Sorting algorithms
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The document discusses various sorting algorithms. It describes how sorting algorithms arrange elements of a list in a certain order. Efficient sorting is important as a subroutine for algorithms that require sorted input, such as search and merge algorithms. Common sorting algorithms covered include insertion sort, selection sort, bubble sort, merge sort, and quicksort. Quicksort is highlighted as an efficient divide and conquer algorithm that recursively partitions elements around a pivot point.
Sorting algorithms
- 1. Sorting Algorithms Trupti Agrawal 1
- 2. Sorting Algorithms • A sorting algorithm is an algorithm that puts elements of a list in a certain order. • Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) which require input data to be in sorted lists Trupti Agrawal 2
- 3. Why Sorting? “When in doubt, sort” – one of the principles of algorithm design. Sorting used as a subroutine in many of the algorithms: Searching in databases: we can do binary search on sorted data A large number of computer graphics and computational geometry problems Closest pair, element uniqueness, frequency distribution Trupti Agrawal 3
- 4. Why Sorting? (2) A large number of algorithms developed representing different algorithm design techniques. A lower bound for sorting W(n log n) is used to prove lower bounds of other problems Trupti Agrawal 4
- 5. Sorting Algorithms so far Insertion sort, selection sort, bubble sort Worst-case running time Q(n2); in-place Merge sort Worst-case running time Q(n log n); but requires additional memory Trupti Agrawal 5
- 6. Insertion sort • Card players all know how to sort … – First card is already sorted – With all the rest, Scan back from the end until you find the first card larger than the new one, Move all the lower ones up one slot insert it Q 2 9 A K 10 J 2 2 9 Trupti Agrawal 6
- 7. Insertion Sort To insert 12, we need to make room for it by moving first 36 and then 24. Trupti Agrawal 7
- 8. 8 Insertion Sort Trupti Agrawal
- 9. Insertion Sort Trupti Agrawal 9
- 10. Insertion Sort input array 5 2 4 6 1 3 at each iteration, the array is divided in two sub-arrays: left sub-array right sub-array sorted unsorted Trupti Agrawal 10
- 11. Insertion Sort Trupti Agrawal 11
- 12. Insertion Sort - Summary • Advantages – Good running time for “almost sorted” arrays Q(n) • Disadvantages – Q(n2) running time in worst and average case – n2/2 comparisons and exchanges Trupti Agrawal 12
- 13. Selection Sort • Idea: – Find the smallest element in the array – Exchange it with the element in the first position – Find the second smallest element and exchange it with the element in the second position – Continue until the array is sorted • Disadvantage: – Running time depends only slightly on the amount of order in the file Trupti Agrawal 13
- 14. Example-Selection Sort 8 4 6 9 2 3 1 1 4 6 9 2 3 8 1 2 6 9 4 3 8 1 2 3 9 4 6 8 1 2 3 4 9 6 8 1 2 3 4 6 9 8 1 2 3 4 6 8 9 1 2 3 4 6 8 9 Trupti Agrawal 14
- 15. Bubble Sort • Idea: – Repeatedly pass through the array – Swaps adjacent elements that are out of order i 1 2 3 n 8 4 6 9 2 3 1 j • Easier to implement, but slower than Insertion sort Trupti Agrawal 15
- 16. Example - Bubble Sort Trupti Agrawal 16
- 17. Quicksort Efficient sorting algorithm Discovered by C.A.R. Hoare Example of Divide and Conquer algorithm Two phases Partition phase Divides the work into half Sort phase Conquers the halves! Trupti Agrawal 17
- 18. Quicksort Partition / Divide Choose a pivot Find the position for the pivot so that all elements to the left are less all elements to the right are greater < pivot pivot > pivot Trupti Agrawal 18
- 19. Quicksort Conquer Apply the same algorithm to each half < pivot > pivot < p’ p’ > p’ pivot < p” p” > p” Trupti Agrawal 19
- 20. Quicksort - Example Trupti Agrawal 20
- 21. Review of Algorithms Selection Sort An algorithm which orders items by repeatedly looking through remaining items to find the least one and moving it to a final location Bubble Sort Sort by comparing each adjacent pair of items in a list in turn, swapping the items if necessary, and repeating the pass through the list until no swaps are done Insertion Sort Sort by repeatedly taking the next item and inserting it into the final data structure in its proper order with respect to items already inserted. Merge Sort An algorithm which splits the items to be sorted into two groups, recursively sorts each group, and merges them into a final, sorted sequence Quick Sort An in-place sort algorithm that uses the divide and conquer paradigm. It picks an element from the array (the pivot), partitions the remaining elements into those greater than and less than this pivot, and recursively sorts the partitions. Trupti Agrawal 21
- 22. THANK YOU….. !!! Trupti Agrawal 22