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2011 changed files with 35081 additions and 3229 deletions
109
Task/Weird-numbers/Ada/weird-numbers-1.ada
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109
Task/Weird-numbers/Ada/weird-numbers-1.ada
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pragma Ada_2022;
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with Ada.Text_IO;
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with Ada.Containers.Vectors;
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with Ada.Containers.Ordered_Sets;
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procedure Weird_Numbers is
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package IO renames Ada.Text_IO;
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-- allows us to type "IO.Put_Line" instead of "Ada.Text_IO.Put_Line"
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package IntVecs is new Ada.Containers.Vectors
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(Index_Type => Positive, Element_Type => Natural);
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subtype IntVec is IntVecs.Vector;
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-- use all type IntVec;
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Factor_Cache : IntVec;
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-- used to keep track of the factors on each iteration
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package Intsets is new Ada.Containers.Ordered_Sets
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(Element_Type => Positive);
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subtype Intset is Intsets.Set;
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Semiperfect_Cache : Intset;
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Not_Abundant_Cache : Intset;
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function Proper_Divisors (Value : Positive) return IntVec is
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Cofactors : IntVec;
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begin
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Factor_Cache.Clear;
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begin
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Factor_Cache.Append (1);
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for Factor in 2 .. Value / 2 loop
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if Value rem Factor = 0 then
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Factor_Cache.Append (Factor);
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end if;
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end loop;
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return Factor_Cache;
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end;
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end Proper_Divisors;
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function Is_Abundant (Value : Positive) return Boolean is
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begin
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if Not_Abundant_Cache.Contains (Value)
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or else Semiperfect_Cache.Contains (Value)
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then
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return False;
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end if;
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if Proper_Divisors (Value)'Reduce ("+", 0) > Value then
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return True;
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end if;
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Not_Abundant_Cache.Insert (Value);
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return False;
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end Is_Abundant;
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function Subset_Of (Factors : IntVec; Ith : Positive) return IntVec is
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-- returns the Ith subset of Factors
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-- if Factors has N elements, then there are 2**N possibilities
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-- this maps Ith to one of these possibilities using its binary representation
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Result : IntVec;
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Index : Natural := 1;
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Ith_Remainder : Natural := Ith;
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begin
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while Ith_Remainder /= 0 loop
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if Ith_Remainder rem 2 = 1 then
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Result.Append (Factors (Index));
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Ith_Remainder := @ - 1;
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end if;
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Ith_Remainder := @ / 2;
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Index := @ + 1;
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end loop;
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return Result;
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end Subset_Of;
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function Is_Semiperfect (Value : Positive) return Boolean is
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Factors : constant IntVec := Factor_Cache;
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Subset : IntVec;
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Sum : Natural;
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begin
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if (for some Previous of Semiperfect_Cache => Value rem Previous = 0)
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then
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return True;
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end if;
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for Ith in reverse 1 .. (2**Positive (Factors.Length) - 1) loop
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Subset := Subset_Of (Factors, Positive (Ith));
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Sum := Subset'Reduce ("+", 0);
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if Sum = Value then
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Semiperfect_Cache.Insert (Value);
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return True;
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end if;
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end loop;
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return False;
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end Is_Semiperfect;
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function Is_Weird (Value : Positive) return Boolean is
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(Is_Abundant (Value) and then not Is_Semiperfect (Value));
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Current : Positive := 2;
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Number_Found : Natural := 0;
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begin
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IO.Put ("The first 25 weird numbers are");
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while Number_Found < 25 loop
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if Is_Weird (Current * 2) then
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IO.Put (Integer'Image (Current * 2));
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Number_Found := @ + 1;
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end if;
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Current := @ + 1;
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end loop;
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IO.New_Line;
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end Weird_Numbers;
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105
Task/Weird-numbers/Ada/weird-numbers-2.ada
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105
Task/Weird-numbers/Ada/weird-numbers-2.ada
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@ -0,0 +1,105 @@
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pragma Ada_2022;
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with Ada.Text_IO;
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with Ada.Containers.Vectors;
