Assignment 8

Suggested Problems (not to be turned in)

• Rose, Sec. 11.1, ex: 1, 3
• Rosen, Sec. 11.2, ex: 1 (use insertion algorithm in text), 3, 5
• Given a binary search tree and given a given value, write pseudocode for a procedure that will return (not print) how many times the given value appears in the tree. (Processing with this code should be efficient, in that no more nodes should be visited than is absolutely necessary.) The initial call for the procedure should be:

       findNmberOccurencesBST (root, value);
    

• Given a binary tree (not necessarily a search tree) and given integers low and high, write pseudocode for a procedure that will return (not print) the number of nodes with values between low and high inclusive. (The count should include all nodes containing the values low or high.) The initial call for the procedure should be:

       printLevel (root, low, high);
    

Required Problems, due October 21

Submission Instructions

• Submissions are to be submitted on paper, with one submission from each assigned pair of students, unless a student has explicit (written) permission from the instructor.

• Both partners should collaborate on every problem, and both names should be at the top of the first page. Since this is a collaborative effort, both partners should agree that the work represents their agreement in the correctness of the answers, and the same grade will be recorded for each assignment.

• Problems for each section (each bullet item in the assignment) should begin on a new page, and problems within a section should be in numeric order.

• If a problem requires the writing of a Python program, then the submission should include a printout of the code, a listing of appropriate test runs, and a statement regarding how the test runs provide sufficient evidence to conclude the program works properly.

• Each problem from Rosen's text should be identified with its section number and problem number. Each problem written out as a separate bullet point should be identified in a phrase or sentence, so it is clear which question is being answered.

• When a problem asks for a conclusion, the solution must include both a statement of the conclusion and an argument justifying that conclusion.

• Answers should be placed in Section and problem order, so the first page (more if needed) should give answers for the problems in the first assignment bullet. Answers for subsequent bullets should be in the order of the bullets on the Assignment sheet.

• Although the rules of this course allow the use of sources beyond the discussions of a student pair, any outside references (e.g., from the textbook, from Web sources, from discussions with others, etc.) must be fully cited.

Problems to be Turned In

• Rose, Sec. 11.1, ex: 2, 4
• Rosen, Sec. 11.2, ex: 2 (use insertion algorithm in text), 4
• Which of the following are binary search trees. (In each case justify your answer.)
  
• Given a binary tree (not necessarily a binary search tree), in which each node stores a positive number, write pseudocode for a procedure that will find the maximum value stored in the tree. The call for the procedure should be:

       findMax (root);
  

• Given a binary search tree, in which each node stores an alphabetic string, write pseudocode for a procedure that will print the strings of even length in reverse alphabetical order. The call for the procedure should be:

       printEvenLength (root);
  

• Given a binary tree and given an integer L, write pseudocode for a procedure that will print values in all nodes that are at level L or more. The initial call for the procedure should be:

       printLevel (root, L);
  

• Given a binary search tree and given integers low and high, write pseudocode for a procedure that will print values in all nodes that are between low and high. (In this work, any nodes containing the values low or high should be included in the output.) The initial call for the procedure should be:

       printLevel (root, low, high);
    

  This code should be as efficient as possible, so that processing should not visit any more nodes than are necessary.

• Given a binary tree, write pseudocode for a procedure that will return the number of nodes that have no (non-null) left children. The initial call for the procedure should be:

       printNullLeft (root, L);
  

created July 22, 2021 revised October 15, 2021
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.