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日期：2018-09-10 04:11

COP5612 – Fall 2013

Alin Dobra

August 29, 2018

• Due Date: September 10, Midnight

• One submission per group

• Submit using eLearning

• What to include:

– README file including group members, other requirements specified

below

– Lastnames.zip the code for the project

1 Problem definition

An interesting problem in arithmetic with deep implications to elliptic curve

theory is the problem of finding perfect squares that are sums of consecutive

squares. A classic example is the Pythagorean identity:

32 + 42 = 52(1)

that reveals that the sum of squares of 3, 4 is itself a square. A more interesting

example is Lucas‘ Square Pyramid:

12 + 22 + ... + 242 = 702(2)

In both of these examples, sums of squares of consecutive integers form the

square of another integer.

The goal of this first project is to use Elixir and the actor model to build a

good solution to this problem that runs well on multi-core machines.

2 Requirements

Input: The input provided (as command line to your program, e.g. my app)

will be two numbers: N and k. The overall goal of your program is to find all

k consecutive numbers starting at 1 and up to N, such that the sum of squares

is itself a perfect square (square of an integer).

Output: Print, on independent lines, the first number in the sequence for each

solution.

Example 1:

mix run proj1.exs 3 2

indicates that sequences of length 2 with start point between 1 and 3 contain

3,4 as a solution since 32 + 42 = 52

.

Example 1:

mix run proj1.exs 40 24

indicates that sequences of length 24 with start point between 1 and 40 contain

1,2,...,24 as a solution since 12 + 22 + ... + 242 = 702

.

Actor modeling: In this project you have to use exclusively the actor facility

in Elixir (projects that do not use multiple actors or use any other form

of parallelism will receive no credit). A model similar to the one indicated

in class for the problem of adding up a lot of numbers can be used here, in

particular define worker actors that are given a range of problems to solve and

a boss that keeps track of all the problems and perform the job assignment.

README file In the README file you have to include the following material:

• Size of the work unit that you determined results in best performance for

your implementation and an explanation on how you determined it. Size

of the work unit refers to the number of sub-problems that a worker gets

in a single request from the boss.

• The result of running your program for

mix run proj1.exs 1000000 4

• The running time for the above as reported by time for the above, i.e.

run time scala project1.scala 1000000 4 and report the time. The

ratio of CPU time to REAL TIME tells you how many cores were effectively

used in the computation. If your are close to 1 you have almost no

parallelism (points will be subtracted).

• The largest problem you managed to solve.

3 BONUS – 15%

Use remote actors and run you program on 2+ machines. Use your solution to

solve a really large instance such as: mix run proj1.exs 100000000 20. To

get the bonus points you have to give a demo to the instructor and explain your

solution.