5300 HW Answer.pdf - CS 5300 01 Advanced Algorithm Design...

( Total : 100 points)
1. Let X(1..n) and Y(1..n) contain two lists of n integers, each sorted in nondecreasing
order. Give the best (worst-case complexity) algorithm that you can think for finding
(a) the largest integer of all 2n combined elements.
(b) the second largest integer of all 2n combined elements.
(c) the median (or the n th smallest integer) of all 2n combined elements.
For instance, X = (4, 7, 8, 9, 12) and Y = (1, 2, 5, 9, 10), then median = 7, the n th
smallest, in the combined list (1, 2, 4, 5, 7, 8, 9, 9, 10, 12). [Hint: use the concept
similar to binary search]
2.
1-to-2 PARTITION:
Instance: A finite set of positive integers Z = { z
1
, z
2
, ... , z
n
Question: Is there a subset Z' of Z such that
Sum of all numbers in Z' = 2 * Sum of all numbers in
(a) Obtain the dynamic programming functional equation to solve the 1-to-2 PARTITION
problem.
}.
Z-Z'
1