# Homework Assignments

The following homework problems have been assigned for both sections of CMSC441. Read and follow the homework guidelines. All Homework is due at the beginning of class. Late work is not accepted.
Homework 1,  Due Tuesday, September 8.
1. Exercise 1.3-7, page 16.
2. Problem 2-2, page 38. Briefly justify your answers for each case. For part (d), provide a full proof.
3. Problem 2-4, page 39.
4. Exercise 3.2-2, page 52.

Homework 2, Due Tuesday, September 15.
1. Problem 4-1, page 72. In the cases where you use the Master Theorem, clearly state which case you are using and the asymptotic upper and lower bounds on T(n).
2. Exercise 4.4-2, page 72.
3. Problem 8-3, page 169.

Homework 3, Due Tuesday, September 22.
1. Consider the proposition of Exercise 7.3-3 on page 147.
1. (a) Explain the difference between the following concepts, as defined by the textbook: node height, node depth, node level.

(b) Give an example of a binary tree T and nodes x and y in T such that x and y have the same level but different heights.

(c) First prove the proposition for the special case of complete binary trees.  Explicitly state your proof strategy.

(d) Does the proposition remain true if the noun "height" is replaced by the noun "depth" or "level"? Prove your answers.

(e) Prove the proposition for the general case, in which the heap might not be a complete tree.

(f) Does your argument given in part (e) still hold if the noun "height" is replaced by the noun "depth"?  If not, explicitly identify the first sentence of your proof that fails with this textual substitution.  Is your answer to part (f) consistent with your answer to part (d)?

2. Problem 8-4, page 169.
3. Exercise 9.3-4, page 180.

Homework 4, Due Tuesday, October 6.
1. Exercise 9.2-2, page 177.
2. Exercise 10.3-8, page 192.
3. Exercise 10.3-9, page 192.

Homework 5, Due Tuesday, October 13.
1. Exercise 10.3-7, page 192.
2. Exercise 12.3-2, page 232.
3. Exercise 12.3-3, page 232.

Homework 6, Due Tuesday, October  20.
1. Exercise 14.1-3, page 265.
2. Exercise 14.2-5, page 267.
3. Exercise 14.3-3, page 272.

Homework 7, Due Tuesday, October 27.
1. Exercise 16.4-2, page 324.
2. Problem 16-2, page 325.
3. Problem 16-3, page 326.

Homework 8, Due Tuesday, November 3.
1. Exercise 16-4, page 326.
2. Exercise 22.3-3, page 450.
3. Exercise 23.1-6, page 468.

Homework 9, Due Tuesday, November 17.
1. Exercise 23.2-6, page 476.
2. Exercise 23.4-5, page 488.
3. Exercise 23.5-4, page 494.

Homework 10, Due Tuesday, November 24.
1. Problem 24-1, page 511.
2. Exercise 25.2-2, page 531.
3. Exercise 25.2-5, page 532.
4. Exercise 26.1-8, page 558.