Algorithms Q&A - Recent questions in Greedy Algorithms

Show that Greedy Algorithm is suboptimal for Gold Rod Question

Sat, 04 May 2019 17:29:51 +0000

Consider a greedy algorithm based approach for gold rod question: http://notexponential.com/623/gold-is-a-precious-metal

Show that greedy algorithm based approach is not optimal, by giving a counter example.

Is Greed the best choice?

Sun, 04 Mar 2018 04:27:36 +0000

Argue whether or not you would apply Greedy technique to the following problems:

a. Chess

b. Sorting

c. Shortest path computation

d. knapsack

Explain the reasoning behind each.

Symbol Frequency

Sun, 04 Mar 2018 04:25:55 +0000

Given a set of symbols and their frequency of usage, find a binary code for each symbol, such that:

a. Binary code for any symbol is not the prefix of the binary code of another symbol.

b. The weighted length of codes for all the symbols (weighted by the usage frequency) is minimized

Maximize Party Planning Reward

Sun, 04 Mar 2018 03:38:40 +0000

You are asked to be an organizer for n parties and are provided with their start and end times. (For example: P1: 7 AM - 9 AM; P2: 8 AM to 3 PM; P3: 4 AM to 8 AM.) You can only be organizing one party at a time, so you need to choose. For every party that you organize, you are given a fixed reward (1000$) irrespective of the length of the party. How do you select the parties to maximize your reward? What is the time complexity of your algorithm in terms of n?

Maximum Product Spanning Tree

Sun, 04 Mar 2018 03:35:47 +0000

Consider problem similar to a minimum or maximum spanning tree, but instead we want to find the maximum product spanning tree, that is a tree that maximums the product of weights of the edges. Describe an efficient algorithm to find the maximum product spanning tree.

[Assume each edge weight is at least 1.]

Maximum Spanning Tree

Sun, 04 Mar 2018 03:34:27 +0000

Consider problem similar to a minimum spanning tree, but instead we want to find the maximum spanning tree, that is, a tree that maximums the sum of weight of the edges. Describe an efficient algorithm to find the maximum spanning tree.

Interval Scheduling

Sun, 04 Mar 2018 03:32:49 +0000

Suppose you are given a list of lectures with there start time and end times. How can you choose the maximum number of non-overlapping lectures?

Chromatic Number, Relation to Max Degree

Wed, 22 Nov 2017 10:15:23 +0000

The chromatic number of G is denoted as χ(G) and is defined as the smallest number of colors needed to color the graph so that no two adjacent nodes receive the same color. Using a greedy coloring algorithm prove that the χ(G) ≤ ∆(G)+1, where ∆(G) is the largest degree in the graph.

"Fast Response" Locating a Proxy Server for the network

Wed, 12 Jul 2017 17:44:29 +0000

"Fast response". A series of client machines are located along a linear network. The i-th client generates amount of traffic that is given by w[i]. You want to put a server somewhere along the linear network that minimizes the total amount of traffic carried by the network. Provide an O(n) algorithm to identify the location of the server.

Adjustment to Greedy Knapsack Algorithm to Guarantee Atleast 50% value of Optimal

Tue, 16 Feb 2016 22:40:32 +0000

How can we change the greedy knapsack algorithm a little bit to guarantee at least 50% value of optimal?