FutureLearn - Functional Programming in Erlang 1.21 - Tail Recursion

recursion.erl

-module(recursion).
-export([test/0,fib/1,loop/1,sum/1,max/1,perfect/1]).

% Typical loop in Erlang
loop(N) when N>0 ->
    io:format("~p~n", [N]),
    loop(N-1);
loop(_) -> % implies N = 0
    io:format("bye~n").

% Sum of values F(0), F(1), ... F(N-1), F(N).
sum(N) ->
    sum(N,0).

sum(N,A) when N>0 ->
    sum(N-1, N+A);
sum(_,A) -> % N = 0
    A.

% Max value of F(0), F(1), ... F(N-1), F(N).
% Probably did not get a good sense of what was asked...
max(N) ->
    max_loop(N,N).

max_loop(N,A) when N>0 ->
    max_loop(N-1, max(N,A));
max_loop(_,A) -> % N = 0
    A.

% Tail recursive Fibonacci with 2 accumulator (last 2 numbers).
% Starts with the first 2 fibonacci numbers than swap and add to get the
% two next ones
fib(N) ->
    fib_loop(N, 0, 1).

fib_loop(0,A,_) ->
    A;
fib_loop(N, A, B) when N>0 ->
    fib_loop(N-1, B, A+B).

% Step by step fib(4):
% fib(4) = fib_loop(4,0,1)
%        = fib_loop(3,1,1)
%        = fib_loop(2,1,2)
%        = fib_loop(1,2,3)
%        = fib_loop(0,3,5)
%        = 3

% Perfect number
% A positive integer is perfect when it is the sum of its divisors,
% e.g. 6=1+2+3, 28=1+2+4+7+14.
perfect(0) ->
    false;
perfect(N) ->
    perfect(N,N-1,0).

perfect(N,0,A) ->
    N == A;
perfect(N,D,A) when N rem D =:= 0 ->
    perfect(N,D-1,A+D);
perfect(N,D,A) -> % D not a divisor
    perfect(N,D-1,A).

% Test perfect number samples
test() ->
    test_perfect() and test_non_perfect().

% Perfect numbers
test_perfect() ->
    lists:all(fun(X) -> X == true end,
              [perfect(6),perfect(28),perfect(496),perfect(8128)]).

% Non perfect numbers
test_non_perfect() ->
    lists:all(fun(X) -> X == false end,
              [perfect(0),perfect(1),perfect(29),perfect(1000),perfect(5000)]).