hwork.erl

-module(hwork1).
-export([area/1,perimeter/1,enclose/1,bits/1,bits_tail/1]).


max_three(X,Y,Z)->	      
    max(max(X,Y),Z).

area({circle,{_X,_Y},R})->
    math:pi()*R*R;
area({rectangle,{_X,_Y},H,W}) -> 
    H*W;
area({triangle,{_X,_Y},A,B,C})->
    P = perimeter({triangle,{_X,_Y},A,B,C})/2,
    math:sqrt(P*(P-A)*(P-B)*(P-C)).%Heron's formula

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

enclose({circle,{X,Y},R})->
    {rectangle,{X,Y},2*R,2*R};
enclose({rectangle,{X,Y},H,W})->
    {rectangle,{X,Y},H,W};
enclose({triangle,{X,Y},A,B,C}) ->
    W = max_three(A,B,C),
    H = 2*area({triangle,{X,Y},A,B,C})/W,
    {rectangle,{X,Y},H,W}.
%I am cheating here as the center of the triangle is defined as the center of the 
% coresponding rectangle and I am not sure how to get the center of the rectangle from the 
% centroid or some other center of the triangle.

bits(0) ->
    0;
bits(N) ->
    bits(N div 2)+N rem 2.

%The tail-recursive version

bits_tail(N)->
    bits_tail_acc(N,0).

bits_tail_acc(0,Acc)->
    Acc;
bits_tail_acc(N,Acc) ->
    bits_tail_acc(N div 2, Acc + (N rem 2)).