Vampire number
A vampire number is a natural decimal number with an even number of digits, that can be factored into two integers.
You are encouraged to solve this task according to the task description, using any language you may know.
These two factors are called the fangs, and must have the following properties:
- they each contain half the number of the decimal digits of the original number
- together they consist of exactly the same decimal digits as the original number
- at most one of them has a trailing zero
An example of a vampire number and its fangs: 1260 : (21, 60)
- Task
- Print the first 25 vampire numbers and their fangs.
- Check if the following numbers are vampire numbers and, if so, print them and their fangs:
16758243290880, 24959017348650, 14593825548650
Note that a vampire number can have more than one pair of fangs.
- See also
11l
-V Pow10 = (0..18).map(n -> Int64(10) ^ n)
F isOdd(n)
R (n [&] 1) != 0
F fangs(n)
[(Int64, Int64)] r
V nDigits = sorted(String(n))
I isOdd(nDigits.len)
R r
V fangLen = nDigits.len I/ 2
V inf = Pow10[fangLen - 1]
L(d) inf .< inf * 10
I n % d != 0
L.continue
V q = n I/ d
I q < d
R r
V dDigits = String(d)
V qDigits = String(q)
I qDigits.len > fangLen
L.continue
I qDigits.len < fangLen
R r
I nDigits != sorted(dDigits‘’qDigits)
L.continue
I dDigits.last != ‘0’ | qDigits.last != ‘0’
r.append((d, q))
R r
print(‘First 25 vampire numbers with their fangs:’)
V count = 0
V n = 10
V limit = 100
L count != 25
V fangList = fangs(n)
I !fangList.empty
count++
print((‘#2: #6 =’.format(count, n))‘ ’fangList.map(it -> ‘#3 x #3’.format(it[0], it[1])).join(‘ = ’))
n++
I n == limit
n *= 10
limit *= 10
print()
L(n) [16'758'243'290'880, 24'959'017'348'650, 14'593'825'548'650]
V fangList = fangs(n)
I fangList.empty
print(n‘ is not vampiric.’)
E
print(n‘ = ’fangList.map(it -> ‘#. x #.’.format(it[0], it[1])).join(‘ = ’))- Output:
First 25 vampire numbers with their fangs: 1: 1260 = 21 x 60 2: 1395 = 15 x 93 3: 1435 = 35 x 41 4: 1530 = 30 x 51 5: 1827 = 21 x 87 6: 2187 = 27 x 81 7: 6880 = 80 x 86 8: 102510 = 201 x 510 9: 104260 = 260 x 401 10: 105210 = 210 x 501 11: 105264 = 204 x 516 12: 105750 = 150 x 705 13: 108135 = 135 x 801 14: 110758 = 158 x 701 15: 115672 = 152 x 761 16: 116725 = 161 x 725 17: 117067 = 167 x 701 18: 118440 = 141 x 840 19: 120600 = 201 x 600 20: 123354 = 231 x 534 21: 124483 = 281 x 443 22: 125248 = 152 x 824 23: 125433 = 231 x 543 24: 125460 = 204 x 615 = 246 x 510 25: 125500 = 251 x 500 16758243290880 = 1982736 x 8452080 = 2123856 x 7890480 = 2751840 x 6089832 = 2817360 x 5948208 24959017348650 = 2947050 x 8469153 = 2949705 x 8461530 = 4125870 x 6049395 = 4129587 x 6043950 = 4230765 x 5899410 14593825548650 is not vampiric.
AutoHotkey
The following code should work for older (1.0.*) AHK versions as well:
SetBatchLines -1 ; used to improve performance
; (you can make it much faster by removing the informative tooltips)
;********************
; CONFIG
;********************
StartingNumber := 10
NumberLimit := 126030
CounterLimit := 25 ; calculations stop when one of these limits is reached
AdditionalNumbers := "16758243290880,24959017348650,14593825548650"
;********************
CurrentCounter := 0, CurrentNumber := StartingNumber
Loop {
if !Mod(A_Index,75) ; informative tooltip (every 75 calculations, to avoid slowing down)
ToolTip, % "Checking numbers...`nNumber: " CurrentNumber
. "/" NumberLimit "`nFound: " CurrentCounter "/" CounterLimit
if ( CurrentCounter >= CounterLimit ) || ( CurrentNumber >= NumberLimit )
Break
if Mod(StrLen(CurrentNumber),2)
CurrentNumber *= 10
else if ( ( CurrentResult := GetFangs(CurrentNumber) ) <> "" )
Output .= "`n" CurrentNumber ":`t" CurrentResult, CurrentCounter++
CurrentNumber++
}
ToolTip ; hide informative tooltip
MsgBox % SubStr(Output,2) ; show output (first part)
Output := ""
Loop, Parse, AdditionalNumbers, % ","
{
ToolTip, % "Getting fangs for " A_LoopField " ..." ; informative tooltip
Output .= "`n" A_LoopField ":`n`t" GetFangs(A_LoopField) "`n"
}
ToolTip ; hide informative tooltip
MsgBox % SubStr(Output,2) ; show output (second part - additional numbers)
ExitApp
;----------------------------------------------------------------------------------
CharSorter(Input) { ; required by GetFangs()
Loop, Parse, Input
Output .= A_LoopField "`n"
Sort, Output
StringReplace, Output, Output, % "`n",, All
Return Output
}
;----------------------------------------------------------------------------------
GetFangs(CurrentNumber) { ; requires CharSorter()
ResultIndex := 1
Length := StrLen(CurrentNumber)
Power := (Length//2)-1
if Mod(Length,2) OR !Power
Return ""
NumberLimit := Floor(Sqrt(CurrentNumber))
Lower := 10 ** Power
Loop, % NumberLimit - Lower {
if !Mod(CurrentNumber,Lower) {
FactorTwo := CurrentNumber//Lower
if ( !Mod(Lower,10) && !Mod(FactorTwo,10) )
Return ""
Check := CharSorter( Lower . FactorTwo )
if (CharSorter(CurrentNumber) = Check) && (StrLen(Lower) = StrLen(FactorTwo))
Output .= "`n`t[" Lower "," FactorTwo "]"
}
Lower++
}
Return SubStr(Output,3) ; 3 = 1 + length of "`n`t"
}
- Output:
1260: [21,60] 1395: [15,93] 1435: [35,41] 1530: [30,51] 1827: [21,87] 2187: [27,81] 6880: [80,86] 102510: [201,510] 104260: [260,401] 105210: [210,501] 105264: [204,516] 105750: [150,705] 108135: [135,801] 110758: [158,701] 115672: [152,761] 116725: [161,725] 117067: [167,701] 118440: [141,840] 123354: [231,534] 124483: [281,443] 125248: [152,824] 125433: [231,543] 125460: [204,615] [246,510] 125500: [251,500] 126027: [201,627] ------------------------------------ 16758243290880: [1982736,8452080] [2123856,7890480] [2751840,6089832] [2817360,5948208] 24959017348650: [2947050,8469153] [2949705,8461530] [4125870,6049395] [4129587,6043950] [4230765,5899410] 14593825548650:
AWK
function H(n,i, d, h) {
h=!split(n,d,X)
asort(d)
for(i in d)h=h d[i]
return h
}
BEGIN{
for(n=1000;n<=1000000;n++){
if(split(n,d,X)%2)continue
l=length(n)
if(l%2)break
A=0
t=l/2
for(f=10^(t-1);f<=int(sqrt(n));f++)
if((n%f==0&&g=n/f)&&(length(f)==t&&length(g)==t&&!(f%10==0&&g%10==0)&&H(f g)==H(n)&&A=1))break
if(A)print n
}
}
Bracmat
( ( vampire
= N len R fangsList
. !arg:@(?N:? [?len)
& 1/2*!len:~/:?len
& ( R
= len numpart left right allowed fangs rdigits
, tried digit untried head tail found
. !arg:(?len.?left.?numpart.?allowed)
& :?found
& ( !len:>0
& ( @( !numpart
: ?tried
( #%@?digit
& !allowed:?head !digit ?tail
& !head !tail:?allowed
)
( ?untried
& R
$ ( !len+-1
. 10*!left+!digit
. str$(!tried !untried)
. 0 1 2 3 4 5 6 7 8 9
)
: ?fangs
& !found !fangs:?found
& ~
)
)
| !found
)
| !N*!left^-1:~/?right:~<!left:?rdigits
& (!left*1/10:/|!right*1/10:/)
& ( @( !numpart
: ?
( #%@?digit ?