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with Ada.Containers.Ordered_Sets;
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procedure Weird_Numbers is
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package IO renames Ada.Text_IO;
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package IntVecs is new Ada.Containers.Vectors
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(Index_Type => Positive, Element_Type => Positive);
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subtype IntVec is IntVecs.Vector;
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use all type IntVec;
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Factor_Cache : IntVec;
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package Intsets is new Ada.Containers.Ordered_Sets
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(Element_Type => Positive);
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subtype Intset is Intsets.Set;
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Semiperfect_Cache : Intset;
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Not_Abundant_Cache : Intset;
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function Proper_Divisors (Value : Positive) return IntVec is
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Cofactors : IntVec;
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begin
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Factor_Cache.Clear;
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begin
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Factor_Cache.Append (1);
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for Factor in 2 .. Value / 2 loop
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if Factor * Factor > Value then
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exit;
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end if;
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if Value rem Factor = 0 then
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Factor_Cache.Append (Factor);
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if Factor * Factor /= Value then
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Cofactors.Append (Value / Factor);
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end if;
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end if;
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end loop;
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Factor_Cache.Prepend_Vector (Cofactors);
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-- this ordering is REALLY curious
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-- for instance, the factors of 12 are ordered as 6, 4, 1, 2, 3
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-- AND THIS MATTERS
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-- both strictly ascending and strictly descending orders are much slower
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return Factor_Cache;
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end;
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end Proper_Divisors;
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function Is_Abundant (Value : Positive) return Boolean is
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begin
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if Not_Abundant_Cache.Contains (Value)
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or else Semiperfect_Cache.Contains (Value)
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then
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return False;
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end if;
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if Proper_Divisors (Value)'Reduce ("+", 0) > Value then
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return True;
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end if;
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Not_Abundant_Cache.Insert (Value);
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return False;
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end Is_Abundant;
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function Alternate_Semiperfect (Value : Positive) return Boolean is
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function Reroute
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(Value : Positive; First : Positive) return Boolean
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is
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Head : Positive;
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begin
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if Factor_Cache.Last_Index >= First then
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Head := Factor_Cache (First);
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if Value < Head then
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return Reroute (Value, First + 1);
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else
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return
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Value = Head
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or else Reroute (Value - Head, First + 1)
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or else Reroute (Value, First + 1);
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end if;
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else
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return False;
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end if;
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end Reroute;
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begin
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return
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Reroute
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(Value, Factor_Cache.First_Index);
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end Alternate_Semiperfect;
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function Is_Weird (Value : Positive) return Boolean is
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(Is_Abundant (Value) and then not Alternate_Semiperfect (Value));
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Current : Positive := 2;
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Number_Found : Natural := 0;
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begin
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IO.Put ("The first 25 weird numbers are");
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while Number_Found < 25 loop
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if Is_Weird (Current * 2) then
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IO.Put (Integer'Image (Current * 2));
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Number_Found := @ + 1;
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end if;
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Current := @ + 1;
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end loop;
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IO.New_Line;
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end Weird_Numbers;
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51
Task/Weird-numbers/Python/weird-numbers-2.py
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51
Task/Weird-numbers/Python/weird-numbers-2.py
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@ -0,0 +1,51 @@
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# anySum :: Int -> [Int] -> [Int]
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from time import time
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start = time()
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primitivesp_nos = set(); primes = []
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def main():
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x = 2; weird_nos = []
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n = 50
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while n > 0:
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if isweird(x) == 1: weird_nos.append(x); n = n - 1
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x = x + 1
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print("First", len(weird_nos), "weird nos:\n", weird_nos)
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def isweird(n):
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global primes; global primitivesp_nos; pr_fctrs = []; a = n
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for i in primes:
