Sorting Algorithm
Download as ODP, PDF3 likes375 views
The document discusses several sorting algorithms: insertion sort, selection sort, bubble sort, and merge sort. It provides descriptions of how each algorithm works and comparisons of their time complexities. For insertion sort, it notes its advantage for nearly sorted data but quadratic worst-case time. Selection sort runs in quadratic time with little advantage for ordered data. Bubble sort is easy to implement but slower than insertion sort. Merge sort works by recursively dividing the array into halves and then merging the sorted halves.
![Bubble Sort
Alg.: BUBBLESORT(A)
for i ← 1 to length[A]
do for j ← length[A] downto i + 1
do if A[j] < A[j -1]
then exchange A[j] ↔ A[j-1]
1329648
i = 1 j
i](https://image.slidesharecdn.com/algorithm-161124202203/85/Sorting-Algorithm-16-320.jpg)
Sorting Algorithm
- 2. GROUP MEMBERS Mohd. Iftiar Hossain – 152-15-5605 Md.Maruf Hasan – 152-15-5604 Md. Abu Shaik – 152-15-5612 Md. Abid Islam Riton – 152-15-5806 Trupti Agrawal
- 3. CONTENT INSRETION SORT SELECTION SORT BUBBLE SORT MERGE SORT
- 4. • 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 Sorting Algorithms
- 5. 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 p Q o 2 o 9 m A m K m 10 n J n 2 m 2 o 9 ‚ ƒ „
- 6. To insert 12, we need to make room for it by moving first 36 and then 24. Insertion Sort 6 10 24 12 36
- 7. 6 10 24 Insertion Sort 36 12
- 8. Insertion Sort 6 10 24 36 12
- 9. Insertion Sort 5 2 4 6 1 3 input array left sub-array right sub-array at each iteration, the array is divided in two sub-arrays: sorted unsorted
- 10. Insertion Sort
- 11. Insertion Sort - Summary • Advantages – Good running time for “almost sorted” arrays Θ(n) • Disadvantages – Θ(n2 ) running time in worst and average case – ≈ n2 /2 comparisons and exchanges
- 12. 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
- 14. Bubble Sort • Idea: – Repeatedly pass through the array – Swaps adjacent elements that are out of order • Easier to implement, but slower than Insertion sort 1 2 3 n i 1329648 j
- 15. Example - Bubble Sort
- 16. Bubble Sort Alg.: BUBBLESORT(A) for i ← 1 to length[A] do for j ← length[A] downto i + 1 do if A[j] < A[j -1] then exchange A[j] ↔ A[j-1] 1329648 i = 1 j i
- 17. Merge Sort Approach • Divide – Divide the n-element sequence to be sorted into two subsequences of n/2 elements each • Conquer – Sort the subsequences recursively using merge sort – When the size of the sequences is 1 there is nothing more to do • Combine – Merge the two sorted subsequences