Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -11,10 +11,10 @@ F lah(BigInt n, BigInt k)
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print(‘Unsigned Lah numbers: L(n, k):’)
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print(‘n/k ’, end' ‘ ’)
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L(i) 13
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L(i) 0.<13
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print(‘#11’.format(i), end' ‘ ’)
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print()
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L(row) 13
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L(row) 0.<13
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print(‘#<4’.format(row), end' ‘ ’)
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L(i) 0 .. row
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V l = lah(row, i)
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@ -1,70 +0,0 @@
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-- Rosetta Code Task written in Ada
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-- Lah numbers
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-- https://rosettacode.org/wiki/Lah_numbers
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-- (Mostly) translated from the AWK example
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-- Proper formatting of the Big Integers would be nice.
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-- Not important here, but in general, the factorials should be cached for greater performance.
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-- Could use alternate libraries for large integers...
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-- January 2025, R. B. E.
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-- Using GNAT Big Integers, GNAT version 14.2, MacOS 15.3, M1 chip
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pragma Ada_2022;
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with Ada.Text_IO; use Ada.Text_IO;
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with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
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with Ada.Numerics.Big_Numbers.Big_Integers; use Ada.Numerics.Big_Numbers.Big_Integers;
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procedure Lah_Numbers is
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function Factorial (F : Natural) return Big_Positive is
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Prod : Big_Positive := To_Big_Integer (1);
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begin
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for I in reverse 2..F loop
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Prod := Prod * To_Big_Integer (I);
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end loop;
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return Prod;
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end Factorial;
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function Lah (N, K : Natural) return Big_Natural is
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begin
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if (K = 1) then
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return Factorial (N);
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end if;
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if (K = N) then
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return (To_Big_Integer (1));
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end if;
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if (K > N) then
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return (To_Big_Integer (0));
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end if;
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if ((K < 1) or (N < 1)) then
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return (To_Big_Integer (0));
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end if;
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return (Factorial (N) * Factorial (N-1)) / (Factorial (K) * Factorial (K-1)) / Factorial (N-K);
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end Lah;
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Biggest_Lah_Number_in_Row_100 : Big_Natural := To_Big_Integer (0);
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Candidate_Biggest_Lah_Number_in_Row_100 : Big_Positive;
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begin
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Put_Line ("unsigned Lah numbers: L(n,k)");
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Put ("n/k");
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for I in 0..12 loop
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Put (I, 3);
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end loop;
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New_Line;
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for Row in 0..12 loop
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Put (Row, 2);
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for Col in 0..Row loop
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Put (To_String (Lah (Row, Col)));
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end loop;
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New_Line;
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end loop;
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New_Line;
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for Col in 0..12 loop
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Candidate_Biggest_Lah_Number_in_Row_100 := Lah (100, Col);
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if Biggest_Lah_Number_in_Row_100 < Candidate_Biggest_Lah_Number_in_Row_100 then
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Biggest_Lah_Number_in_Row_100 := Candidate_Biggest_Lah_Number_in_Row_100;
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end if;
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end loop;
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Put_Line ("Maximum value of L(n,k) where n = 100:");
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Put_Line (To_String (Biggest_Lah_Number_in_Row_100));
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end Lah_Numbers;
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@ -1,8 +1,6 @@
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func fac n .
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r = 1
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for i = 2 to n
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r *= i
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.
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for i = 2 to n : r *= i
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return r
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.
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print 0
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@ -1,44 +1,42 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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with javascript_semantics
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include mpfr.e
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<span style="color: #008080;">constant</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">lim1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lim</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">12</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim1</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lim1</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #004080;">mpz</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m100</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
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<span style="color: #7060A8;">mpz_fdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
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<span style="color: #7060A8;">mpz_fdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
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<span style="color: #7060A8;">mpz_fdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Unsigned Lah numbers: l(n, k):\n n k:"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">last</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%6d "</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n--- %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">*</span><span style="color: #000000;">11</span><span style="color: #0000FF;">+</span><span style="color: #000000;">6</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">last</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d "</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%10s "</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim1</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">l100k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lim1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l100k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m100</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">></span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l100k</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nThe maximum l(100,k): %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m100</span><span style="color: #0000FF;">)))</span>
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<!--
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constant lim = 100,
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lim1 = lim+1,
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last = 12
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sequence l = repeat(0,lim1)
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for n=1 to lim1 do
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l[n] = mpz_inits(lim1)
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mpz_set_si(l[n][n],1)
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if n!=2 then
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mpz_fac_ui(l[n][2],n-1)
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end if
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end for
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mpz {t, m100} = mpz_inits(2)
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for n=1 to lim do
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for k=1 to n do
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mpz_mul(t,l[n+1][2],l[n][2])
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mpz_fdiv_q(t, t, l[k+1][2])
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mpz_fdiv_q(t, t, l[k][2])
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mpz_fdiv_q(l[n+1][k+1], t, l[n-k+1][2])
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end for
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end for
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printf(1,"Unsigned Lah numbers: l(n, k):\n n k:")
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for i=0 to last do
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printf(1,"%6d ", i)
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end for
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printf(1,"\n--- %s\n",repeat('-',last*11+6))
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for n=0 to last do
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printf(1,"%2d ", n)
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for k=1 to n+1 do
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printf(1,"%10s ",{mpz_get_str(l[n+1][k])})
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end for
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printf(1,"\n")
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end for
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for k=1 to lim1 do
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mpz l100k = l[lim1][k]
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if mpz_cmp(l100k,m100) > 0 then
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mpz_set(m100,l100k)
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end if
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end for
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printf(1,"\nThe maximum l(100,k): %s\n",shorten(mpz_get_str(m100)))
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@ -1,53 +0,0 @@
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' Lah numbers - VBScript - 04/02/2021
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Function F(i,n)
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Dim c: c=CCur(i): If n>Len(c) Then F=Space(n-Len(c))&c Else F=c
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End Function 'F
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Function Fact(ByVal n)
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Dim res
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If n=0 Then
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Fact = 1
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Else
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res = 1
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While n>0
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res = res*n
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n = n-1
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Wend
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Fact = res
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End If
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End Function 'Fact
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Function Lah(n, k)
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If k=1 Then
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Lah = Fact(n)
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ElseIf k=n Then
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Lah = 1
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ElseIf k>n Then
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Lah=0
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ElseIf k < 1 Or n < 1 Then
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Lah = 0
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Else
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Lah = (Fact(n) * Fact(n-1)) / (Fact(k) * Fact(k-1)) / Fact(n-k)
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End If
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End Function 'Lah
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Sub Main()
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ns=12: p=10
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WScript.Echo "Unsigned Lah numbers: Lah(n,k):"
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buf = "n/k "
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For k=1 To ns
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buf = buf & F(k,p) & " "
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Next 'k
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WScript.Echo buf
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For n=1 To ns
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buf = F(n,3) & " "
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For k=1 To n
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l = Lah(n,k)
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buf = buf & F(l,p) & " "
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Next 'k
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WScript.Echo buf
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Next 'n
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End Sub 'Main
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Main()
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