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Ingy döt Net 2026-02-01 16:33:20 -08:00
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Task/Lah-numbers/Ada/lah-numbers.ada
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-- Rosetta Code Task written in Ada
-- Lah numbers
-- https://rosettacode.org/wiki/Lah_numbers
-- (Mostly) translated from the AWK example
-- Proper formatting of the Big Integers would be nice.
-- Not important here, but in general, the factorials should be cached for greater performance.
-- Could use alternate libraries for large integers...
-- January 2025, R. B. E.
-- Using GNAT Big Integers, GNAT version 14.2, MacOS 15.3, M1 chip
pragma Ada_2022;
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Ada.Numerics.Big_Numbers.Big_Integers; use Ada.Numerics.Big_Numbers.Big_Integers;
procedure Lah_Numbers is
function Factorial (F : Natural) return Big_Positive is
Prod : Big_Positive := To_Big_Integer (1);
begin
for I in reverse 2..F loop
Prod := Prod * To_Big_Integer (I);
end loop;
return Prod;
end Factorial;
function Lah (N, K : Natural) return Big_Natural is
begin
if (K = 1) then
return Factorial (N);
end if;
if (K = N) then
return (To_Big_Integer (1));
end if;
if (K > N) then
return (To_Big_Integer (0));
end if;
if ((K < 1) or (N < 1)) then
return (To_Big_Integer (0));
end if;
return (Factorial (N) * Factorial (N-1)) / (Factorial (K) * Factorial (K-1)) / Factorial (N-K);
end Lah;
Biggest_Lah_Number_in_Row_100 : Big_Natural := To_Big_Integer (0);
Candidate_Biggest_Lah_Number_in_Row_100 : Big_Positive;
begin
Put_Line ("unsigned Lah numbers: L(n,k)");
Put ("n/k");
for I in 0..12 loop
Put (I, 3);
end loop;
New_Line;
for Row in 0..12 loop
Put (Row, 2);
for Col in 0..Row loop
Put (To_String (Lah (Row, Col)));
end loop;
New_Line;
end loop;
New_Line;
for Col in 0..12 loop
Candidate_Biggest_Lah_Number_in_Row_100 := Lah (100, Col);
if Biggest_Lah_Number_in_Row_100 < Candidate_Biggest_Lah_Number_in_Row_100 then
Biggest_Lah_Number_in_Row_100 := Candidate_Biggest_Lah_Number_in_Row_100;
end if;
end loop;
Put_Line ("Maximum value of L(n,k) where n = 100:");
Put_Line (To_String (Biggest_Lah_Number_in_Row_100));
end Lah_Numbers;