De Bruijn sequences: Difference between revisions
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:* An OEIS entry: [https://oeis.org/A166315 A166315 lexicographically earliest binary de Bruijn sequences, B(2,n)] --- Not B(10,4), but possibly relevant.
<br><br>
=={{header|Go}}==
<lang go>package main
import (
"bytes"
"fmt"
"strconv"
"strings"
)
const digits = "0123456789"
func deBruijn(k, n int) string {
alphabet := digits[0:k]
a := make([]byte, k*n)
var seq []byte
var db func(int, int) // recursive closure
db = func(t, p int) {
if t > n {
if n%p == 0 {
seq = append(seq, a[1:p+1]...)
}
} else {
a[t] = a[t-p]
db(t+1, p)
for j := int(a[t-p] + 1); j < k; j++ {
a[t] = byte(j)
db(t+1, t)
}
}
}
db(1, 1)
var buf bytes.Buffer
for _, i := range seq {
buf.WriteByte(alphabet[i])
}
b := buf.String()
return b + b[0:n-1] // as cyclic append first (n-1) digits
}
func allDigits(s string) bool {
for _, b := range s {
if b < '0' || b > '9' {
return false
}
}
return true
}
func validate(db string) {
le := len(db)
found := make([]int, 10000)
var errs []string
// Check all strings of 4 consecutive digits within 'db'
// to see if all 10,000 combinations occur without duplication.
for i := 0; i < le-3; i++ {
s := db[i : i+4]
if allDigits(s) {
n, _ := strconv.Atoi(s)
found[n]++
}
}
for i := 0; i < 10000; i++ {
if found[i] == 0 {
errs = append(errs, fmt.Sprintf(" PIN number %04d missing", i))
} else if found[i] > 1 {
errs = append(errs, fmt.Sprintf(" PIN number %04d occurs %d times", i, found[i]))
}
}
lerr := len(errs)
if lerr == 0 {
fmt.Println(" No errors found")
} else {
pl := "s"
if lerr == 1 {
pl = ""
}
fmt.Printf(" %d error%s found:\n", lerr, pl)
fmt.Println(strings.Join(errs, "\n"))
}
}
func reverse(s string) string {
bytes := []byte(s)
for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
bytes[i], bytes[j] = bytes[j], bytes[i]
}
return string(bytes)
}
func main() {
db := deBruijn(10, 4)
le := len(db)
fmt.Println("The length of the de Bruijn sequence is", le)
fmt.Println("\nThe first 130 digits of the de Bruijn sequence are:")
fmt.Println(db[0:130])
fmt.Println("\nThe last 130 digits of the de Bruijn sequence are:")
fmt.Println(db[le-130:])
fmt.Println("\nValidating the de Bruijn sequence:")
validate(db)
fmt.Println("\nValidating the reversed de Bruijn sequence:")
dbr := reverse(db)
validate(dbr)
bytes := []byte(db)
bytes[4443] = '.'
db = string(bytes)
fmt.Println("\nValidating the overlaid de Bruijn sequence:")
validate(db)
}</lang>
{{out}}
<pre>
The length of the de Bruijn sequence is 10003
The first 130 digits of the de Bruijn sequence are:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350
The last 130 digits of the de Bruijn sequence are:
6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000
Validating the de Bruijn sequence:
No errors found
Validating the reversed de Bruijn sequence:
No errors found
Validating the overlaid de Bruijn sequence:
4 errors found:
PIN number 1459 missing
PIN number 4591 missing
PIN number 5814 missing
PIN number 8145 missing
</pre>
=={{header|Perl 6}}==
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