Binomial transform: Difference between revisions
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=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
'''Works with both jq and gojq, the C and Go implementations of jq'''
<syntaxhighlight lang=jq>
# nCk assuming n >= k
def binomial(n; k):
if k > n / 2 then binomial(n; n-k)
else reduce range(1; k+1) as $i (1; . * (n - $i + 1) / $i)
end;
def forward:
. as $a
| ($a|length) as $c
| reduce range(0;$c) as $n (null;
reduce range(0;$n+1) as $k (.;
.[$n] += binomial($n; $k) * $a[$k] ) );
def inverse:
. as $b
| ($b|length) as $c
| reduce range (0;$c) as $n (null;
reduce range(0; $n+1) as $k (.;
(if (($n - $k) % 2 == 0) then 1 else -1 end) as $sign
| .[$n] += binomial($n; $k) * $b[$k] * $sign ));
def selfInverting:
. as $a
| ($a|length) as $c
| reduce range(0;$c) as $n (null;
reduce range(0; $n+1) as $k (.;
(if $k % 2 == 0 then 1 else -1 end) as $sign
| .[$n] += binomial($n; $k) * $a[$k] * $sign ));
def seqs: [
[1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190],
[0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0],
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181],
[1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37]
];
def names: [
"Catalan number sequence:",
"Prime flip-flop sequence:",
"Fibonacci number sequence:",
"Padovan number sequence:"
];
def task:
range(0; seqs|length) as $i
| names[$i],
(seqs[$i]|join(" ")),
"Forward binomial transform:",
( (seqs[$i]|forward)
| join(" "),
"Inverse binomial transform:",
((seqs[$i]|inverse)|join(" ")),
"Round trip:",
(inverse|join(" ")) ),
"Self-inverting:",
( (seqs[$i]|selfInverting)
| join(" "),
"Re-inverted:",
(selfInverting|join(" ")) ),
(select($i < (seqs|length - 1) ) | "") ;
task
</syntaxhighlight>
{{output}}
Exactly as at [[#Wren|Wren]].
=={{header|Julia}}==
| |||