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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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