Question: Consider the following game. You are given a sequence of n positive numbers (a1, a2, ..., ,an). Initially, they are all colored black. At

Consider the following game. You are given a sequence of n positive numbers (a1, a2, ..., ,an). Initially, they are all colored black. At each move, you choose a black number ak and color it and its immediate neighbors (if any) red (the immediate neighbors are the elements ak-1, ak+1). You get ak points for this move. The game ends when all numbers are colored red. The goal is to get as many points as possible. (a) Describe a greedy algorithm for this problem. Verify that it does not always maximize the number of points by giving a counter-example.

Step by Step Solution

★★★★★

3.39 Rating (146 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The image contains a problem statement about a game involving a sequence of positive numbers You are ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Programming Questions!

The exchange rate is $1.20/ Exchange rate volatility is 15%. The dollar interest rate is 5%. The euro interest rate is 9%. Both are continuously compounded rates. The price evolution of the euro...

It is the post-apocalyptic era, and hardship and depression run rampant. You are currently at the bottom of a staircase in the basement of an abandoned building looking at what is pure...

You are given a sequence of n elements to sort. The input sequence consists of n/k subsequences, each containing k elements. The elements in a given subsequence are all smaller than the elements in...

You will invest in a bond that will give you a payment of $20 two times each year. It matures in 19 years. Investments of this risk should earn 4.03%. How much is it worth today? Answer:

This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What are these trees called? [1 mark] (ii) If one were building a grammar for English...

You have been provided with the description of a programming language, J, intended for scripting applications. Its syntax is similar to a cut-down version of Java in that it consists of function...

Q1. Let's consider a searching problem as follow: Input: A sequence of n numbers a1,a2,,an stored in array A[1:n] and a value x. Output: An index i such that x equals to A[i] or the special value NIL...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

The new line character is utilized solely as the last person in each message. On association with the server, a client can possibly (I) question the situation with a client by sending the client's...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

The thermal resistance of a seal's fur and blubber combined is 0.33 K/W. If the seal's internal temperature is 37C and the temperature of the sea is about 0C, what must be the heat output of the seal...

Refer to the table below. Assume that the company involved now finds that the learning rate is 85 percent. The 85 percent learning rate coefficient is -0.234465; that is b = -0.234465 in the formula...

a ) Consider the function a r c t a n ( x 2 ) . Write a partial sum for the power series which represents this function consisting of the first 4 nonzero terms. For example, if the series were n = 0...

After discovering a new gold vein in the Colorado Mountains CTC Mining Corporation must decide whether to mine the deposit. The most cost-effective method of mining gold is sulfuric acid extraction,...

Refer to the Merck income statement presented at the very beginning of the chapter, and note that the company reported climbing profits of $3.4 billion, $7.9 billion, and $13 billion in 2007, 2008,...

State whether you would use Raoults law or Henrys law to perform vaporliquid equilibrium calculations for each component in the following liquid mixtures: (a) Water and dissolved nitrogen; (b)...

A dry gas containing 10.0% NH 3 by volume is contacted with water at 10C and 1 atm in a single-stage bubble contactor. The effluent liquid and gas streams may be considered to be in equilibrium with...

Transactions include the following: 1. Declaration of stock dividend. 2. Purchase of 50 percent of the outstanding stock of another company. 3. Payment of previously accrued interest payable. 4....

What is the definition of differntiation?Group of answer choicesA company that has several different business, either related or unrelated, to spread out its risk and increase its revenue streams.A...

Give an efficient algorithm to determine if there exists an integer i such that Ai = I in an array of integers A1

Show the result of performing three deleteMin operations in the heap of the previous exercise.

Java 7 adds syntax that allows a switch statement to work with the String type (instead of the primitive integer types). Explain how hash tables can be used by the compiler to implement this language...

Based on the sample data in the following frequency distribution, conduct a test to determine whether the population from which the sample data were selected is Poisson distributed with mean equal to...

The Cooper Company discussed in Problem 13-40 has a second contract with a private firm for which it makes fuses for an electronic instrument. The quality control department at Cooper periodically...

Referring to the displayed regression model, what percent of variation in the y variable is explained by the x variable in the model?