& @(!rdigits:?head !digit ?tail)
& str$(!head !tail):?rdigits
& ~
)
)
| !rdigits:&(!left,!right)
)
)
)
& R$(!len.0.!N.1 2 3 4 5 6 7 8 9)
: (
| ?fangsList
& out$(!N !fangsList)
& 1+!count:?count
)
)
& 0:?count
& 10:?i
& 16758243290880 24959017348650 14593825548650:?bignums
& whl
' ( ( vampire$!i&1+!i:?i
| !i*10:?i
)
& (!count:<25|!bignums:%?i ?bignums)
)
);Output:
1260 (21,60) 1395 (15,93) 1435 (35,41) 1530 (30,51) 1827 (21,87) 2187 (27,81) 6880 (80,86) 102510 (201,510) 104260 (260,401) 105210 (210,501) 105264 (204,516) 105750 (150,705) 108135 (135,801) 110758 (158,701) 115672 (152,761) 116725 (161,725) 117067 (167,701) 118440 (141,840) 120600 (201,600) 123354 (231,534) 124483 (281,443) 125248 (152,824) 125433 (231,543) 125460 (246,510) (204,615) 125500 (251,500) 16758243290880 (1982736,8452080) (2123856,7890480) (2751840,6089832) (2817360,5948208) 24959017348650 (2949705,8461530) (2947050,8469153) (4230765,5899410) (4129587,6043950) (4125870,6049395)
C
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <math.h>
typedef uint64_t xint;
typedef unsigned long long ull;
xint tens[20];
inline xint max(xint a, xint b) { return a > b ? a : b; }
inline xint min(xint a, xint b) { return a < b ? a : b; }
inline int ndigits(xint x)
{
int n = 0;
while (x) n++, x /= 10;
return n;
}
inline xint dtally(xint x)
{
xint t = 0;
while (x) t += 1<<((x%10) * 6), x /= 10;
return t;
}
int fangs(xint x, xint *f)
{
int n = 0;
int nd = ndigits(x);
if (nd & 1) return 0;
nd /= 2;
xint lo, hi;
lo = max(tens[nd-1], (x + tens[nd] - 2)/ (tens[nd] - 1));
hi = min(x / lo, sqrt(x));
xint a, b, t = dtally(x);
for (a = lo; a <= hi; a++) {
b = x / a;
if (a * b == x && ((a%10) || (b%10)) && t == dtally(a) + dtally(b))
f[n++] = a;
}
return n;
}
void show_fangs(xint x, xint *f, xint cnt)
{
printf("%llu", (ull)x);
int i;
for (i = 0; i < cnt; i++)
printf(" = %llu x %llu", (ull)f[i], (ull)(x / f[i]));
putchar('\n');
}
int main(void)
{
int i, j, n;
xint x, f[16], bigs[] = {16758243290880ULL, 24959017348650ULL, 14593825548650ULL, 0};
tens[0] = 1;
for (i = 1; i < 20; i++)
tens[i] = tens[i-1] * 10;
for (x = 1, n = 0; n < 25; x++) {
if (!(j = fangs(x, f))) continue;
printf("%2d: ", ++n);
show_fangs(x, f, j);
}
putchar('\n');
for (i = 0; bigs[i]; i++) {
if ((j = fangs(bigs[i], f)))
show_fangs(bigs[i], f, j);
else
printf("%llu is not vampiric\n", (ull)bigs[i]);
}
return 0;
}
1: 1260 = 21 x 60 2: 1395 = 15 x 93 3: 1435 = 35 x 41 4: 1530 = 30 x 51 5: 1827 = 21 x 87 6: 2187 = 27 x 81 7: 6880 = 80 x 86 8: 102510 = 201 x 510 9: 104260 = 260 x 401 10: 105210 = 210 x 501 11: 105264 = 204 x 516 12: 105750 = 150 x 705 13: 108135 = 135 x 801 14: 110758 = 158 x 701 15: 115672 = 152 x 761 16: 116725 = 161 x 725 17: 117067 = 167 x 701 18: 118440 = 141 x 840 19: 120600 = 201 x 600 20: 123354 = 231 x 534 21: 124483 = 281 x 443 22: 125248 = 152 x 824 23: 125433 = 231 x 543 24: 125460 = 204 x 615 = 246 x 510 25: 125500 = 251 x 500 16758243290880 = 1982736 x 8452080 = 2123856 x 7890480 = 2751840 x 6089832 = 2817360 x 5948208 24959017348650 = 2947050 x 8469153 = 2949705 x 8461530 = 4125870 x 6049395 = 4129587 x 6043950 = 4230765 x 5899410 14593825548650 is not vampiric
C#
using System;
namespace RosettaVampireNumber
{
class Program
{
static void Main(string[] args)
{
int i, j, n;
ulong x;
var f = new ulong[16];
var bigs = new ulong[] { 16758243290880UL, 24959017348650UL, 14593825548650UL, 0 };
ulong[] tens = new ulong[20];
tens[0] = 1;
for (i = 1; i < 20; i++)
tens[i] = tens[i - 1] * 10;
for (x = 1, n = 0; n < 25; x++)
{
if ((j = fangs(x, f, tens)) == 0) continue;
Console.Write(++n + ": ");
show_fangs(x, f, j);
}
Console.WriteLine();
for (i = 0; bigs[i] > 0 ; i++)
{
if ((j = fangs(bigs[i], f, tens)) > 0)
show_fangs(bigs[i], f, j);
else
Console.WriteLine(bigs[i] + " is not vampiric.");
}
Console.ReadLine();
}
private static void show_fangs(ulong x, ulong[] f, int cnt)
{
Console.Write(x);
int i;
for (i = 0; i < cnt; i++)
Console.Write(" = " + f[i] + " * " + (x / f[i]));
Console.WriteLine();
}
private static int fangs(ulong x, ulong[] f, ulong[] tens)
{
int n = 0;
int nd = ndigits(x);
if ((nd & 1) > 0) return 0;
nd /= 2;
ulong lo, hi;
lo = Math.Max(tens[nd - 1], (x + tens[nd] - 2) / (tens[nd] - 1));
hi = Math.Min(x / lo, (ulong) Math.Sqrt(x));
ulong a, b, t = dtally(x);
for (a = lo; a <= hi; a++)
{
b = x / a;
if (a * b == x && ((a % 10) > 0 || (b % 10) > 0) && t == dtally(a) + dtally(b))
f[n++] = a;
}
return n;
}
private static ulong dtally(ulong x)
{
ulong t = 0;
while (x > 0)
{
t += 1UL << (int)((x % 10) * 6);
x /= 10;
}
return t;
}
private static int ndigits(ulong x)
{
int n = 0;
while (x > 0)
{
n++;
x /= 10;
}
return n;
}
}
}
- Output:
1: 1260 = 21 * 60 2: 1395 = 15 * 93 3: 1435 = 35 * 41 4: 1530 = 30 * 51 5: 1827 = 21 * 87 6: 2187 = 27 * 81 7: 6880 = 80 * 86 8: 102510 = 201 * 510 9: 104260 = 260 * 401 10: 105210 = 210 * 501 11: 105264 = 204 * 516 12: 105750 = 150 * 705 13: 108135 = 135 * 801 14: 110758 = 158 * 701 15: 115672 = 152 * 761 16: 116725 = 161 * 725 17: 117067 = 167 * 701 18: 118440 = 141 * 840 19: 120600 = 201 * 600 20: 123354 = 231 * 534 21: 124483 = 281 * 443 22: 125248 = 152 * 824 23: 125433 = 231 * 543 24: 125460 = 204 * 615 = 246 * 510 25: 125500 = 251 * 500 16758243290880 = 1982736 * 8452080 = 2123856 * 7890480 = 2751840 * 6089832 = 2817360 * 5948208 24959017348650 = 2947050 * 8469153 = 2949705 * 8461530 = 4125870 * 6049395 = 4129587 * 6043950 = 4230765 * 5899410 14593825548650 is not vampiric.
