-module(assignment1).
-export([perimeter/1, area/1, enclose/1, bits/1, directBits/1]).

%%%ASSIGNEMENT ABOUT perimeter, area and enclose functions

perimeter({'circle', {_X,_Y}, R}) -> (R+R)*math:pi();
perimeter({'rectangle', {_X,_Y}, H,W}) -> (H+W)*2;
perimeter({'triangle', {_X,_Y}, A,B,C}) -> A+B+C.

area({'circle', {_X,_Y}, R}) -> (R*R)*math:pi();
area({'rectangle', {_X,_Y}, H,W}) -> (H*W);
area({'triangle', {_X,_Y}, A,B,C}) -> triangleArea(A,B,C).

enclose({'circle', {X,Y}, R}) -> {'rectangle', {X,Y}, R*2,R*2};
enclose({'rectangle', {X,Y}, H,W}) -> {'rectangle', {X,Y}, H,W};
enclose(Triangle={'triangle', {X,Y}, A,B,C}) ->
MaxSide = max(max(A,B),C),
TriangleHeight = 2*area(Triangle)/MaxSide, %retrieving triangle height
{'rectangle', {X,Y}, MaxSide,TriangleHeight}.


%Heron's formula to calculate triangle area
triangleArea(A,B,C) ->
  S = (A+B+C)/2,
  math:sqrt(S*(S-A)*(S-B)*(S-C)).


%%%HERE COMES THE ASSIGNMENT ABOUT BITS%%%

%this is the exposed function
bits(NUMBER) ->
  %first, transform the input number to a boolean value, then invoke the recursive function
  recursiveBits(integer_to_list(NUMBER,2), 0).

  %%%TAIL RECURSIVE FUNCTION%%%
  %%%It works as follow:
  %%%unit case: if the list in input is empty, returns the accumulated value of bits
  %%%when the list is not empty and its head value is '1' bit, call the recursive function increasing the number of bits
  %%%otherwise call the recursive function over the tail of the list.
  recursiveBits([], BITS) -> BITS;
  recursiveBits(LIST, BITS) when hd(LIST) == 49 -> recursiveBits(tl(LIST),BITS+1);
  recursiveBits(LIST, BITS) -> recursiveBits(tl(LIST),BITS).


directBits(NUMBER) ->
  N = integer_to_list(NUMBER,2),
  directRecursiveBits(N).


%%%DIRECT RECURSIVE BITS%%%
%%%It is a recursion function that does not use any accumulator.
%%%Maybe in this exercise the drawback in using a direct recursive approach are not so big because of
%%&the generally small size of the list to iterate on.
directRecursiveBits([]) -> 0;
directRecursiveBits(LIST) when (length(LIST) == 1) and (hd(LIST) == 49) -> 1;
directRecursiveBits(LIST) when hd(LIST) == 49 -> 1 + directRecursiveBits(tl(LIST));
directRecursiveBits(LIST) -> directRecursiveBits(tl(LIST)).