Binomial transform: Difference between revisions
Added Wren
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Round trip:
1 0 0 1 0 1 1 1 2 2 3 4 5 7 9 12 16 21 28 37</pre>
=={{header|Wren}}==
{{libheader|Wren-long}}
This hard-codes the sequences to be tested as I couldn't see much point in repeating code from the related tasks.
<syntaxhighlight lang="ecmascript">import "./math" for Int
import "./long" for Long, ULong
class BT {
static forward(a) {
var c = a.count
var b = List.filled(c, null)
for (n in 0...c) {
var sum = ULong.zero
for (k in 0..n) sum = sum + ULong.binomial(n, k) * a[k]
b[n] = sum.toNum
}
return b
}
static inverse(b) {
var c = b.count
var a = List.filled(c, null)
for (n in 0...c) {
var sum = Long.zero
for (k in 0..n) {
var sign = (-1).pow(n-k)
sum = sum + ULong.binomial(n, k).toLong * b[k] * sign
a[n] = sum.toNum
}
}
return a
}
}
var 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]
]
var names = [
"Catalan number sequence:",
"Prime flip-flop sequence:",
"Fibonacci number sequence:",
"Padovan number sequence:"
]
var fwd
for (i in 0...seqs.count) {
System.print(names[i])
System.print(seqs[i].join(" "))
System.print("Forward binomial transform:")
System.print((fwd = BT.forward(seqs[i])).join(" "))
System.print("Inverse binomial transform:")
System.print(BT.inverse(seqs[i]).join(" "))
System.print("Round trip:")
System.print(BT.inverse(fwd).join(" "))
if (i < seqs.count - 1) System.print()
}</syntaxhighlight>
{{out}}
<pre>
Catalan number sequence:
1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 477638700 1767263190
Forward binomial transform:
1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 8140539950 37463689775 173164232965
Inverse binomial transform:
1 0 1 1 3 6 15 36 91 232 603 1585 4213 11298 30537 83097 227475 625992 1730787 4805595
Round trip:
1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 477638700 1767263190
Prime flip-flop sequence:
0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0
Forward binomial transform:
0 1 3 6 11 20 37 70 134 255 476 869 1564 2821 5201 9948 19793 40562 84271 174952
Inverse binomial transform:
0 1 -1 0 3 -10 25 -56 118 -237 456 -847 1540 -2795 5173 -9918 19761 -40528 84235 -174914
Round trip:
0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0
Fibonacci number sequence:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181
Forward binomial transform:
0 1 3 8 21 55 144 377 987 2584 6765 17711 46368 121393 317811 832040 2178309 5702887 14930352 39088169
Inverse binomial transform:
0 1 -1 2 -3 5 -8 13 -21 34 -55 89 -144 233 -377 610 -987 1597 -2584 4181
Round trip:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181
Padovan number sequence:
1 0 0 1 0 1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
Forward binomial transform:
1 1 1 2 5 12 28 65 151 351 816 1897 4410 10252 23833 55405 128801 299426 696081 1618192
Inverse binomial transform:
1 -1 1 0 -3 10 -24 49 -89 145 -208 245 -174 -176 1121 -3185 7137 -13920 24301 -37926
Round trip:
1 0 0 1 0 1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
</pre>
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