C++
#include <vector>
#include <utility>
#include <algorithm>
#include <iostream>
#include <sstream>
#include <string>
#include <cmath>
bool isVampireNumber( long number, std::vector<std::pair<long, long> > & solution ) {
std::ostringstream numberstream ;
numberstream << number ;
std::string numberstring( numberstream.str( ) ) ;
std::sort ( numberstring.begin( ) , numberstring.end( ) ) ;
int fanglength = numberstring.length( ) / 2 ;
long start = static_cast<long>( std::pow( 10 , fanglength - 1 ) ) ;
long end = sqrt(number) ;
for ( long i = start ; i <= end ; i++ ) {
if ( number % i == 0 ) {
long quotient = number / i ;
if ( ( i % 10 == 0 ) && ( quotient % 10 == 0 ) )
continue ;
numberstream.str( "" ) ; //clear the number stream
numberstream << i << quotient ;
std::string divisorstring ( numberstream.str( ) ) ;
std::sort ( divisorstring.begin( ) , divisorstring.end( ) ) ;
if ( divisorstring == numberstring ) {
std::pair<long , long> divisors = std::make_pair( i, quotient ) ;
solution.push_back( divisors ) ;
}
}
}
return !solution.empty( ) ;
}
void printOut( const std::pair<long, long> & solution ) {
std::cout << "[ " << solution.first << " , " << solution.second << " ]" ;
}
int main( ) {
int vampireNumbersFound = 0 ;
std::vector<std::pair<long , long> > solutions ;
double i = 1.0 ;
while ( vampireNumbersFound < 25 ) {
long start = static_cast<long>( std::pow( 10 , i ) ) ;
long end = start * 10 ;
for ( long num = start ; num < end ; num++ ) {
if ( isVampireNumber( num , solutions ) ) {
vampireNumbersFound++ ;
std::cout << vampireNumbersFound << " :" << num << " is a vampire number! These are the fangs:\n" ;
std::for_each( solutions.begin( ) , solutions.end( ) , printOut ) ;
std::cout << "\n_______________" << std::endl ;
solutions.clear( ) ;
if ( vampireNumbersFound == 25 )
break ;
}
}
i += 2.0 ;
}
std::vector<long> testnumbers ;
testnumbers.push_back( 16758243290880 ) ;
testnumbers.push_back( 24959017348650 ) ;
testnumbers.push_back( 14593825548650 ) ;
for ( std::vector<long>::const_iterator svl = testnumbers.begin( ) ;
svl != testnumbers.end( ) ; svl++ ) {
if ( isVampireNumber( *svl , solutions ) ) {
std::cout << *svl << " is a vampire number! The fangs:\n" ;
std::for_each( solutions.begin( ) , solutions.end( ) , printOut ) ;
std::cout << std::endl ;
solutions.clear( ) ;
} else {
std::cout << *svl << " is not a vampire number!" << std::endl ;
}
}
return 0 ;
}
- Output:
1 :1260 is a vampire number! These are the fangs: [ 21 , 60 ] _______________ 2 :1395 is a vampire number! These are the fangs: [ 15 , 93 ] _______________ 3 :1435 is a vampire number! These are the fangs: [ 35 , 41 ] _______________ 4 :1530 is a vampire number! These are the fangs: [ 30 , 51 ] _______________ 5 :1827 is a vampire number! These are the fangs: [ 21 , 87 ] _______________ 6 :2187 is a vampire number! These are the fangs: [ 27 , 81 ] _______________ 7 :6880 is a vampire number! These are the fangs: [ 80 , 86 ] _______________ 8 :102510 is a vampire number! These are the fangs: [ 201 , 510 ] _______________ 9 :104260 is a vampire number! These are the fangs: [ 260 , 401 ] _______________ 10 :105210 is a vampire number! These are the fangs: [ 210 , 501 ] _______________ 11 :105264 is a vampire number! These are the fangs: [ 204 , 516 ] _______________ 12 :105750 is a vampire number! These are the fangs: [ 150 , 705 ] _______________ 13 :108135 is a vampire number! These are the fangs: [ 135 , 801 ] _______________ 14 :110758 is a vampire number! These are the fangs: [ 158 , 701 ] _______________ 15 :115672 is a vampire number! These are the fangs: [ 152 , 761 ] _______________ 16 :116725 is a vampire number! These are the fangs: [ 161 , 725 ] _______________ 17 :117067 is a vampire number! These are the fangs: [ 167 , 701 ] _______________ 18 :118440 is a vampire number! These are the fangs: [ 141 , 840 ] _______________ 19 :120600 is a vampire number! These are the fangs: [ 201 , 600 ] _______________ 20 :123354 is a vampire number! These are the fangs: [ 231 , 534 ] _______________ 21 :124483 is a vampire number! These are the fangs: [ 281 , 443 ] _______________ 22 :125248 is a vampire number! These are the fangs: [ 152 , 824 ] _______________ 23 :125433 is a vampire number! These are the fangs: [ 231 , 543 ] _______________ 24 :125460 is a vampire number! These are the fangs: [ 204 , 615 ][ 246 , 510 ] _______________ 25 :125500 is a vampire number! These are the fangs: [ 251 , 500 ] _______________ 16758243290880 is a vampire number! The fangs: [ 1982736 , 8452080 ][ 2123856 , 7890480 ][ 2751840 , 6089832 ][ 2817360 , 5948208 ] 24959017348650 is a vampire number! The fangs: [ 2947050 , 8469153 ][ 2949705 , 8461530 ][ 4125870 , 6049395 ][ 4129587 , 6043950 ][ 4230765 , 5899410 ] 14593825548650 is not a vampire number!
Clojure
(defn factor-pairs [n]
(for [x (range 2 (Math/sqrt n))
:when (zero? (mod n x))]
[x (quot n x)]))
(defn fangs [n]
(let [dlen (comp count str)
half (/ (dlen n) 2)
halves? #(apply = (cons half (map dlen %)))
digits #(sort (apply str %))]
(filter #(and (halves? %)
(= (sort (str n)) (digits %)))
(factor-pairs n))))
(defn vampiric? [n]
(let [fangs (fangs n)]
(if (empty? fangs) nil [n fangs])))
(doseq [n (take 25 (keep vampiric? (range)))]
(prn n))
(doseq [n [16758243290880, 24959017348650, 14593825548650]]
(println (or (vampiric? n) (str n " is not vampiric."))))
Common Lisp
(defun trailing-zerop (number)
"Is the lowest digit of `number' a 0"
(zerop (rem number 10)))
(defun integer-digits (integer)
"Return the number of digits of the `integer'"
(assert (integerp integer))
(length (write-to-string integer)))
(defun paired-factors (number)
"Return a list of pairs that are factors of `number'"
(loop
:for candidate :from 2 :upto (sqrt number)
:when (zerop (mod number candidate))
:collect (list candidate (/ number candidate))))
(defun vampirep (candidate &aux
(digits-of-candidate (integer-digits candidate))
(half-the-digits-of-candidate (/ digits-of-candidate
2)))
"Is the `candidate' a vampire number?"
(remove-if #'(lambda (pair)
(> (length (remove-if #'null (mapcar #'trailing-zerop pair)))
1))
(remove-if-not #'(lambda (pair)
(string= (sort (copy-seq (write-to-string candidate))
#'char<)
(sort (copy-seq (format nil "~A~A" (first pair) (second pair)))
#'char<)))
(remove-if-not #'(lambda (pair)
(and (eql (integer-digits (first pair))
half-the-digits-of-candidate)
(eql (integer-digits (second pair))
half-the-digits-of-candidate)))
(paired-factors candidate)))))
(defun print-vampire (candidate fangs &optional (stream t))
(format stream
"The number ~A is a vampire number with fangs: ~{ ~{~A~^, ~}~^; ~}~%"
candidate
fangs))
;; Print the first 25 vampire numbers
(loop
:with count := 0
:for candidate :from 0
:until (eql count 25)
:for fangs := (vampirep candidate)
:do
(when fangs
(print-vampire candidate fangs)
(incf count)))
;; Check if 16758243290880, 24959017348650, 14593825548650 are vampire numbers
(dolist (candidate '(16758243290880 24959017348650 14593825548650))
(let ((fangs (vampirep candidate)))
(when fangs
(print-vampire candidate fangs))))
- Output:
The number 1260 is a vampire number with fangs: 21, 60 The number 1395 is a vampire number with fangs: 15, 93 The number 1435 is a vampire number with fangs: 35, 41 The number 1530 is a vampire number with fangs: 30, 51 The number 1827 is a vampire number with fangs: 21, 87 The number 2187 is a vampire number with fangs: 27, 81 The number 6880 is a vampire number with fangs: 80, 86 The number 102510 is a vampire number with fangs: 201, 510 The number 104260 is a vampire number with fangs: 260, 401 The number 105210 is a vampire number with fangs: 210, 501 The number 105264 is a vampire number with fangs: 204, 516 The number 105750 is a vampire number with fangs: 150, 705 The number 108135 is a vampire number with fangs: 135, 801 The number 110758 is a vampire number with fangs: 158, 701 The number 115672 is a vampire number with fangs: 152, 761 The number 116725 is a vampire number with fangs: 161, 725 The number 117067 is a vampire number with fangs: 167, 701 The number 118440 is a vampire number with fangs: 141, 840 The number 120600 is a vampire number with fangs: 201, 600 The number 123354 is a vampire number with fangs: 231, 534 The number 124483 is a vampire number with fangs: 281, 443 The number 125248 is a vampire number with fangs: 152, 824 The number 125433 is a vampire number with fangs: 231, 543 The number 125460 is a vampire number with fangs: 204, 615; 246, 510 The number 125500 is a vampire number with fangs: 251, 500 The number 16758243290880 is a vampire number with fangs: 1982736, 8452080; 2123856, 7890480; 2751840, 6089832; 2817360, 5948208 The number 24959017348650 is a vampire number with fangs: 2947050, 8469153; 2949705, 8461530; 4125870, 6049395; 4129587, 6043950; 4230765, 5899410 The number 16758243290880 is a vampire number with fangs: 1982736, 8452080; 2123856, 7890480; 2751840, 6089832; 2817360, 5948208 The number 24959017348650 is a vampire number with fangs: 2947050, 8469153; 2949705, 8461530; 4125870, 6049395; 4129587, 6043950; 4230765, 5899410
D
The two versions show two styles of D code: compact script-like mostly-functional code, and efficient lower-level code.
