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Catalan numbers: Difference between revisions
added Liberty BASIC
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catalan'!:15
1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440</lang>
=={{header|Liberty BASIC}}==
<lang lb>
print "non-recursive version"
print catNonRec(5)
for i = 0 to 15
print i;" = "; catNonRec(i)
next
print
print "recursive version"
print catRec(5)
for i = 0 to 15
print i;" = "; catRec(i)
next
print
print "recursive with memoisation"
redim cats(20) 'clear the array
print catRecMemo(5)
for i = 0 to 15
print i;" = "; catRecMemo(i)
next
print
wait
function catNonRec(n) 'non-recursive version
catNonRec=1
for i=1 to n
catNonRec=((2*((2*i)-1))/(i+1))*catNonRec
next
end function
function catRec(n) 'recursive version
if n=0 then
catRec=1
else
catRec=((2*((2*n)-1))/(n+1))*catRec(n-1)
end if
end function
function catRecMemo(n) 'recursive version with memoisation
if n=0 then
catRecMemo=1
else
if cats(n-1)=0 then 'call it recursively only if not already calculated
prev = catRecMemo(n-1)
else
prev = cats(n-1)
end if
catRecMemo=((2*((2*n)-1))/(n+1))*prev
end if
cats(n) = catRecMemo 'memoisation for future use
end function
</lang>
Output:
<pre>
non-recursive version
42
0 = 1
1 = 1
2 = 2
3 = 5
4 = 14
5 = 42
6 = 132
7 = 429
8 = 1430
9 = 4862
10 = 16796
11 = 58786
12 = 208012
13 = 742900
14 = 2674440
15 = 9694845
recursive version
42
0 = 1
1 = 1
2 = 2
3 = 5
4 = 14
5 = 42
6 = 132
7 = 429
8 = 1430
9 = 4862
10 = 16796
11 = 58786
12 = 208012
13 = 742900
14 = 2674440
15 = 9694845
recursive with memoisation
42
0 = 1
1 = 1
2 = 2
3 = 5
4 = 14
5 = 42
6 = 132
7 = 429
8 = 1430
9 = 4862
10 = 16796
11 = 58786
12 = 208012
13 = 742900
14 = 2674440
15 = 9694845</pre>
=={{header|Mathematica}}==
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