EKG sequence convergence: Difference between revisions
Ada version
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EKG(5) and EKG(7) converge at index 21
</pre>
=={{header|Ada}}==
{{trans|Go}}
<lang Ada>with Ada.Text_IO;
with Ada.Containers.Generic_Array_Sort;
procedure EKG_Sequences is
type Element_Type is new Integer;
type Index_Type is new Integer range 1 .. 100;
subtype Show_Range is Index_Type range 1 .. 30;
type Sequence is array (Index_Type range <>) of Element_Type;
subtype EKG_Sequence is Sequence (Index_Type);
function GCD (Left, Right : Element_Type) return Integer is
A : Element_Type := Left;
B : Element_Type := Right;
begin
while A /= B loop
if A > B
then A := A - B;
else B := B - A;
end if;
end loop;
return Integer (A);
end GCD;
function Contains (A : Sequence;
B : Element_Type;
Last : Index_Type) return Boolean
is (for some Value of A (A'First .. Last) => Value = B);
function Are_Same (S, T : EKG_Sequence; Last : Index_Type) return Boolean is
S_Copy : Sequence := S (S'First .. Last);
T_Copy : Sequence := T (T'First .. Last);
procedure Sort is
new Ada.Containers.Generic_Array_Sort (Index_Type => Index_Type,
Element_Type => Element_Type,
Array_Type => Sequence);
begin
Sort (S_Copy);
Sort (T_Copy);
return S_Copy = T_Copy;
end Are_Same;
function Create_EKG (Start : Element_Type) return EKG_Sequence is
EKG : EKG_Sequence := (1 => 1, 2 => Start, others => 0);
begin
for N in 3 .. Index_Type'Last loop
for I in 2 .. Element_Type'Last loop
-- A potential sequence member cannot already have been used
-- and must have a factor in common with previous member
if not Contains (EKG, I, N)
and then GCD (EKG (N - 1), I) > 1
then
EKG (N) := I;
exit;
end if;
end loop;
end loop;
return EKG;
end Create_EKG;
procedure Converge (Seq_A, Seq_B : Sequence;
Term : out Index_Type;
Do_Converge : out Boolean) is
begin
for I in 3 .. Index_Type'Last loop
if Seq_A (I) = Seq_B (I) and then Are_Same (Seq_A, Seq_B, I) then
Do_Converge := True;
Term := I;
return;
end if;
end loop;
Do_Converge := False;
Term := Index_Type'Last;
end Converge;
procedure Put (Seq : Sequence) is
use Ada.Text_IO;
begin
Put ("[");
for E of Seq (Show_Range) loop
Put (E'Image);
end loop;
Put ("]");
end Put;
use Ada.Text_IO;
EKG_2 : constant EKG_Sequence := Create_EKG (2);
EKG_5 : constant EKG_Sequence := Create_EKG (5);
EKG_7 : constant EKG_Sequence := Create_EKG (7);
EKG_9 : constant EKG_Sequence := Create_EKG (9);
EKG_10 : constant EKG_Sequence := Create_EKG (10);
begin
Put ("EKG( 2): "); Put (EKG_2); New_Line;
Put ("EKG( 5): "); Put (EKG_5); New_Line;
Put ("EKG( 7): "); Put (EKG_7); New_Line;
Put ("EKG( 9): "); Put (EKG_9); New_Line;
Put ("EKG(10): "); Put (EKG_10); New_Line;
-- Now compare EKG5 and EKG7 for convergence
declare
Term : Index_Type;
Do_Converge : Boolean;
begin
Converge (EKG_5, EKG_7, Term, Do_Converge);
New_Line;
if Do_Converge then
Put_Line ("EKG(5) and EKG(7) converge at term "
& Term'Image);
else
Put_Line ("EKG5(5) and EKG(7) do not converge within "
& Term'Image & " terms");
end if;
end;
end EKG_Sequences;</lang>
{{out}}
<pre>
EKG( 2): [ 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36]
EKG( 5): [ 1 5 10 2 4 6 3 9 12 8 14 7 21 15 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32]
EKG( 7): [ 1 7 14 2 4 6 3 9 12 8 10 5 15 18 16 20 22 11 33 21 24 26 13 39 27 30 25 35 28 32]
EKG( 9): [ 1 9 3 6 2 4 8 10 5 15 12 14 7 21 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32]
EKG(10): [ 1 10 2 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32]
EKG(5) and EKG(7) converge at term 21
</pre>
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