High-Level Version
(Runtime about 1.34 seconds with dmd.)
import std.stdio, std.range, std.algorithm, std.typecons, std.conv;
auto fangs(in long n) pure nothrow @safe {
auto pairs = iota(2, cast(int)(n ^^ 0.5)) // n.isqrt
.filter!(x => !(n % x)).map!(x => [x, n / x]);
enum dLen = (in long x) => x.text.length;
immutable half = dLen(n) / 2;
enum halvesQ = (long[] p) => p.all!(u => dLen(u) == half);
enum digits = (long[] p) => dtext(p[0], p[1]).dup.sort();
const dn = n.to!(dchar[]).sort();
return tuple(n, pairs.filter!(p => halvesQ(p) && dn == digits(p)));
}
void main() {
foreach (v; int.max.iota.map!fangs.filter!q{ !a[1].empty }
.take(25).chain([16758243290880, 24959017348650,
14593825548650].map!fangs))
writefln("%d: (%(%(%s %)) (%))", v[]);
}
- Output:
1260: (21 60) 1395: (15 93) 1435: (35 41) 1530: (30 51) 1827: (21 87) 2187: (27 81) 6880: (80 86) 102510: (201 510) 104260: (260 401) 105210: (210 501) 105264: (204 516) 105750: (150 705) 108135: (135 801) 110758: (158 701) 115672: (152 761) 116725: (161 725) 117067: (167 701) 118440: (141 840) 120600: (201 600) 123354: (231 534) 124483: (281 443) 125248: (152 824) 125433: (231 543) 125460: (204 615) (246 510) 125500: (251 500) 16758243290880: (1982736 8452080) (2123856 7890480) (2751840 6089832) (2817360 5948208) 24959017348650: (2947050 8469153) (2949705 8461530) (4125870 6049395) (4129587 6043950) (4230765 5899410) 14593825548650: ()
Fast Version
(Runtime about 0.27 seconds with dmd, about 0.25 seconds with ldc2 compilers.)
import std.stdio, std.math, std.algorithm, std.array, std.traits;
T[N] pows(T, size_t N)() pure nothrow @safe @nogc {
typeof(return) result;
result[0] = 1;
foreach (immutable i, ref r; result[1 .. $])
r = result[i] * 10;
return result;
}
__gshared immutable tenPowsU = pows!(uint, 10);
__gshared immutable tenPowsUL = pows!(ulong, 20);
size_t nDigits(T)(in T x) pure nothrow @safe @nogc {
Unqual!T y = x;
size_t n = 0;
while (y) {
n++;
y /= 10;
}
return n;
}
T dTally(T)(in T x) pure nothrow @safe @nogc {
Unqual!T y = x;
T t = 0;
while (y) {
t += 1 << ((y % 10) * 6);
y /= 10;
}
return t;
}
T[] fangs(T)(in T x, T[] f)
pure nothrow @safe @nogc if (is(T == uint) || is(T == ulong)) {
alias tenPows = Select!(is(T == ulong), tenPowsUL, tenPowsU);
immutable nd0 = nDigits(x);
if (nd0 & 1)
return null;
immutable nd = nd0 / 2;
immutable lo = max(tenPows[nd - 1],
(x + tenPows[nd] - 2) / (tenPows[nd] - 1));
immutable hi = min(x / lo, cast(T)sqrt(real(x)));
immutable t = x.dTally;
size_t n = 0;
foreach (immutable a; lo .. hi + 1) {
immutable b = x / a;
if (a * b == x
&& (a % 10 || b % 10)
&& t == (a.dTally + b.dTally)) {
f[n] = a;
n++;
}
}
return f[0 .. n];
}
void showFangs(T)(in T x, in T[] fs) {
x.write;
foreach (immutable fi; fs)
writef(" = %d x %d", fi, x / fi);
writeln;
}
void main() {
uint[16] fu;
for (uint x = 1, n = 0; n < 25; x++) {
const fs = fangs(x, fu);
if (fs.empty)
continue;
n++;
writef("%2d: ", n);
showFangs(x, fs);
}
writeln;
static immutable ulong[3] bigs = [16_758_243_290_880UL,
24_959_017_348_650UL,
14_593_825_548_650UL];
ulong[fu.length] ful;
foreach (immutable bi; bigs) {
const fs = fangs(bi, ful);
if (fs.empty)
writeln(bi, " is not vampiric");
else
showFangs(bi, fs);
}
}
- Output:
2: 1395 = 15 x 93 3: 1435 = 35 x 41 4: 1530 = 30 x 51 5: 1827 = 21 x 87 6: 2187 = 27 x 81 7: 6880 = 80 x 86 8: 102510 = 201 x 510 9: 104260 = 260 x 401 10: 105210 = 210 x 501 11: 105264 = 204 x 516 12: 105750 = 150 x 705 13: 108135 = 135 x 801 14: 110758 = 158 x 701 15: 115672 = 152 x 761 16: 116725 = 161 x 725 17: 117067 = 167 x 701 18: 118440 = 141 x 840 19: 120600 = 201 x 600 20: 123354 = 231 x 534 21: 124483 = 281 x 443 22: 125248 = 152 x 824 23: 125433 = 231 x 543 24: 125460 = 204 x 615 = 246 x 510 25: 125500 = 251 x 500 16758243290880 = 1982736 x 8452080 = 2123856 x 7890480 = 2751840 x 6089832 = 2817360 x 5948208 24959017348650 = 2947050 x 8469153 = 2949705 x 8461530 = 4125870 x 6049395 = 4129587 x 6043950 = 4230765 x 5899410 14593825548650 is not vampiric
EasyLang
func dtally x .
while x > 0
t += bitshift 1 (x mod 10 * 6)
x = x div 10
.
return t
.
proc fangs x . f[] .
f[] = [ ]
nd = floor log10 x + 1
if nd mod 2 = 1
return
.
nd = nd div 2
lo = higher pow 10 (nd - 1) (x + pow 10 nd - 2) div (pow 10 nd - 1)
hi = lower (x / lo) sqrt x
t = dtally x
for a = lo to hi
b = x div a
if a * b = x and (a mod 10 > 0 or b mod 10 > 0) and t = dtally a + dtally b
f[] &= a
.
.
.
proc show_fangs x f[] . .
write x & " "
for f in f[]
write " = " & f & " x " & x div f
.
print ""
.
x = 1
while n < 25
fangs x f[]
if len f[] > 0
n += 1
write n & ": "
show_fangs x f[]
.
x += 1
.
bigs[] = [ 16758243290880 24959017348650 14593825548650 ]
for x in bigs[]
fangs x f[]
if len f[] > 0
show_fangs x f[]
else
print x & " is not vampiric"
.
.
Eiffel
class
APPLICATION
create
make
feature
fang_check (original, fang1, fang2: INTEGER_64): BOOLEAN
-- Are 'fang1' and 'fang2' correct fangs of the 'original' number?
require
original_positive: original > 0
fangs_positive: fang1 > 0 and fang2 > 0
local
original_length: INTEGER
fang, ori: STRING
sort_ori, sort_fang: SORTED_TWO_WAY_LIST [CHARACTER]
do
create sort_ori.make
create sort_fang.make
create ori.make_empty
create fang.make_empty
original_length := original.out.count // 2
if fang1.out.count /= original_length or fang2.out.count /= (original_length) then
Result := False
elseif fang1.out.ends_with ("0") and fang2.out.ends_with ("0") then
Result := False
else
across
1 |..| original.out.count as c
loop
sort_ori.extend (original.out [c.item])
end
across
sort_ori as o
loop
ori.extend (o.item)
end
across
1 |..| fang1.out.count as c
loop
sort_fang.extend (fang1.out [c.item])
sort_fang.extend (fang2.out [c.item])
end
across
sort_fang as f
loop
fang.extend (f.item)
end
Result := fang.same_string (ori)
end
ensure
fangs_right_length: Result implies original.out.count = fang1.out.count + fang2.out.count
end
make
-- Uses fang_check to find vampire nubmers.
