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Computer Science Assignment: Implementing and Comparing AVL Trees, 2-3 Trees, and Heapsort, Assignments of Algorithms and Programming

University of the Pacific (UOP)Algorithms and Programming

A computer science assignment where students are required to implement and empirically verify the performance of avl trees, 2-3 trees, and heapsort. The assignment includes instructions for each exercise, as well as guidelines for adding instrumentation and creating random data sets to test the implementations.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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koofers-user-grt ๐Ÿ‡บ๐Ÿ‡ธ

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COMP157๎˜ƒFall07๎˜ƒAssignment๎˜ƒ6๎˜ƒ
Homework๎˜ƒAssignment๎˜ƒ6:๎˜ƒdue๎˜ƒFriday,๎˜ƒNovember๎˜ƒ2.๎˜ƒ
Do๎˜ƒany๎˜ƒtwo๎˜ƒof๎˜ƒthe๎˜ƒfollowing๎˜ƒthree๎˜ƒexercises:๎˜ƒ
๎˜ƒ
1) Implement๎˜ƒan๎˜ƒAVL๎˜ƒtree.๎˜ƒ๎˜ƒ
Your๎˜ƒimplementation๎˜ƒmust๎˜ƒsupport๎˜ƒinsertion๎˜ƒand๎˜ƒsearch๎˜ƒoperations.๎˜ƒ๎˜ƒ
You๎˜ƒdo๎˜ƒnot๎˜ƒhave๎˜ƒto๎˜ƒimplement๎˜ƒa๎˜ƒdeletion๎˜ƒoperation.๎˜ƒ
Verify๎˜ƒyour๎˜ƒimplementation๎˜ƒempirically๎˜ƒas๎˜ƒfollows:๎˜ƒ
โ€ข Add๎˜ƒinstrumentation๎˜ƒto๎˜ƒyour๎˜ƒsearch๎˜ƒoperation๎˜ƒto๎˜ƒcount๎˜ƒcomparisons.๎˜ƒ
โ€ข Create๎˜ƒrandom๎˜ƒtrees๎˜ƒof๎˜ƒn=100,๎˜ƒn=1000๎˜ƒand๎˜ƒn=10000๎˜ƒnodes๎˜ƒ(at๎˜ƒleast๎˜ƒ10๎˜ƒof๎˜ƒeach).๎˜ƒ
(Be๎˜ƒsure๎˜ƒthat๎˜ƒyou๎˜ƒare๎˜ƒinserting๎˜ƒn๎˜ƒunique๎˜ƒrandom๎˜ƒvalues.)๎˜ƒ
โ€ข For๎˜ƒeach๎˜ƒtree,๎˜ƒrun๎˜ƒat๎˜ƒleast๎˜ƒ100๎˜ƒsearches.๎˜ƒ
โ€ข Compute๎˜ƒaverage๎˜ƒcomparisons๎˜ƒfor๎˜ƒeach๎˜ƒtree๎˜ƒsize๎˜ƒand๎˜ƒcompare๎˜ƒyour๎˜ƒresults๎˜ƒto๎˜ƒ
theoretical๎˜ƒexpectations.๎˜ƒ
๎˜ƒ
2) Implement๎˜ƒa๎˜ƒ2โ€3๎˜ƒtree.๎˜ƒ๎˜ƒ
Your๎˜ƒimplementation๎˜ƒmust๎˜ƒsupport๎˜ƒinsertion๎˜ƒand๎˜ƒsearch๎˜ƒoperations.๎˜ƒ๎˜ƒ
You๎˜ƒdo๎˜ƒnot๎˜ƒhave๎˜ƒto๎˜ƒimplement๎˜ƒa๎˜ƒdeletion๎˜ƒoperation.๎˜ƒ
Verify๎˜ƒyour๎˜ƒimplementation๎˜ƒempirically,๎˜ƒby๎˜ƒthe๎˜ƒsame๎˜ƒprocedure๎˜ƒdescribed๎˜ƒfor๎˜ƒAVL๎˜ƒtrees.๎˜ƒ
๎˜ƒ
3) Implement๎˜ƒHeapsort.๎˜ƒ๎˜ƒ
Verify๎˜ƒyour๎˜ƒimplementation๎˜ƒempirically๎˜ƒas๎˜ƒfollows:๎˜ƒ
โ€ข Add๎˜ƒinstrumentation๎˜ƒto๎˜ƒyour๎˜ƒsort๎˜ƒoperation๎˜ƒto๎˜ƒcount๎˜ƒcomparisons.๎˜ƒ
โ€ข Create๎˜ƒrandom๎˜ƒarrays๎˜ƒof๎˜ƒn=100,๎˜ƒn=1000๎˜ƒand๎˜ƒn=10000๎˜ƒnodes๎˜ƒ(at๎˜ƒleast๎˜ƒ10๎˜ƒof๎˜ƒeach).๎˜ƒ
โ€ข Compute๎˜ƒthe๎˜ƒaverage๎˜ƒsorting๎˜ƒcost๎˜ƒfor๎˜ƒeach๎˜ƒtree๎˜ƒsize๎˜ƒand๎˜ƒcompare๎˜ƒyour๎˜ƒresults๎˜ƒto๎˜ƒ
theoretical๎˜ƒexpectations.๎˜ƒ
๎˜ƒ
๎˜ƒ

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COMP157 Fall07 Assignment 6

Homework Assignment 6 : due Friday, November 2. Do any two of the following three exercises:

  1. Implement an AVL tree. Your implementation must support insertion and search operations. You do not have to implement a deletion operation. Verify your implementation empirically as follows:
  • Add instrumentation to your search operation to count comparisons.
  • Create random trees of n=100, n=1000 and n=10000 nodes (at least 10 of each). (Be sure that you are inserting n unique random values.)
  • For each tree, run at least 100 searches.
  • Compute average comparisons for each tree size and compare your results to theoretical expectations.
  1. Implement a 2 โ€ 3 tree. Your implementation must support insertion and search operations. You do not have to implement a deletion operation. Verify your implementation empirically, by the same procedure described for AVL trees.
  2. Implement Heapsort. Verify your implementation empirically as follows:
  • Add instrumentation to your sort operation to count comparisons.
  • Create random arrays of n=100, n=1000 and n=10000 nodes (at least 10 of each).
  • Compute the average sorting cost for each tree size and compare your results to theoretical expectations.