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@Arnauld
Last active Feb 27, 2017
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-module(shabits).
-author("Arnauld").
%% ------------------------------------------------------------------
%% API Function Exports
%% ------------------------------------------------------------------
-export([perimeter/1, area/1, enclose/1]).
-export([bits/1, bits_tailrec/1]).
%% ------------------------------------------------------------------
%% API Function Definitions
%% ------------------------------------------------------------------
%
% All shapes are identified by the coordinates of their characterics points.
%
perimeter({triangle, A = {_Xa, _Ya}, B = {_Xb, _Yb}, C = {_Xc, _Yc}}) ->
distance(A, B) + distance(B, C) + distance(C, A);
perimeter({rectangle, A = {Xmin, Ymin}, _C = {Xmax, Ymax}}) ->
% ^
% |
% x...D-----------C
% | | |
% x...A-----------B
% | : :
% +---x-----------x--------->
%
B = {Xmax, Ymin},
D = {Xmin, Ymax},
2 * (distance(A, D) + distance(A, B)).
area({triangle, A = {_Xa, _Ya}, B = {_Xb, _Yb}, C = {_Xc, _Yc}}) ->
% Heron's formula
DA = distance(A, B),
DB = distance(B, C),
DC = distance(C, A),
S = (DA + DB + DC) / 2,
math:sqrt(S * (S - DA) * (S - DB) * (S - DC));
area({rectangle, A = {Xmin, Ymin}, {Xmax, Ymax}}) ->
B = {Xmax, Ymin},
D = {Xmin, Ymax},
distance(A, D) * distance(A, B).
enclose({triangle, {X1, Y1}, {X2, Y2}, {X3, Y3}}) ->
%
% A...................Ymax
% _,.-'"\
% _,.-'" \
% _,.-'" \
% _,.-'" \
% C ('-._ \
% : '-._ \
% : '-._ \
% : '-._ \
% : '-._ \
% : '-._ \
% : '-:_ \
% : '-._ \
% : '-._)B......Ymin
% : :
% Xmin Xmax
{Xmin, Xmax} = min_max([X1, X2, X3], X1, X1),
{Ymin, Ymax} = min_max([Y1, Y2, Y3], Y1, Y1),
{rectangle, {Xmin, Ymin}, {Xmax, Ymax}};
enclose(Rectangle = {rectangle, _A, _C}) ->
Rectangle.
% distance between two points characterized by their coordinates {X,Y}
distance({X1, Y1}, {X2, Y2}) ->
DX = (X2 - X1),
DY = (Y2 - Y1),
math:sqrt(DX * DX + DY * DY).
% returns the minimum and the maximum of a list of numbers.
min_max([], Min, Max) -> {Min, Max};
min_max([X | XS], Min, Max) when X < Min -> min_max(XS, X, Max);
min_max([X | XS], Min, Max) when X > Max -> min_max(XS, Min, X);
min_max([_ | XS], Min, Max) -> min_max(XS, Min, Max).
bits(N) when is_integer(N), N >= 0 ->
bits0(N).
bits0(0) -> 0;
bits0(N) -> (N band 2#1) + bits0(N bsr 1).
% Accumulator
% 0
% 010001001 & 1 = 1 1 010001001 >> 1 = 01000100
% 01000100 & 1 = 0 1 01000100 >> 1 = 0100010
% 0100010 & 1 = 0 1 0100010 >> 1 = 010001
% 010001 & 1 = 1 2 010001 >> 1 = 01000
% ...
bits_tailrec(N) when is_integer(N), N >= 0 ->
bits_tailrec(N, 0).
bits_tailrec(0, Acc) -> Acc;
bits_tailrec(N, Acc) -> bits_tailrec(N bsr 1, (N band 2#1) + Acc).
% -------------------------------------
% TEST
% -------------------------------------
%
% eunit:test(shabits).
%
-include_lib("eunit/include/eunit.hrl").
distance_test() ->
?assertEqual(4.0, distance({0, 0}, {4, 0})),
?assertEqual(math:sqrt(2), distance({0, 0}, {1, 1})).
min_max_test() ->
?assertEqual({0, 0}, min_max([], 0, 0)),
?assertEqual({1, 2}, min_max([1], 2, 2)),
?assertEqual({2, 12}, min_max([4, 5, 6, 2, 11, 7, 12, 11], 4, 4)).
perimeter_test() ->
?assertEqual(1.0 * (3 + 3 + 4 + 4), perimeter({rectangle, {0, 0}, {3, 4}})),
?assertEqual(1.0 * (3 + 4 + 5), perimeter({triangle, {0, 0}, {3, 0}, {0, 4}})).
area_test() ->
?assertEqual(1.0 * (3 * 4), area({rectangle, {0, 0}, {3, 4}})),
?assertEqual(0.5 * (3 * 4), area({triangle, {0, 0}, {3, 0}, {0, 4}})).
enclose_test() ->
?assertEqual({rectangle, {0, 0}, {3, 4}}, enclose({rectangle, {0, 0}, {3, 4}})),
?assertEqual({rectangle, {0, 0}, {3, 4}}, enclose({triangle, {0, 0}, {3, 0}, {0, 4}})).
bits_test() ->
?assertEqual(0, bits(2#0)),
?assertEqual(1, bits(2#1)),
?assertEqual(3, bits(2#111)),
?assertEqual(4, bits(2#100011100)).
bits_tailrec_test() ->
?assertEqual(0, bits_tailrec(2#0)),
?assertEqual(1, bits_tailrec(2#1)),
?assertEqual(3, bits_tailrec(2#111)),
?assertEqual(4, bits_tailrec(2#100011100)).
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