Calkin-Wilf sequence: Difference between revisions
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83116/51639 is at index: 123456789
</pre>
=={{header|Vlang}}==
{{trans|Go}}s.
<lang vlang>import math.fractions
import math
import strconv
fn calkin_wilf(n int) []fractions.Fraction {
mut cw := []fractions.Fraction{len: n+1}
cw[0] = fractions.fraction(1, 1)
one := fractions.fraction(1, 1)
two := fractions.fraction(2, 1)
for i in 1..n {
mut t := cw[i-1]
mut f := t.f64()
f = math.floor(f)
t = fractions.approximate(f)
t*=two
t-= cw[i-1]
t+=one
t=t.reciprocal()
cw[i] = t
}
return cw
}
fn to_continued(r fractions.Fraction) []int {
idx := r.str().index('/') or {0}
mut a := r.str()[..idx].i64()
mut b := r.str()[idx+1..].i64()
mut res := []int{}
for {
res << int(a/b)
t := a % b
a, b = b, t
if a == 1 {
break
}
}
le := res.len
if le%2 == 0 { // ensure always odd
res[le-1]--
res << 1
}
return res
}
fn get_term_number(cf []int) ?int {
mut b := ""
mut d := "1"
for n in cf {
b = d.repeat(n)+b
if d == "1" {
d = "0"
} else {
d = "1"
}
}
i := strconv.parse_int(b, 2, 64)?
return int(i)
}
fn commatize(n int) string {
mut s := "$n"
if n < 0 {
s = s[1..]
}
le := s.len
for i := le - 3; i >= 1; i -= 3 {
s = s[0..i] + "," + s[i..]
}
if n >= 0 {
return s
}
return "-" + s
}
fn main() {
cw := calkin_wilf(20)
println("The first 20 terms of the Calkin-Wilf sequnence are:")
for i := 1; i <= 20; i++ {
println("${i:2}: ${cw[i-1]}")
}
println('')
r := fractions.fraction(83116, 51639)
cf := to_continued(r)
tn := get_term_number(cf) or {0}
println("$r is the ${commatize(tn)}th term of the sequence.")
}</lang>
{{out}}
<pre>
The first 20 terms of the Calkin-Wilf sequnence are:
1: 1/1
2: 1/2
3: 2/1
4: 1/3
5: 3/2
6: 2/3
7: 3/1
8: 1/4
9: 4/3
10: 3/5
11: 5/2
12: 2/5
13: 5/3
14: 3/4
15: 4/1
16: 1/5
17: 5/4
18: 4/7
19: 7/3
20: 3/8
83116/51639 is the 123,456,789th term of the sequence.
</pre>
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