16- size := size-1 17- return Enhanced Selection Sort (array , size) 18- else 19- return array 20- end if
- 6. Analysis a) In the best-case scenario; if the input array is already sorted (ascending order), then there is no need to make swapping, since each element is in the correct place. b) In the average-case scenario; if the input array is sorted in reverse (descending order), then the total number of swapping operations is: floor of (n/2). Since swapping the maximum value with the last element means that the maximum and the minimum values are in the correct places. For example, if we have a descending sorted array as follows: Then the algorithm will swap the first element (max) with the last element, as follows: Since the last element before swapping was the minimum value, it is after swapping got in the correct place and cannot be the maximum value in any of the next comparisons. In the next comparison, the second element now is the maximum value and it will be swapped with the fourth (size-1)the element. The array now is sorted and the algorithm required two swap operations to sort the input array of five elements. That means, the swapping operations that are needed to sort a descending sorted array is floor of (n/2). c) In the worst case; if the input array is unsorted neither ascending nor descending, then the required swapping operations are approximately operations.
- 7. Enhanced Bubble Sort The proposed algorithm is considered as an enhancement to the original Bubble sort algorithm and it works as follows: Inserting an array of elements and sorting these elements in the same array (in place) by finding the minimum and the maximum elements and exchanging The minimum with the first element and the maximum with the last element, and then decreasing the size of the array by two for next call
- 8. Procedures 1. Inserting all elements of the array. 2. Defining and initializing two variables, (firstindex = 0) and (lastindex = size-1). 3. Calling the "Enhanced Bubble Sort" function with passing the array, its size, firstindex, and lastindex as parameters of the function. 4. In the "Enhanced Bubble Sort" function, the operation now is to find the maximum and the minimum elementsand saving the index value of the max of the array in the variable maxcounter, and the index value of the minin the variable mincounter. 5. Put the max in the lastindex and min in the firstindex of the array without losing the last values of the first index and the last index of the original array. 6. Decreasing the value of lastindex by one and increasing the value of firstindex by one. Operationally, the size of the array after the first call became (size-2), and after the second call it actually became (size-4), and soon. 7. Calling the "Enhanced Bubble Sort " array recursively while the size of the array is greater than one (size>1). Then returning the sorted array.
- 9. Pseudocode
- 10. Case Study This section presents a real-world case study to sort students of Al al-Bayt University in Jordan by the university number (students IDs) in ascending order. In this case study, BS, SS, shell sort, enhanced shell sort, ESS, and EBS algorithms are applied with 12500 as total number of students.
- 12. Conclusions In this paper, two new sorting algorithms are presented. ESS has complexity, but it is faster than SS, especially if the input array is stored in secondary memory, since it performs less number of swap operations. EBS is definitely faster than BSS can be specially implemented to be stable. Furthermore, the proposed algorithms are compared with some recent sorting algorithms; shell sort and enhanced shell sort. These algorithms are applied on a real-world case study of sorting a database of (12500) records and the results showed that the EBS also increases the efficiency of both shell sort and enhanced shell sort algorithms.