local
i, numbers: INTEGER
fang1, fang2: INTEGER_64
num: ARRAY [INTEGER_64]
math: DOUBLE_MATH
do
create math
from
i := 1000
until
numbers > 25
loop
if i.out.count \\ 2 = 0 then
from
fang1 := 10
until
fang1 >= math.sqrt (i)
loop
if (i \\ fang1 = 0) then
fang2 := i // fang1
if i \\ 9 = (fang1 + fang2) \\ 9 then
if fang1 * fang2 = i and fang1 <= fang2 and then fang_check (i, fang1, fang2) then
numbers := numbers + 1
io.put_string (i.out + ": " + fang1.out + " " + fang2.out)
io.new_line
end
end
end
fang1 := fang1 + 1
end
end
i := i + 1
end
num := <<16758243290880, 24959017348650, 14593825548650>>
across
num as n
loop
from
fang1 := 1000000
until
fang1 >= math.sqrt (n.item) + 1
loop
if (n.item \\ fang1 = 0) then
fang2 := (n.item // fang1)
if fang1 * fang2 = n.item and fang1 <= fang2 and then fang_check (n.item, fang1, fang2) then
io.put_string (n.item.out + ": " + fang1.out + " " + fang2.out + "%N")
end
end
fang1 := fang1 + 1
end
end
end
end
- Output:
1260: 21, 60 1395: 15, 93 1435: 35, 41 1530: 30, 51 1827: 21, 87 2187: 27, 81 6880: 80, 86 102510: 201, 510 104260: 260, 401 105210: 210, 501 105264: 204, 516 105750: 150, 705 108135: 135, 801 110758: 158, 701 115672: 152, 761 116725: 161, 725 117067: 167, 701 118440: 141, 840 120600: 201, 600 123354: 231, 534 124483: 281, 443 125248: 152, 824 125433: 231, 543 125460: 204, 615 125460: 246, 510 125500: 251, 500 126027: 201, 627 16758243290880: 1982736, 8452080 16758243290880: 2123856, 7890480 16758243290880: 2751840, 6089832 16758243290880: 2817360, 5948208 24959017348650: 2947050, 8469153 24959017348650: 2949705, 8461530 24959017348650: 4125870, 6049395 24959017348650: 4129587, 6043950 24959017348650: 4230765, 5899410
Elixir
defmodule Vampire do
def factor_pairs(n) do
first = trunc(n / :math.pow(10, div(char_len(n), 2)))
last = :math.sqrt(n) |> round
for i <- first .. last, rem(n, i) == 0, do: {i, div(n, i)}
end
def vampire_factors(n) do
if rem(char_len(n), 2) == 1 do
[]
else
half = div(length(to_char_list(n)), 2)
sorted = Enum.sort(String.codepoints("#{n}"))
Enum.filter(factor_pairs(n), fn {a, b} ->
char_len(a) == half && char_len(b) == half &&
Enum.count([a, b], fn x -> rem(x, 10) == 0 end) != 2 &&
Enum.sort(String.codepoints("#{a}#{b}")) == sorted
end)
end
end
defp char_len(n), do: length(to_char_list(n))
def task do
Enum.reduce_while(Stream.iterate(1, &(&1+1)), 1, fn n, acc ->
case vampire_factors(n) do
[] -> {:cont, acc}
vf -> IO.puts "#{n}:\t#{inspect vf}"
if acc < 25, do: {:cont, acc+1}, else: {:halt, acc+1}
end
end)
IO.puts ""
Enum.each([16758243290880, 24959017348650, 14593825548650], fn n ->
case vampire_factors(n) do
[] -> IO.puts "#{n} is not a vampire number!"
vf -> IO.puts "#{n}:\t#{inspect vf}"
end
end)
end
end
Vampire.task
- Output:
1260: [{21, 60}]
1395: [{15, 93}]
1435: [{35, 41}]
1530: [{30, 51}]
1827: [{21, 87}]
2187: [{27, 81}]
6880: [{80, 86}]
102510: [{201, 510}]
104260: [{260, 401}]
105210: [{210, 501}]
105264: [{204, 516}]
105750: [{150, 705}]
108135: [{135, 801}]
110758: [{158, 701}]
115672: [{152, 761}]
116725: [{161, 725}]
117067: [{167, 701}]
118440: [{141, 840}]
120600: [{201, 600}]
123354: [{231, 534}]
124483: [{281, 443}]
125248: [{152, 824}]
125433: [{231, 543}]
125460: [{204, 615}, {246, 510}]
125500: [{251, 500}]
16758243290880: [{1982736, 8452080}, {2123856, 7890480}, {2751840, 6089832}, {2817360, 5948208}]
24959017348650: [{2947050, 8469153}, {2949705, 8461530}, {4125870, 6049395}, {4129587, 6043950}, {4230765, 5899410}]
14593825548650 is not a vampire number!
Factor
USING: combinators.short-circuit fry io kernel lists lists.lazy math
math.combinatorics math.functions math.primes.factors math.statistics
math.text.utils prettyprint sequences sets ;
IN: rosetta-code.vampire-number
: digits ( n -- m )
log10 floor >integer 1 + ;
: same-digits? ( n n1 n2 -- ? )
[ 1 digit-groups ] tri@ append [ histogram ] bi@ = ;
: half-len-factors ( n -- seq )
[ divisors ] [ digits ] bi 2/ '[ digits _ = ] filter ;
: same-digit-factors ( n -- seq )
dup half-len-factors 2 <combinations> [ first2 same-digits? ] with filter ;
: under-two-trailing-zeros? ( seq -- ? )
[ 10 mod ] map [ 0 = ] count 2 < ;
: tentative-fangs ( n -- seq )
same-digit-factors [ under-two-trailing-zeros? ] filter ;
: fangs ( n -- seq )
[ tentative-fangs ] [ ] bi '[ product _ = ] filter ;
: vampire? ( n -- ? )
{ [ digits even? ] [ fangs empty? not ] } 1&& ;
: first25 ( -- seq )
25 0 lfrom [ vampire? ] lfilter ltake list>array ;
: .vamp-with-fangs ( n -- )
[ pprint bl ] [ fangs [ pprint bl ] each ] bi nl ;
: part1 ( -- )
first25 [ .vamp-with-fangs ] each ;
: part2 ( -- ) { 16758243290880 24959017348650 14593825548650 }
[ dup vampire? [ .vamp-with-fangs ] [ drop ] if ] each ;
: main ( -- ) part1 part2 ;
MAIN: main
- Output:
1260 { 21 60 }
1395 { 15 93 }
1435 { 35 41 }
1530 { 30 51 }
1827 { 21 87 }
2187 { 27 81 }
6880 { 80 86 }
102510 { 201 510 }
104260 { 260 401 }
105210 { 210 501 }
105264 { 204 516 }
105750 { 150 705 }
108135 { 135 801 }
110758 { 158 701 }
115672 { 152 761 }
116725 { 161 725 }
117067 { 167 701 }
118440 { 141 840 }
120600 { 201 600 }
123354 { 231 534 }
124483 { 281 443 }
125248 { 152 824 }
125433 { 231 543 }
125460 { 204 615 } { 246 510 }
125500 { 251 500 }
16758243290880 { 1982736 8452080 } { 2123856 7890480 } { 2751840 6089832 } { 2817360 5948208 }
24959017348650 { 2947050 8469153 } { 2949705 8461530 } { 4125870 6049395 } { 4129587 6043950 } { 4230765 5899410 }
Forth
: sqrt ( u -- sqrt ) ( Babylonian method )
dup 2/ ( first square root guess is half )
dup 0= if drop exit then ( sqrt[0]=0, sqrt[1]=1 )
begin dup >r 2dup / r> + 2/ ( stack: square old-guess new-guess )
2dup > while ( as long as guess is decreasing )
nip repeat ( forget old-guess and repeat )
drop nip ;
: ndigits ( n -- n ) 10 / dup 0<> if recurse then 1+ ;
: dtally ( n -- n )
10 /mod
dup 0<> if recurse then
swap 6 * 1 swap lshift + ;
: ?product ( x a b -- f ) * = ;
: ?dtally ( x a b -- f ) dtally rot dtally rot dtally rot + = ;
: ?ndigits ( a b -- f ) ndigits swap ndigits = ;
: ?0trail ( a b -- f ) 10 mod 0= swap 10 mod 0= and invert ;
: ?fang ( x a -- f )
2dup / 2>r
dup 2r@ ?product
swap 2r@ ?dtally and
2r@ ?ndigits and
2r> ?0trail and ;
: next-fang ( n a -- false | a true )
over sqrt swap 1+ ?do
dup i ?fang if drop i true unloop exit then
loop drop false ;
: ?vampire ( n -- false | a true ) 0 next-fang ;
: next-vampire ( n -- n a ) begin 1+ dup ?vampire until ;
: .product ( n a -- ) dup . ." x " / . ." = " ;
: .vampire ( n a -- )
cr
begin 2dup .product
over swap next-fang
while repeat
. ;
: .fangs ( n -- ) dup ?vampire if .vampire else cr . ." is not vampiric." then ;
: vampires ( n -- )
1 swap
0 do next-vampire over swap .vampire loop drop ;
25 vampires
16758243290880 .fangs
24959017348650 .fangs
14593825548650 .fangs
- Output:
25 vampires21 x 60 = 1260 15 x 93 = 1395 35 x 41 = 1435 30 x 51 = 1530 21 x 87 = 1827 27 x 81 = 2187 80 x 86 = 6880 201 x 510 = 102510 260 x 401 = 104260 210 x 501 = 105210 204 x 516 = 105264 150 x 705 = 105750 135 x 801 = 108135 158 x 701 = 110758 152 x 761 = 115672 161 x 725 = 116725 167 x 701 = 117067 141 x 840 = 118440 201 x 600 = 120600 231 x 534 = 123354 281 x 443 = 124483 152 x 824 = 125248 231 x 543 = 125433 204 x 615 = 246 x 510 = 125460 251 x 500 = 125500 ok 16758243290880 .fangs 1982736 x 8452080 = 2123856 x 7890480 = 2751840 x 6089832 = 2817360 x 5948208 = 16758243290880 ok 24959017348650 .fangs 2947050 x 8469153 = 2949705 x 8461530 = 4125870 x 6049395 = 4129587 x 6043950 = 4230765 x 5899410 = 24959017348650 ok 14593825548650 .fangs
14593825548650 is not vampiric. ok
FreeBASIC
'Vampire numbers.
