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22/08/2022
CS5200 Homework – 2
(Deadline: 10-06-2023 11:59pm)
Instructor: Huiyuan Yang
q Theory questions [60%] :
Q1.[10%] Given an unordered list, show the corresponding heap after each step.
§ Build a Max-Heap by calling Max-Heapify() algorithm [3%]
§ Delete the maximum item; [2%]
§ Insert an item with value of 80; [2%]
§ Show the heap after 30 is sorted when performing heapsort.[3%]
Q2. [10%] Given a Binary Search Tree,
§ Print out all the keys in the BST in Pre-order, In-order and Post-order; [6%]
§ Show the BST after performing insert(13), insert(40) and delete(35) respectively; [4%]
Q3: [10%] Find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is:
§ Print the corresponding m-table, s-table and an optimal parenthesization solution..
Q4.[15%] Given strings X=CACMYCCA, and Y=YMCMAMYCCMA
§ Find the longest common subsequence for the strings X and Y. Show the table with the lengths
and arrows (“← “, ” ↑ “, ” ↖ “) [10%]
§ Find the longest contiguous subsequence. Show the table with the lengths. [5%]
Q5. [15%] Constructing the optimal binary tree, given
§ Show the dynamic programming tables, optimal binary tree and expected search cost.
q Programming [35%]
Dynamic programming solution for LCS.
§ [35%] Given two strings, find the length of the longest subsequence present in both of them. For
example:
o LCS for input Sequences “ABCDGH” and “AEDFHR” is “ADH” of length 3.
o LCS for input Sequences “AGGTAB” and “GXTXAYB” is “GTAB” of length 4.
§ [Extra 10%] Given two strings, find the length of the longest contiguous subsequence present in
both of them. For example:
o LCS for input Sequences “ABCDEEF” and “AEDEEF” is “DEEF” of length 4.
q Bonus: [Extra 10%]
Design a dynamic programming algorithm to solve the sum of subsets problem:
Problem statement: There are n positive integers ???? = [????!, ????”, … , ????#] and a positive integer sum ????. Is
there a subset of A such that the sum of the integers in the subset is ????. If there is such a subset, the
output of the program is true, otherwise it is false.
Example:
§ ???? = [3, 5, 11] ???????????? ???? = 16. In this case the output is true since 5 + 11 = 16
§ ???? = [3, 5, 11] ???????????? ???? = 18. In this case the output is false since ????ℎ???????????? ???????? ???????? ????????????????????????????????.
§ ???? = [3, 5, 11,15, 22, ] ???????????? ???? = 30. In this case the output is true since 3 + 5 + 22 = 30
This problem can be solved with dynamic programming.
1) Define the optimal substructure, and write the recurrence for the solution. [5%]
2) Write pseudo code, and apply dynamic programming to the following problem: ???? =
[1, 2, 4] ???????????? ???? = 6. Show your dynamic programming table. [5%]
q Submission requirements: [5%]
Put the theory part and code into a folder with the name: [YourStudentID-YourName-HW*].zip
§ Following all the submission requirements [5%]
§ Theory part:
o You solution should be clear, concise but also contain enough details.
o Only PDF format is allowed.
o Please make sure the scanned PDF file is high-resolution and easily readable if you wrote
your solution on paper.
§ Programming part:
o A sanity check to test the correctness of your algorithm.
o Your program will read an input file and write an output file.
o Your program will be called like this: prompt>./hw* ./input.txt. ./output.txt
o Your code should be complied by calling the makefile.
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