Question
Dene the median of a collection of N distinct comparable elements to be an element v from that collection that is larger than exactly N
Dene the median of a collection of N distinct comparable elements to be an element v from that collection that is larger than exactly N/2 (or, equivalently, smaller than exactly N/21) other elements from the same collection.
Consider the problem of nding the median of the elements in two sorted lists of sizes m and n (not necessarily equal), respectively.
1. Express this problem formally (unique name, input conditions, output conditions).
2. (a) Describe a simple algorithm to compute that median. (b) Find its tight (Big-Theta) asymptotically complexity as a function of the total number of elements.
3. (a) Show how you can use the medians of the two lists to reduce an instance of this problem to smaller sub-instances. (b) State a precise self-reduction for this problem.
4. (a) State a recursive algorithm that solves the problem based on your reduction. (b) For the special case when m = n, obtain from it a recurrence expressing its running time as a function of n. (c) Solve the recurrence and nd a tight (Big-Theta) asymptotic bound on the complexity in the worst case.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started