'FreeBASIC version 24. Windows
'Vampire.bas
Function WithinString(n As Ulongint,f As Ulongint) As Integer
var m=Str(n),p=Str(f)
For z As Integer=0 To Len(p)-1
var i=Instr(m,Chr(p[z]))
If i Then
m=Mid(m,1,i-1)+Mid(m,i+1)
Else
Return 0
End If
Next z
Return -1
End Function
Sub AllFactors(N As Ulongint,factors() As Ulongint)
Dim As String Sn=Str(n)
Dim As Integer half=Len(sn)\2
Redim factors(1 To 1)
#macro bsort(array)
For p1 As Integer = 1 To Ubound(array) - 1
For p2 As Integer = p1 + 1 To Ubound(array)
If array(p1)>array(p2) Then Swap array(p1),array(p2)
Next p2
Next p1
#endmacro
Dim As Ulongint c
For i As Ulongint = 1 To Sqr(N)
If N Mod i=0 Then
If Len(Str(i))=half Then
If WithinString(N,i) Then
c=c+1
Redim Preserve factors(1 To c)
factors(c)=i
End If
End If
If N <> i*i Then
If Len(Str(n\i))=half Then
If WithinString(N,n\i) Then
c=c+1
Redim Preserve factors(1 To c)
factors(c)=n\i
End If
End If
End If
End If
Next i
bsort(factors)
End Sub
Function VampireNumbers(N As Ulongint) As Integer
Dim As Integer flag
Dim As Ulongint LastFactor
Redim As Ulongint Factor()
AllFactors(N,Factor())
For p1 As Integer = 1 To Ubound(Factor)
For p2 As Integer=1 To Ubound(Factor)
If Factor(p1)*Factor(p2)=n Then
If Factor(p1) Mod 10<>0 Or Factor(p2) Mod 10 <>0 Then
If WithinString(n,valulng(Str(Factor(p1))+Str(Factor(p2)))) Then
If LastFactor=Factor(p2) Then Exit For,For
flag=1
Print n;": [";Factor(p1);",";Factor(p2);"]"
LastFactor=Factor(p1)
End If
End If
End If
Next p2
Next p1
If flag Then Return -1
End Function
'============== IMPLEMENT ==============================
print "First 28 Vampire numbers"
print
Print "Number: [fangs]"
Print
Dim As Ulongint n=1000
Dim As Integer count
Dim As Double t1,t2
t1=Timer
Do
n=n+1
Var s=Str(n)
If Len(s) Mod 2<>0 Then n=n*10
If vampireNumbers(n) Then count=count+1
Loop Until count=27
Print
print "Individual tests:"
print
'individual tests
n=16758243290880ull
If Not vampirenumbers(n) Then Print n;": [returns no fangs]"
Print
n=24959017348650ull
If Not vampirenumbers(n) Then Print n;": [returns no fangs]"
print
n=14593825548650ull
If Not vampirenumbers(n) then print n;": [returns no fangs]"
t2=Timer
print
Print "Completed in ";
Print t2-t1;" Seconds"
Sleep
- Output:
First 28 Vampire numbers Number: [fangs] 1260: [21,60] 1395: [15,93] 1435: [35,41] 1530: [30,51] 1827: [21,87] 2187: [27,81] 6880: [80,86] 102510: [201,510] 104260: [260,401] 105210: [210,501] 105264: [204,516] 105750: [150,705] 108135: [135,801] 110758: [158,701] 115672: [152,761] 116725: [161,725] 117067: [167,701] 118440: [141,840] 120600: [201,600] 123354: [231,534] 124483: [281,443] 125248: [152,824] 125433: [231,543] 125460: [204,615] 125460: [246,510] 125500: [251,500] 126027: [201,627] 126846: [261,486] Individual tests: 16758243290880: [1982736,8452080] 16758243290880: [2123856,7890480] 16758243290880: [2751840,6089832] 16758243290880: [2817360,5948208] 24959017348650: [2947050,8469153] 24959017348650: [2949705,8461530] 24959017348650: [4125870,6049395] 24959017348650: [4129587,6043950] 24959017348650: [4230765,5899410] 14593825548650: [returns no fangs] Completed in 1.286374813709699 Seconds
Go
package main
import (
"fmt"
"math"
)
func max(a, b uint64) uint64 {
if a > b {
return a
}
return b
}
func min(a, b uint64) uint64 {
if a < b {
return a
}
return b
}
func ndigits(x uint64) (n int) {
for ; x > 0; x /= 10 {
n++
}
return
}
func dtally(x uint64) (t uint64) {
for ; x > 0; x /= 10 {
t += 1 << (x % 10 * 6)
}
return
}
var tens [20]uint64
func init() {
tens[0] = 1
for i := 1; i < 20; i++ {
tens[i] = tens[i-1] * 10
}
}
func fangs(x uint64) (f []uint64) {
nd := ndigits(x)
if nd&1 == 1 {
return
}
nd /= 2
lo := max(tens[nd-1], (x+tens[nd]-2)/(tens[nd]-1))
hi := min(x/lo, uint64(math.Sqrt(float64(x))))
t := dtally(x)
for a := lo; a <= hi; a++ {
b := x / a
if a*b == x &&
(a%10 > 0 || b%10 > 0) &&
t == dtally(a)+dtally(b) {
f = append(f, a)
}
}
return
}
func showFangs(x uint64, f []uint64) {
fmt.Print(x)
if len(f) > 1 {
fmt.Println()
}
for _, a := range f {
fmt.Println(" =", a, "×", x/a)
}
}
func main() {
for x, n := uint64(1), 0; n < 26; x++ {
if f := fangs(x); len(f) > 0 {
n++
fmt.Printf("%2d: ", n)
showFangs(x, f)
}
}
fmt.Println()
for _, x := range []uint64{16758243290880, 24959017348650, 14593825548650} {
if f := fangs(x); len(f) > 0 {
showFangs(x, f)
} else {
fmt.Println(x, "is not vampiric")
}
}
}
- Output:
1: 1260 = 21 × 60 2: 1395 = 15 × 93 3: 1435 = 35 × 41 4: 1530 = 30 × 51 5: 1827 = 21 × 87 6: 2187 = 27 × 81 7: 6880 = 80 × 86 8: 102510 = 201 × 510 9: 104260 = 260 × 401 10: 105210 = 210 × 501 11: 105264 = 204 × 516 12: 105750 = 150 × 705 13: 108135 = 135 × 801 14: 110758 = 158 × 701 15: 115672 = 152 × 761 16: 116725 = 161 × 725 17: 117067 = 167 × 701 18: 118440 = 141 × 840 19: 120600 = 201 × 600 20: 123354 = 231 × 534 21: 124483 = 281 × 443 22: 125248 = 152 × 824 23: 125433 = 231 × 543 24: 125460 = 204 × 615 = 246 × 510 25: 125500 = 251 × 500 26: 126027 = 201 × 627 16758243290880 = 1982736 × 8452080 = 2123856 × 7890480 = 2751840 × 6089832 = 2817360 × 5948208 24959017348650 = 2947050 × 8469153 = 2949705 × 8461530 = 4125870 × 6049395 = 4129587 × 6043950 = 4230765 × 5899410 14593825548650 is not vampiric
Haskell
import Data.List (sort)
import Control.Arrow ((&&&))
-- VAMPIRE NUMBERS ------------------------------------------------------------
vampires :: [Int]
vampires = filter (not . null . fangs) [1 ..]
fangs :: Int -> [(Int, Int)]
fangs n
| odd w = []
| otherwise = ((,) <*> quot n) <$> filter isfang (integerFactors n)
where
ndigit :: Int -> Int
ndigit 0 = 0
ndigit n = 1 + ndigit (quot n 10)
w = ndigit n
xmin = 10 ^ (quot w 2 - 1)
xmax = xmin * 10
isfang x =
x > xmin &&
x < y &&
y < xmax && -- same length
(quot x 10 /= 0 || quot y 10 /= 0) && -- not zero-ended
sort (show n) == sort (show x ++ show y)
where
y = quot n x
-- FACTORS --------------------------------------------------------------------
integerFactors :: Int -> [Int]
integerFactors n
| n < 1 = []
| otherwise =
lows ++
(quot n <$>
(if intSquared == n -- A perfect square,
then tail -- and cofactor of square root would be redundant.
else id)
(reverse lows))
where
(intSquared, lows) =
(^ 2) &&& (filter ((0 ==) . rem n) . enumFromTo 1) $
floor (sqrt $ fromIntegral n)
-- TEST -----------------------------------------------------------------------
main :: IO [()]
main =
mapM
(print . ((,) <*>) fangs)
(take 25 vampires ++ [16758243290880, 24959017348650, 14593825548650])
- Output:
(1260,[(21,60)]) (1395,[(15,93)]) (1435,[(35,41)]) (1530,[(30,51)]) (1827,[(21,87)]) (2187,[(27,81)]) (6880,[(80,86)]) (102510,[(201,510)]) (104260,[(260,401)]) (105210,[(210,501)]) (105264,[(204,516)]) (105750,[(150,705)]) (108135,[(135,801)]) (110758,[(158,701)]) (115672,[(152,761)]) (116725,[(161,725)]) (117067,[(167,701)]) (118440,[(141,840)]) (120600,[(201,600)]) (123354,[(231,534)]) (124483,[(281,443)]) (125248,[(152,824)]) (125433,[(231,543)]) (125460,[(204,615),(246,510)]) (125500,[(251,500)]) (16758243290880,[(1982736,8452080),(2123856,7890480),(2751840,6089832),(2817360,5948208)]) (24959017348650,[(2947050,8469153),(2949705,8461530),(4125870,6049395),(4129587,6043950),(4230765,5899410)]) (14593825548650,[])
Icon and Unicon
The following works in both languages.
