Big O of Different
sorting Algorithm
Week 7
Sorting Algorithms
•Bubblesort
–Brute-force method of sorting
–Loop inside of a loop
•Mergesort
–Divide and conquer approach
–Recursively call, splitting in half
–Merge sorted halves together
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Analysis of Bubblesort and Mergesort Algorithms: Complexity and Runtime, Essays (high school) of Computer science
An in-depth analysis of the Bubblesort and Mergesort algorithms, including the number of comparisons and passes, complexity, and runtime examples. Students of computer science and engineering will find this information useful for understanding the efficiency of different sorting methods.
Typology: Essays (high school)
2017/2018
1 / 8
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Analysis of Bubblesort and Mergesort Algorithms: Complexity and Runtime and more Essays (high school) Computer science in PDF only on Docsity!
Big O of Different
sorting Algorithm
Week 7
Sorting Algorithms
- Bubblesort
- Brute-force method of sorting
- Loop inside of a loop
- Mergesort
- Divide and conquer approach
- Recursively call, splitting in half
- Merge sorted halves together
Bubblesort Review
Bubblesort works by comparing and swapping values in a list
Bubblesort Review
Bubblesort works by comparing and swapping values in a list
Largest value correctly placed
Bubblesort Complexity
Look at the relationship between the two loops:
- Inner is nested inside outer
- Inner will be executed for each iteration of outer
Therefore the complexity is:
O((N-1)*(N/2)) = O(N 2 /2 – N/2) = O(N 2 )
LB
O(N 2 ) Runtime Example
Assume you are sorting 250,000,000 items N = 250,000, N 2 = 6.25 x 10^16 If you can do one operation per nanosecond (10-9^ sec) which is fast! It will take 6.25 x 10 7 seconds So 6.25 x 10 7 60 x 60 x 24 x 365 = 1.98 years
Mergesort
Log N
Log N
Analysis of Mergesort
Phase I
- Divide the list of N numbers into two lists of N/ numbers
- Divide those lists in half until each list is size 1 Log N steps for this stage.
Phase II
- Build sorted lists from the decomposed lists
- Merge pairs of lists, doubling the size of the sorted lists each time Log N steps for this stage.
O(NLogN) Runtime Example
Assume same 250,000,000 items N*Log(N) = 250,000,000 x 8. = 2, 099, 485, 002
With the same processor as before
2 seconds