Lecture 5a Sorting

Merge sort (divide and conquer)

1. divide
2. recur
3. conquer

uses recursion to make it work

1. first while loop will check which element is the smaller one
2. removes the element and moves it to the back of S if so
3. keeps iterating with same procedure
4. if first while loop ends, continues to the second while loop with same steps
5. keep repeating same steps until all elements are put to S in order

If 7 element exist, why 4 on the left, 3 on the right

mid = (0 + 6) / 2 = 3
MergeSort(S, 0, 3) // has 4 elements
MergeSort(S, 4, 6) // has 3 elements

generally if there’s odd number of elements, the extra one in the middle will be put to the left

Analysis of merge sort

• height h of the merge sort tree is 0(log n)
• total running time of merge sort is 0(n log n)
• overall amount or work done at the nodes of depth i is 0(n)

depth	seqs	size
0	1	n
1	2	n/2
i	$2^i$	$n/2^i$

Bucket sort

Analysis

• phase 1 takes 0(n) time
• phase 2 takes 0(n + N) time

$n$ is the number of items needs to be inserted N is the number of times to iterate the entire list

Bucket sort takes 0(n + N) time

Radix sort

radix sort runs in time 0(d(n+1))

sorting in sequence of 4-bit integers its doing bucket sort in 4 bit integer lmao

Selection Algorithm

Quick Select

smallest, k = 0 2nd smallest, k = 1 5th smallest, k = 4

77 99 22 66 55 44 11 88 33_ 22 11 33* 77 99 66 55 44 88_ pi= 2 < k k > pi

22 11 33* 77 66 55 44_ 88* 99 pi= 7 k < pi

22 1 133* 44* 77 66 55_ 44 88* 99 pi= 3 k > pi

22 11 33* 44* 55* 77 66 88* 99 pi = 4 = k, found 5th smallest = 55

0(n)