CISC 320 Algorithms, Fall 2007
Homework set #4, due Fri, Nov. 2.

1. Exercise 4.5

2. Show how to reduce exercise problem 4.6 to problem 4.7. In other words, assume you have a function Goog(p, f) which takes arrays p and f of length n each, where p_i and f_i have the meaning described in 4.7 concerning the i-th job. Goog returns a schedule for the jobs ( a list of the job numbers in the appropriate order). Use Goog to help solve problem 4.6, where the input is three arrays of swim, bike, and run times respectively.

3. Given two sorted arrays A and B of sizes m and n respectively, using O(log(m)+log(n)) comparisons of array entries, determine the median value in the arrays. You may assume the m+n values are distinct. The median is the value that would be in position (m + n)/2, rounded up, if the m + n entries were put together in a single array and sorted (1-base indexing). For instance with m = 3 and n = 6, the median is the 5th in order of the 9 elements. With m = 3 and n = 5, the median would be the 4th of the 8 values. Write pseudocode and explain why your algorithm correctly finds the median and uses only O(log(mn)) comparisons. Note: The case when m = n is exercise 5.1 which we solved in class.

4. Exercise 5.4, but simplify the formula to F_j = q₁q_j + q₂q_j + q₃q_j + ... q_j-1q_j - q_j+1q_j - q_j+2q_j - ... q_nq_j.

5. Extra credit: Implement Goog (see first hw problem above), i.e. solve exercise 4.7.