procedure main()
write("First 25 vampire numbers and their fangs:")
every fangs := vampire(n := seq())\25 do write(right(n,20),":",fangs)
write("\nOther numbers:")
every n := 16758243290880 | 24959017348650 | 14593825548650 do
write(right(n,20),": ",vampire(n)|"toothless")
end
procedure vampire(n)
ns := string(n)
if *ns % 2 = 1 then fail
every (fangs := "") ||:= " "||fangCheck(n, *ns/2, f1 := 2 to integer(sqrt(n)), n/f1)
if *fangs > 0 then return fangs
end
procedure fangCheck(n, n2, f1, f2)
if f1*f2 ~= n then fail
if n2 ~= *(f1|f2) then fail
if (f1|f2) % 10 ~= 0 then
if csort(f1||f2) == csort(n) then return "("||f1||","||f2||")"
end
procedure csort(s) # Adapted from csort(s) in Icon IPL
every (s1 := "", c := !cset(s)) do every find(c, s) do s1 ||:= c
return s1
end
Output:
First 25 vampire numbers and their fangs:
1260: (21,60)
1395: (15,93)
1435: (35,41)
1530: (30,51)
1827: (21,87)
2187: (27,81)
6880: (80,86)
102510: (201,510)
104260: (260,401)
105210: (210,501)
105264: (204,516)
105750: (150,705)
108135: (135,801)
110758: (158,701)
115672: (152,761)
116725: (161,725)
117067: (167,701)
118440: (141,840)
120600: (201,600)
123354: (231,534)
124483: (281,443)
125248: (152,824)
125433: (231,543)
125460: (204,615) (246,510)
125500: (251,500)
Other numbers:
16758243290880: (1982736,8452080) (2123856,7890480) (2751840,6089832) (2817360,5948208)
24959017348650: (2947050,8469153) (2949705,8461530) (4125870,6049395) (4129587,6043950) (4230765,5899410)
14593825548650: toothless
J
Filter=: (#~`)(`:6)
odd =: 2&|
even =: -.@:odd
factors =: [: ([: /:~ [: */"1 ([: x: [) ^"1 [: > [: , [: { [: <@:i.@>: ])/ __ q: ]
digits =: 10&(#.inv)
tally =: # : [:
half =: -: : [:
even_number_of_digits =: even@:tally@:digits
same_digits =: digits@:[ -:&(/:~) ,&digits/@:]
assert 1 -: 1234 same_digits 23 14
assert 0 -: 1234 same_digits 23 140
half_the_digits =: (half@:tally@:digits@:[ = tally@:digits&>@:]) # ]
factors_with_half_the_digits =: half_the_digits factors
large =: (> <.@:%:)~ # ]
candidates =: large factors_with_half_the_digits
one_trailing_zero_permitted =: (0 < [: tally 0 -.~ 10&|)"1 Filter
pairs =: (% ,. ]) one_trailing_zero_permitted@:candidates
fangs =: (same_digits"0 1 # ]) pairs
A=:(0 2 -.@:-: $)&>Filter<@fangs"0]1000+i.1e4
B=:(0 2 -.@:-: $)&>Filter<@fangs"0]100000+i.25501
(,: */@:{.&.>)A,B
┌─────┬─────┬─────┬─────┬─────┬─────┬─────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│21 60│15 93│35 41│30 51│21 87│27 81│80 86│201 510│260 401│210 501│204 516│150 705│135 801│158 701│152 761│161 725│167 701│141 840│201 600│231 534│281 443│152 824│231 543│246 510│251 500│
│ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │204 615│ │
├─────┼─────┼─────┼─────┼─────┼─────┼─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│1260 │1395 │1435 │1530 │1827 │2187 │6880 │102510 │104260 │105210 │105264 │105750 │108135 │110758 │115672 │116725 │117067 │118440 │120600 │123354 │124483 │125248 │125433 │125460 │125500 │
└─────┴─────┴─────┴─────┴─────┴─────┴─────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
<@fangs"0[] 16758243290880 24959017348650 14593825548650
┌───────────────┬───────────────┬──┐
│2817360 5948208│4230765 5899410│ │
│2751840 6089832│4129587 6043950│ │
│2123856 7890480│4125870 6049395│ │
│1982736 8452080│2949705 8461530│ │
│ │2947050 8469153│ │
└───────────────┴───────────────┴──┘
fangs f. NB. <laugh>
((10&(#.^:_1)@:[ -:&(/:~) ,&(10&(#.^:_1))/@:])"0 1 # ]) ((% ,. ]) (#~ (0 < [: # :[: 0 -.~ 10&|)"1)@:(((> <.@:%:)~ # ]) (((-: :[:@:(# :[:)@:(10&(#.^:_1))@:[ = # :[:@:(10&(#.^:_1))&>@:]) # ]) ([: ([: /:~ [: */"1 ([: x: [) ^"1 [: > [: , [: { [: <@:i.@>: ])/ __ q: ]))))
Java
import java.util.Arrays;
import java.util.HashSet;
public class VampireNumbers{
private static int numDigits(long num){
return Long.toString(Math.abs(num)).length();
}
private static boolean fangCheck(long orig, long fang1, long fang2){
if(Long.toString(fang1).endsWith("0") && Long.toString(fang2).endsWith("0")) return false;
int origLen = numDigits(orig);
if(numDigits(fang1) != origLen / 2 || numDigits(fang2) != origLen / 2) return false;
byte[] origBytes = Long.toString(orig).getBytes();
byte[] fangBytes = (Long.toString(fang1) + Long.toString(fang2)).getBytes();
Arrays.sort(origBytes);
Arrays.sort(fangBytes);
return Arrays.equals(origBytes, fangBytes);
}
public static void main(String[] args){
HashSet<Long> vamps = new HashSet<Long>();
for(long i = 10; vamps.size() <= 25; i++ ){
if((numDigits(i) % 2) != 0) {i = i * 10 - 1; continue;}
for(long fang1 = 2; fang1 <= Math.sqrt(i) + 1; fang1++){
if(i % fang1 == 0){
long fang2 = i / fang1;
if(fangCheck(i, fang1, fang2) && fang1 <= fang2){
vamps.add(i);
System.out.println(i + ": [" + fang1 + ", " + fang2 +"]");
}
}
}
}
Long[] nums = {16758243290880L, 24959017348650L, 14593825548650L};
for(Long i : nums){
for(long fang1 = 2; fang1 <= Math.sqrt(i) + 1; fang1++){
if(i % fang1 == 0){
long fang2 = i / fang1;
if(fangCheck(i, fang1, fang2) && fang1 <= fang2){
System.out.println(i + ": [" + fang1 + ", " + fang2 +"]");
}
}
}
}
}
}
Output:
1260: [21, 60] 1395: [15, 93] 1435: [35, 41] 1530: [30, 51] 1827: [21, 87] 2187: [27, 81] 6880: [80, 86] 102510: [201, 510] 104260: [260, 401] 105210: [210, 501] 105264: [204, 516] 105750: [150, 705] 108135: [135, 801] 110758: [158, 701] 115672: [152, 761] 116725: [161, 725] 117067: [167, 701] 118440: [141, 840] 120600: [201, 600] 123354: [231, 534] 124483: [281, 443] 125248: [152, 824] 125433: [231, 543] 125460: [204, 615] 125460: [246, 510] 125500: [251, 500] 126027: [201, 627] 16758243290880: [1982736, 8452080] 16758243290880: [2123856, 7890480] 16758243290880: [2751840, 6089832] 16758243290880: [2817360, 5948208] 24959017348650: [2947050, 8469153] 24959017348650: [2949705, 8461530] 24959017348650: [4125870, 6049395] 24959017348650: [4129587, 6043950] 24959017348650: [4230765, 5899410]
Alternative version
public class VampireNumber {
public static void main(String args[]) {
// scan only the ranges that have an even number of digits
// for instance: 10 .. 99, 1000 .. 9999 etc
long countVamps = 0, start = 10, tens = 10;
outer:
for (int numDigits = 2; numDigits <= 18; numDigits += 2) {
long end = start * 10;
for (long i = start; i < end; i++) {
if (countFangs(i, tens) > 0) {
if (++countVamps >= 26)
break outer;
}
}
start *= 100;
tens *= 10;
}
System.out.println();
long[] bigs = {16758243290880L, 24959017348650L,
14593825548650L};
for (long b : bigs)
countFangs(b, 10000000L);
}
private static int countFangs(long n, long tens) {
int countFangs = 0;
// limit the search space for factors (as in C example)
long lo = Math.max(tens / 10, (n + tens - 2) / (tens - 1));
long hi = Math.min(n / lo, (long) Math.sqrt(n));
long nTally = tallyDigits(n);
for (long a = lo; a <= hi; a++) {
long b = n / a;
if (a * b != n)
continue;
// check for mod 9 congruence
if (n % 9 != (a + b) % 9)
continue;
if (a % 10 == 0 && b % 10 == 0)
continue;
if (nTally == tallyDigits(a) + tallyDigits(b)) {
