Algorithm Day1

Algorithm Day 1

• To get understand the impact of algorithm.
• Know about the problem of “Dynamic connectivity”

• Learned there are three ways to solve this problem:

  1. Quick find, Quick Union,
  2. Weighted Quick union,
  3. Weighted Quick union with path compression

  

  

Steps to developing a usable algorithm

1. Model the problem.
2. Find an algorithm to solve it.
3. Fast enough? Fits in memory?
4. If not, figure out why.
5. Find a way to address the problem.
6. Iterate until satisfied.

The scientific method.

Mathematical analysis.

Q1: So, How to solve the Kruskal’s minimum spanning tree with union-find ?

Q2: Social network connectivity. Given a social network containing n members and a log file containing m timestamps at which times pairs of members formed friendships, design an algorithm to determine the earliest time at which all members are connected (i.e., every member is a friend of a friend of a friend … of a friend). Assume that the log file is sorted by timestamp and that friendship is an equivalence relation. The running time of your algorithm should be m*log n or better and use extra space proportional to n.

Q3: Search in a bitonic array. An array is bitonic if it is comprised of an increasing sequence of integers followed immediately by a decreasing sequence of integers. Write a program that, given a bitonic array of n distinct integer values, determines whether a given integer is in the array.

• Standard version: Use ∼3lgn compares in the worst case.
• Signing bonus: Use ∼2lgn compares in the worst case (and prove that no algorithm can guarantee to perform fewer than ∼2lgn compares in the worst case).