Assignment 1 of Functional Programming in Erlang

-module(assignment).
-export([dr_bits/1, bits/1, bits/2, perimeter/1, area/1, enclose/1]).

% Shapes
% Define a function perimeter/1 which takes a shape and
% returns the perimeter of the shape.
% Choose a suitable representation of triangles,
% and augment area/1 and perimeter/1 to handle this case too.
% Define a function enclose/1 that takes a shape and returns the
% smallest enclosing rectangle of the shape.
perimeter({circle, {_,_}, R}) -> 2*math:pi()*R;
perimeter({triangle, {_,_}, E1, E2, E3}) -> E1 + E2 + E3;
perimeter({rectangle,{_,_}, Base, Height}) -> Base * 2 + Height * 2.

area({circle, {_,_}, R}) -> math:pi()*R*R;
area({triangle, {_,_}, E1, E2, E3}) ->
    P = (E1 + E2 + E3) / 2,
    math:sqrt(P*(P-E1)*(P-E2)*(P-E3));
area({rectangle,{_,_}, Base, Height}) -> Base * Height.

enclose({circle, {X,Y}, R}) -> {rectangle,{X,Y}, R, R};
enclose({triangle, {X,Y}, E1, E2, E3}) ->
    Base = E1, % take a side as a base,
    Height = 2 * area({triangle, {X,Y}, E1, E2, E3}) / Base,
    {rectangle, {Base/2, Height/2}, Base, Height};
enclose({rectangle,{X,Y}, Base, Height}) -> {rectangle,{X,Y}, Base, Height}.

% Bits
% Define a function bits/1 that takes a positive integer N and
% returns the sum of the bits in the binary representation.
% For example bits(7) is 3 and bits(8) is 1.
% See whether you can make both a direct recursive and a tail recursive definition.

% Direct recursive bit implementation
dr_bits(N) when N =< 0 ->
    "";
dr_bits(N) when N > 0 ->
    dr_bits(N div 2) ++ integer_to_list(N rem 2).

% Tail recursive bit implementation
bits(N, Acc) when N =< 0 ->
    Acc;
bits(N, Acc) when N > 0 ->
    bits(N div 2, integer_to_list(N rem 2) ++ Acc).

bits(N) -> bits(N, "").