FutureLearn exercises

first.erl

-module(first).
-export([double/1, mult/2, area/3, square/1, treble/1]).

mult(X,Y) ->
  X*Y.

double(X) ->
  mult(X, 2).

area(A,B,C) ->
  S = (A+B+C)/2,
  math:sqrt(S*(S-A)*(S-B)*(S-C)).

square(A) ->
  math:sqrt(A).

treble(A) ->
  A*3.

recur.erl

-module(recur).
-export([fac/1, fib/1, pieces/1]).

% Factorial
fac(0) -> 1;
fac(N) when N > 0 -> N*fac(N-1);
fac(_) -> 1.

% Fibonnacci
fib(0) -> 0;
fib(1) -> 1;
fib(N) when N > 0 -> fib(N - 1) + fib(N - 2);
fib(_) -> 0.

% N Dimensions
pieces(0) -> 1;
pieces(N) -> N + pieces(N - 1).

recur_tail.erl

-module(recur_tail).
-export([fac/1, fib/1, perfect/1]).

%Factorial with tail recursion
fac(N) when N > 0 -> fac_tail(N, 1).
fac_tail(0, Acc) -> Acc;
fac_tail(N, Acc) -> fac_tail(N-1, N*Acc).

%Fibonnacci sequence with tail recursion
fib(N) -> fib_tail(N, 0, 1).
fib_tail(0, Acc1, _) -> Acc1;
fib_tail(1, _, Acc2) -> Acc2;
fib_tail(N, Acc1, Acc2) -> fib_tail(N - 1, Acc2, Acc1+Acc2).

perfect(N) -> perfect_tail(N, 1, 0).
perfect_tail(N, N, N) -> true;
perfect_tail(N, N, _) -> false;
perfect_tail(N, Div, Acc) when N rem Div == 0 -> perfect_tail(N, Div+1, Acc+Div);
perfect_tail(N, Div, Acc) -> perfect_tail(N, Div+1, Acc).

second.erl

-module(second).
-export([hypo/2, peri/2, area/2]).

hypo(A,B) ->
  first:square(A*A + B*B).

peri(A,B) ->
  A + B + hypo(A,B).

area(A,B) ->
  (A*B)/2.