CSC 344
Homework 2

Assigned Feb. 27, due Mar. 18

As you're doing these, think of which one you'd like to present in class, and let me know as soon as you've decided.

Problems I found somewhere

• Here's a silly way to sort a bunch of numbers: generate each of the possible permutations of the numbers, and for each one, test whether it's in order.

  Analyze this algorithm: tell how long it takes, as a function of how many numbers there are, using big-O notation.

• You are given a bunch of floating-point numbers, and you want to find which two of them are closest together. Describe an algorithm (in pseudocode, as efficient as you can) that solves this problem. Analyze the algorithm: tell how long it will take, as a function of how many numbers there are.

Written problems from textbooks

• Shaffer problem 7.6 (which sorting algorithms are stable?)
• Shaffer problem 7.7 (making a non-stable sorting algorithm stable)
• Shaffer problem 7.15 (matching nuts and bolts)
• CLRS problem 6-3 (Young tableaux)
• CLRS exercise 7.4-5 (also discussed on p. 242 of Shaffer)
• CLRS problem 7-6 (fuzzy sorting of intervals)
• CLRS exercise 8.2-4 (answering range queries)
• CLRS exercise 8.4-2 (analysis of bucket-sort)
• CLRS exercise 9.1-1 (find second-smallest)
• CLRS exercise 9.3-5 (given a linear-time median algorithm, write a linear-time k-selection algorithm)
• CLRS exercise 9.3-9 (find optimal location for oil pipeline)

Programming problems

• Shaffer project 7.2 (double insertion sort) OR 7.6 (modifying heap siftdown)