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while a % i == 0: pr_fctrs.append(i); a = a//i
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if i * i > a: break
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if a > 1: pr_fctrs.append(a)
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if a == n: primes.append(n); return 0
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sum_fctrs = 1; divisors = set(pr_fctrs)
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for i in divisors: sum_fctrs = sum_fctrs*(i**(pr_fctrs.count(i)+1)-1)//(i-1)
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difference = sum_fctrs - 2 * n
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if difference <= 0:
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if difference == 0: primitivesp_nos.add(n)
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return 0
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# Next 10 lines from Jerome Richard: stackoverflow.com/questions/6800193
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divisors = [1]; last_prime = 0; fctr = 0; slice_len = 0
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for prime in pr_fctrs:
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if last_prime != prime: slice_len = len(divisors); fctr = prime
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else: fctr *= prime
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for i in range(slice_len):
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d = divisors[i] * fctr
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if d not in primitivesp_nos: divisors.append(d)
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else: return 0
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last_prime = prime
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x = 1; divisors = set(i for i in divisors if i <= difference)
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ns = n - (difference + n - sum(divisors))
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if ns < 0: return 1
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for d in divisors: x |= x << d
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if x >> ns & 1: primitivesp_nos.add(n); return 0
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else: return 1
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main()
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end = time()
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print("Execution time: ", round(end - start, 2), "s")
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-- -> [100,96]
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85
Task/Weird-numbers/Uxntal/weird-numbers.uxnatl
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85
Task/Weird-numbers/Uxntal/weird-numbers.uxnatl
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@ -0,0 +1,85 @@
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( uxncli weird.rom )
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|10 @Console &vector $2 &read $1 &pad $5 &write $1 &error $1
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%MOD2 { DIV2k MUL2 SUB2 }
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|0000
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@c $2
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@n $2
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@i $1
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|0100
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( init )
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;str ptext #0a .Console/write DEO
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( main )
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#000c
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&sieve
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#0000 .c STZ2
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DUP2 DUP2 .n STZ2 divisors
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abundance ?{ semiperfection }
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clear
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INC2 .i LDZ #19 LTH ?&sieve
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POP2
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BRK
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@pdec ( short* -- )
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#2710 [ LIT2r 00fb ]
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&while ( -- )
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DIV2k #000a DIV2k MUL2 SUB2 SWPr EQUk OVR STHkr EQU AND ?{
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DUP [ LIT "0 ] ADD #19 DEO
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INCr }
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POP2 #000a DIV2 SWPr INCr STHkr ?&while
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POP2r POP2 POP2 JMP2r
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@ptext ( str* -- )
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&while
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LDAk .Console/write DEO
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INC2 LDAk ?&while
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POP2
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JMP2r
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@divisors ( short* -- )
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#0000
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&loop
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OVR2 OVR2 MOD2 #0000 GTH2 ?{ DUP2 ;divs .c LDZ2 STH2k ADD2 STA2 STH2r INC2 INC2 .c STZ2 }
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INC2 GTH2k ?&loop POP2 POP2
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JMP2r
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@abundance ( -- flag )
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#0000 STH2
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;divs
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&while
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LDA2k STH2 ADD2r
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#0002 ADD2
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LDA2k NIP ?&while
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POP2
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STH2r .n LDZ2 GTH2 ?{ #01 JMP2r } #00 ( returns 1 when not abundant to skip semiperfection check in main )
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JMP2r
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@semiperfection ( -- )
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#0001 ;divs .c LDZ2 ADD2 STA2
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#0000
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&for
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.n LDZ2
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&loop
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OVR2 OVR2 SWP2 #0002 MUL2 ;divs ADD2 LDA2 SUB2 #0002 MUL2
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;divs .c LDZ2 ADD2 ADD2 LDA2
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#0000 EQU2 ?{ #0001 OVR2 #0002 MUL2 ;divs .c LDZ2 ADD2 ADD2 STA2 }
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#0001 SUB2
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OVR2 #0002 MUL2 ;divs ADD2 LDA2 GTH2k STH EQU2k STHr ORA NIP NIP ?&loop POP2
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INC2 DUP2 .c LDZ2 #0002 DIV2 LTH2 ?&for POP2
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;divs .c LDZ2 ADD2 .n LDZ2 #0002 MUL2 ADD2 LDA2 NIP ?{ .n LDZ2 pdec #20 #18 DEO .i LDZk INC SWP STZ JMP2r }
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JMP2r
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@clear ( -- )
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;divs
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.n LDZ2 .c LDZ2 ADD2
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&while
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SWP2 #0000 SWP2 STA2k NIP2
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INC2 INC2
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SWP2 #0001 SUB2 #0000 GTH2k NIP NIP ?&while POP2 POP2
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JMP2r
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@str "The 20 "first 20 "25 20 "weird 20 "numbers: 00
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@divs
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