Práctica #7: MapReduce con Erlang

Activity Description

Individually or in pairs, solve the following programming exercises using Erlang and the plists:mapreduce function in order to effectively take advantage of any level of parallelism available on the execution environment. Place your functions in a module called mapred.

1. Write the function primes that takes two integer parameters, \(S\) and \(E\) \((0\le S\le E)\). It starts by calling the MapReduce operation with a list of all integer numbers between \(S\) and \(E\) inclusively. The mapping function receives a number \(N\) and emits the tuple {true, N} if \(N\) is a prime number, otherwise it emits the tuple {false, N}. After the reduction, it returns a list with all the prime numbers found between \(S\) and \(E\), or an empty list if none were found. Examples (note that the order of the resulting elements is nondeterministic):

   > mapred:primes(0, 20).
   [2,3,5,7,11,13,17,19]
   > mapred:primes(320, 330).
   []
   > mapred:primes(9999500, 9999900).
   [9999511,9999533,9999601,9999883,9999593,9999889,9999637,
    9999653,9999659,9999761,9999863,9999713,9999823,9999677,
    9999739,9999667,9999749,9999877]
   

2. A number of the form \(2^n\) that contains the consecutive digits 666 (i.e., the beast number) is called an Apocalyptic Number.

   The number \(2^{157}\) is an apocalyptic number, because

   $$ 2^{157} = 182687704666362864775460604089535377456991567872 $$

   which contains the beast number starting at the digit in the 10^th position (starting from the left).

   Write the function apocalyptic that takes two integer parameters, \(S\) and \(E\) \((0 \le S \le E)\). It starts by calling the MapReduce operation with a list of all integer numbers between \(S\) and \(E\) inclusively. The mapping function receives a number \(N\) and determines if \(2^{N}\) is or isn’t an apocalyptic number. If it is, it emits the tuple {true, N}, otherwise it emits the tuple {false, N}. After the reduction, it returns a list with all the apocalyptic numbers found between \(S\) and \(E\), or an empty list if none were found. Examples:

   > mapred:apocalyptic(100, 200).
   [157,192]
   > mapred:apocalyptic(100, 150).
   []
   > mapred:apocalyptic(800, 850).
   [800,807,819,820,822,823,824,826,828,836,838,840,841,842,
    844,846,848,850]
   

3. A sexy prime triplet is a tuple \((p, p+6, p+12)\) of prime numbers that differ by six. The term “sexy prime” stems from the Latin word for six: sex. For example, the first sexy prime triplet is: \((5, 11, 17)\).

   Write the function called sexy that takes two integer parameters \(S\) and \(E\) \((0 \le S \le E)\). This function returns a list with a all the sexy prime triplets \((p, p+6, p+12)\), where \(S \le p \le E\). Examples:

   > mapred:sexy(1, 100).
   [{5,11,17},
    {7,13,19},
    {11,17,23},
    {17,23,29},
    {31,37,43},
    {41,47,53},
    {47,53,59},
    {61,67,73},
    {67,73,79},
    {97,103,109}]
   > mapred:sexy(1500, 1600).
   []
   > mapred:sexy(50000, 51000).
   [{50147,50153,50159},
    {50411,50417,50423},
    {50581,50587,50593},
    {50587,50593,50599}]
   > mapred:sexy(100000, 101000).
   [{100511,100517,100523},{100931,100937,100943}]
   

4. Let \(\varphi(X)\) be the sum of all the digits of \(2^X\). For example, to compute \(\varphi(15)\), first you compute \(2^{15}\), which equals to 32,768, and then you add up all its digits: 3 + 2 + 7 + 6 + 8. The result is 26.

   Write the function called phi13 that takes two integer parameters \(S\) and \(E\) \((0 \le S \le E)\). This function returns a list with all the values of \(K\), where \(S \le K \le E\), such that \(\varphi(K)\) is exactly divisible by 13. Examples:

   > mapred:phi13(0, 100).
   [8,15,21,49,74,77]
   > mapred:phi13(350, 400).
   []
   > mapred:phi13(1000, 1100).
   [1002,1008,1032,1033,1034,1049,1067,1097]
   > mapred:phi13(10000, 10100).
   [10016,10019,10037,10052,10088,10090,10100]
   

Deliverables

No report needs to be handed in.

The program source file must include at the top the authors’ personal information (name and student ID) within comments. For example:

%----------------------------------------------------------
% Práctica #7: MapReduce con Erlang
% Date: April 7, 2019.
% Authors:
%          A01166611 Pepper Pots
%          A01160611 Anthony Stark
%----------------------------------------------------------

Only one team member needs to upload the file.

Due date is Sunday, April 7.

Evaluation

This activity will be evaluated using the following criteria:

-10	The program doesn't contain within comments the author's personal information.
10	The program contains syntax errors.
1	The program was plagiarized in whole or in part.
10-100	Depending on the amount of exercises that were solved correctly.