Sorting Algorithm Analysis

Posted on 2003-11-14
Last Modified: 2010-04-02
Im working on a program that utilizes many of the sorts and allows me to compare them.  However I ran into a situation I am curious about.

For selection sort, for both string and integer sorting, why would the number of comparisons be the same even though the sorting order is different?  Then this also poses another question, why would string sorting take more time?

I also just wanted to confirm some of my findings.  
Either merge-sort or quick sort is good for large input correct? Is there a best?
Selection / Insertion sort for small input?
Also why does the pivot point matter on quicksort? So less items have to be compared?
Question by:killer455

Expert Comment

ID: 9748521
1 -  selection sort is order (n^2)
this because it work as follow
 1 it select the min from 1 -> n and put it in the 1st place (n compareson)
 2 it select the min from 2 ->n  and put it in the 2nd place (n-1 compareson)
 n it select the min from n ->n  and put it in the nth place (n-n compareson)
so always the iteration is n+(n-1)+(n-2)+...+0 = n/2*(n-1) ie n^2

mege sort and quik sort is order n*lg(n) and this is best order for sorting but complectaed so when we user small numbers we user Selection / Insertion since in this case n^2 and  n*lg(n)  will be very near

the most problem in quik sort is the pivot because the the chossing of the pivot may change the order to o(n^2)
for example if you use sorted array and you choose the pivot as 1st element
you then divide array to 2 parts 1 greater than pivot 2 less than or equal pivot (if the pivot divide the array to 2 equal size array you reach optimal) but since array sorted the 1st array will contain 1 element and the second contain (n-1) so it as you do nothing

LVL 11

Accepted Solution

bcladd earned 50 total points
ID: 9748960
How does selection sort work? Think about that for just a second.

Selection sort runs two count controlled loops. One indexes from the first to the last element in the array. The second, inner loop, indexed from the first index to the end of the loop looking for the index of the smallest element in that range. After the inner loop finishes, the smallest element is swapped with the element indexed by the first index.

Do you see anything interesting in that description of selection sort? No matter which element is the smallest in the remaining area to check, one item is compared with the current smallest in each iteration of the inner loop. So the number of times keys are compared is actually CONSTANT for any given input size regardless of the type or ordering of the input.

Your code counts KEY COMPARISONS. That is, comparisons between whole values stored inside the array to be sorted. Thus comparisons conunts comparing two strings exactly the same as it counts comparing two integers. It is true that the assembly code for comparing two integers is one (or two if you count the branch) instructions and comparing strings may be many instructions (it is a loop even if it looks like "=="). So the TIME for comparing two keys depends on the type and (perhaps) value of the key but the number of key comparisons does not.


Featured Post

Is Your Active Directory as Secure as You Think?

More than 75% of all records are compromised because of the loss or theft of a privileged credential. Experts have been exploring Active Directory infrastructure to identify key threats and establish best practices for keeping data safe. Attend this month’s webinar to learn more.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Errors will happen. It is a fact of life for the programmer. How and when errors are detected have a great impact on quality and cost of a product. It is better to detect errors at compile time, when possible and practical. Errors that make their wa…
  Included as part of the C++ Standard Template Library (STL) is a collection of generic containers. Each of these containers serves a different purpose and has different pros and cons. It is often difficult to decide which container to use and …
The viewer will learn how to use the return statement in functions in C++. The video will also teach the user how to pass data to a function and have the function return data back for further processing.
The viewer will learn how to user default arguments when defining functions. This method of defining functions will be contrasted with the non-default-argument of defining functions.

920 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

14 Experts available now in Live!

Get 1:1 Help Now