Lah numbers: Difference between revisions
added RPL
(added RPL) |
|||
| (4 intermediate revisions by 3 users not shown) | |||
Line 87:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
</pre>
=={{header|ABC}}==
<syntaxhighlight lang="abc">HOW TO RETURN fac n:
PUT 1 IN result
FOR i IN {1..n}: PUT result*i IN result
RETURN result
HOW TO RETURN n lah k:
SELECT:
n=k: RETURN 1
n=0 OR k=0: RETURN 0
k=1: RETURN fac n
ELSE: RETURN (((fac n)*fac(n-1)) / ((fac k)*fac(k-1)) )/ fac(n-k)
HOW TO SHOW LAH TABLE UP TO N nmax:
FOR n IN {0..nmax}:
FOR k IN {0..n}:
WRITE (n lah k)>>11
WRITE /
HOW TO RETURN max.lah.number n:
PUT 0 IN max
FOR k IN {0..n}:
PUT n lah k IN cur
IF cur>max: PUT cur IN max
RETURN max
SHOW LAH TABLE UP TO N 12
WRITE /
WRITE "Maximum value where n=100:"/
WRITE max.lah.number 100/</syntaxhighlight>
{{out}}
<pre> 0 1
0 2 1
0 6 6 1
0 24 36 12 1
0 120 240 120 20 1
0 720 1800 1200 300 30 1
0 5040 15120 12600 4200 630 42 1
0 40320 141120 141120 58800 11760 1176 56 1
0 362880 1451520 1693440 846720 211680 28224 2016 72 1
0 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1
0 39916800 199584000 299376000 199584000 69854400 13970880 1663200 118800 4950 110 1
0 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1
Maximum value where n=100:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000</pre>
=={{header|ALGOL 68}}==
Line 845 ⟶ 893:
'''Case 1. Using the routine, generate and show a table showing the signed Lah numbers, L(n, k), up to L(12, 12)'''
[[File:Fōrmulæ - Lah numbers
[[File:Fōrmulæ - Lah numbers 03.png]]
Line 851 ⟶ 899:
'''Case 2. Using the routine, generate and show a table showing the unsigned Lah numbers, L(n, k), up to L(12, 12)'''
[[File:Fōrmulæ - Lah numbers
[[File:Fōrmulæ - Lah numbers 05.png]]
Line 1,939 ⟶ 1,987:
The maximum value (which has 164 decimal digits):
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
</pre>
=={{header|RPL}}==
'''Using local variables'''
« → n k
« '''CASE'''
n k == '''THEN''' 1 '''END'''
n k * NOT '''THEN''' 0 '''END'''
k 1 == '''THEN''' n FACT '''END'''
n 1 - k - 1 COMB n FACT * k FACT /
'''END'''
» » '<span style="color:blue">ULAH</span>' STO
'''Using the stack'''
« '''CASE'''
DUP2 == '''THEN''' DROP2 1 '''END'''
DUP2 * NOT '''THEN''' * '''END'''
DUP 1 == '''THEN''' DROP FACT '''END'''
DUP2 1 - SWAP 1 - SWAP COMB ROT FACT * SWAP FACT /
'''END'''
» '<span style="color:blue">ULAH</span>' STO
« { 12 12 } 0 CON
1 12 '''FOR''' n
1 n '''FOR''' k
n k 2 →LIST n k <span style="color:blue">ULAH</span> PUT
'''NEXT NEXT'''
» '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: [[ 1 0 0 0 0 0 0 0 0 0 0 0 ]
[ 2 1 0 0 0 0 0 0 0 0 0 0 ]
[ 6 6 1 0 0 0 0 0 0 0 0 0 ]
[ 24 36 12 1 0 0 0 0 0 0 0 0 ]
[ 120 240 120 20 1 0 0 0 0 0 0 0 ]
[ 720 1800 1200 300 30 1 0 0 0 0 0 0 ]
[ 5040 15120 12600 4200 630 42 1 0 0 0 0 0 ]
[ 40320 141120 141120 58800 11760 1176 56 1 0 0 0 0 ]
[ 362880 1451520 1693440 846720 211680 28224 2016 72 1 0 0 0 ]
[ 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1 0 0 ]
[ 39916800 199584000 299376000 199584000 69854400 13970880 1663200 118800 4950 110 1 0 ]
[ 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1 ]]
</pre>
Line 1,986 ⟶ 2,075:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
</pre>
=={{header|Scheme}}==
{{works with|Chez Scheme}}
Line 2,040 ⟶ 2,130:
The maximum value of L(n, k) where n = 100:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000</pre>
=={{header|SETL}}==
<syntaxhighlight lang="setl">program lah_numbers;
loop for n in [0..12] do
loop for k in [0..n] do
nprint(lpad(str lah(n,k), 11));
end loop;
print;
end loop;
print("Maximum value for lah(100,k):");
print(max/[lah(100,k) : k in [1..100]]);
op fac(n);
return */{1..n};
end op;
proc lah(n,k);
case of
(n=k): return 1;
(n=0 or k=0): return 0;
(k=1): return fac n;
else return (fac n*fac (n-1)) div
(fac k*fac (k-1)) div
fac (n-k);
end case;
end proc;
end program;</syntaxhighlight>
{{out}}
<pre> 1
0 1
0 2 1
0 6 6 1
0 24 36 12 1
0 120 240 120 20 1
0 720 1800 1200 300 30 1
0 5040 15120 12600 4200 630 42 1
0 40320 141120 141120 58800 11760 1176 56 1
0 362880 1451520 1693440 846720 211680 28224 2016 72 1
0 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1
0 39916800 199584000 299376000 199584000 69854400 13970880 1663200 118800 4950 110 1
0 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1
Maximum value for lah(100,k):
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000</pre>
Line 2,537 ⟶ 2,671:
=={{header|Wren}}==
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
var fact = Fn.new { |n|
Line 2,556 ⟶ 2,690:
System.print("Unsigned Lah numbers: l(n, k):")
System.write("n/k")
for (i in 0..12)
System.print("\n" + "-" * 145)
for (n in 0..12) {
for (k in 0..n)
System.print()
}</syntaxhighlight>
| |||