if (countFangs == 0)
System.out.printf("\n%d : ", n);
System.out.printf("[%d, %d]", a, b);
countFangs++;
}
}
return countFangs;
}
// sum to a unique number to represent set of digits (as in C example)
private static long tallyDigits(long n) {
long total = 0;
while (n > 0) {
total += 1L << ((n % 10) * 6);
n /= 10;
}
return total;
}
}
Output:
1260 : [21, 60] 1395 : [15, 93] 1435 : [35, 41] 1530 : [30, 51] 1827 : [21, 87] 2187 : [27, 81] 6880 : [80, 86] 102510 : [201, 510] 104260 : [260, 401] 105210 : [210, 501] 105264 : [204, 516] 105750 : [150, 705] 108135 : [135, 801] 110758 : [158, 701] 115672 : [152, 761] 116725 : [161, 725] 117067 : [167, 701] 118440 : [141, 840] 120600 : [201, 600] 123354 : [231, 534] 124483 : [281, 443] 125248 : [152, 824] 125433 : [231, 543] 125460 : [204, 615][246, 510] 125500 : [251, 500] 126027 : [201, 627] 16758243290880 : [1982736, 8452080][2123856, 7890480][2751840, 6089832][2817360, 5948208] 24959017348650 : [2947050, 8469153][2949705, 8461530][4125870, 6049395][4129587, 6043950][4230765, 5899410]
jq
Works with gojq, the Go implementation of jq
def count(s): reduce s as $x (0; .+1);
# To take advantage of gojq's arbitrary-precision integer arithmetic:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
# Output: a possibly empty array of pairs
def factor_pairs:
. as $n
| ($n / (10 | power($n|tostring|length / 2) - 1)) as $first
| [range($first|floor; 1 + ($n | sqrt)) | select(($n % .) == 0) | [., $n / .] ] ;
# Output: a stream
def vampire_factors:
def es: tostring|explode;
. as $n
| tostring as $s
| ($s|length) as $nlen
| if ($nlen % 2) == 1 then []
else ($nlen / 2 ) as $half
| [factor_pairs[]
| select(. as [$a, $b]
| ($a|tostring|length) == $half and ($b|tostring|length) == $half
and count($a, $b | select(.%10 == 0)) != 2
and ((($a|es) + ($b|es)) | sort) == ($n|es|sort) ) ]
end ;
def task1($n):
limit($n; range(1; infinite)
| . as $i
| vampire_factors
| select(length>0)
| "\($i):\t\(.)" );
def task2:
16758243290880, 24959017348650, 14593825548650
| vampire_factors as $vf
| if $vf|length == 0
then "\(.) is not a vampire number!"
else "\(.):\t\($vf)"
end;
task1(25),
"",
task2- Output:
1260: [[21,60]] 1395: [[15,93]] 1435: [[35,41]] 1530: [[30,51]] 1827: [[21,87]] 2187: [[27,81]] 6880: [[80,86]] 102510: [[201,510]] 104260: [[260,401]] 105210: [[210,501]] 105264: [[204,516]] 105750: [[150,705]] 108135: [[135,801]] 110758: [[158,701]] 115672: [[152,761]] 116725: [[161,725]] 117067: [[167,701]] 118440: [[141,840]] 120600: [[201,600]] 123354: [[231,534]] 124483: [[281,443]] 125248: [[152,824]] 125433: [[231,543]] 125460: [[204,615],[246,510]] 125500: [[251,500]] 16758243290880: [[1982736,8452080],[2123856,7890480],[2751840,6089832],[2817360,5948208]] 24959017348650: [[2947050,8469153],[2949705,8461530],[4125870,6049395],[4129587,6043950],[4230765,5899410]] 14593825548650 is not a vampire number!
Julia
Functions
function divisors{T<:Integer}(n::T)
!isprime(n) || return [one(T), n]
d = [one(T)]
for (k, v) in factor(n)
e = T[k^i for i in 1:v]
append!(d, vec([i*j for i in d, j in e]))
end
sort(d)
end
function vampirefangs{T<:Integer}(n::T)
fangs = T[]
isvampire = false
vdcnt = ndigits(n)
fdcnt = vdcnt>>1
iseven(vdcnt) || return (isvampire, fangs)
!isprime(n) || return (isvampire, fangs)
vdigs = sort(digits(n))
d = divisors(n)
len = length(d)
len = iseven(len) ? len>>1 : len>>1 + 1
for f in d[1:len]
ndigits(f) == fdcnt || continue
g = div(n, f)
f%10!=0 || g%10!=0 || continue
sort([digits(f), digits(g)]) == vdigs || continue
isvampire = true
append!(fangs, [f, g])
end
if isvampire
fangs = reshape(fangs, (2,length(fangs)>>1))'
end
return (isvampire, fangs)
end
Main
using Printf
function showvampire{T<:Integer}(i::T, n::T, fangs::Array{T,2})
s = @sprintf "%6d %14d %s\n" i n join(fangs[1,:], "\u00d7")
for i in 2:size(fangs)[1]
s *= " "^23*join(fangs[i,:], "\u00d7")*"\n"
end
return s
end
vgoal = 25
vcnt = 0
dcnt = 0
println("Finding the first ", vgoal, " vampire numbers.")
println(" N Vampire Fangs")
while vcnt < vgoal
dcnt += 2
for i in (10^(dcnt-1)):(10^dcnt-1)
(isvampire, fangs) = vampirefangs(i)
isvampire || continue
vcnt += 1
print(showvampire(vcnt, i, fangs))
vcnt < vgoal || break
end
end
test = [16758243290880, 24959017348650, 14593825548650]
println()
println("Checking a few numbers.")
println(" N Vampire Fangs")
for (i, v) in enumerate(test)
(isvampire, fangs) = vampirefangs(v)
if isvampire
print(showvampire(i, v, fangs))
else
println(@sprintf "%6d %14d is not a vampire" i v)
end
end
- Output:
Finding the first 25 vampire numbers.
N Vampire Fangs
1 1260 21×60
2 1395 15×93
3 1435 35×41
4 1530 30×51
5 1827 21×87
6 2187 27×81
7 6880 80×86
8 102510 201×510
9 104260 260×401
10 105210 210×501
11 105264 204×516
12 105750 150×705
13 108135 135×801
14 110758 158×701
15 115672 152×761
16 116725 161×725
17 117067 167×701
18 118440 141×840
19 120600 201×600
20 123354 231×534
21 124483 281×443
22 125248 152×824
23 125433 231×543
24 125460 204×615
246×510
25 125500 251×500
Checking a few numbers.
N Vampire Fangs
1 16758243290880 1982736×8452080
2123856×7890480
2751840×6089832
2817360×5948208
2 24959017348650 2947050×8469153
2949705×8461530
4125870×6049395
4129587×6043950
4230765×5899410
3 14593825548650 is not a vampire
Kotlin
// version 1.1
data class Fangs(val fang1: Long = 0L, val fang2: Long = 0L)
fun pow10(n: Int): Long = when {
n < 0 -> throw IllegalArgumentException("Can't be negative")
else -> {
var pow = 1L
for (i in 1..n) pow *= 10L
pow
}
}
fun countDigits(n: Long): Int = when {
n < 0L -> throw IllegalArgumentException("Can't be negative")
n == 0L -> 1
else -> {
var count = 0
var nn = n
while (nn > 0L) {
count++
nn /= 10L
}
count
}
}
fun hasTrailingZero(n: Long): Boolean = when {
n < 0L -> throw IllegalArgumentException("Can't be negative")
else -> n % 10L == 0L
}
fun sortedString(s: String): String {
val ca = s.toCharArray()
ca.sort()
return String(ca)
}
fun isVampiric(n: Long, fl: MutableList<Fangs>): Boolean {
if (n < 0L) return false
val len = countDigits(n)
if (len % 2L == 1L) return false
val hlen = len / 2
val first = pow10(hlen - 1)
val last = 10L * first
var j: Long
var cd: Int
val ss = sortedString(n.toString())
for (i in first until last) {
if (n % i != 0L) continue
j = n / i
if (j < i) return fl.size > 0
cd = countDigits(j)
if (cd > hlen) continue
if (cd < hlen) return fl.size > 0
if (ss != sortedString(i.toString() + j.toString())) continue
if (!(hasTrailingZero(i) && hasTrailingZero(j))) {
fl.add(Fangs(i, j))
}
}
return fl.size > 0
}
fun showFangs(fangsList: MutableList<Fangs>): String {
var s = ""
for ((fang1, fang2) in fangsList) {
s += " = $fang1 x $fang2"
}
return s
}
fun main(args: Array<String>) {
println("The first 25 vampire numbers and their fangs are:")
var count = 0
var n: Long = 0
val fl = mutableListOf<Fangs>()
while (true) {
if (isVampiric(n, fl)) {
count++
println("${"%2d".format(count)} : $n\t${showFangs(fl)}")
fl.clear()
if (count == 25) break
}
n++
}
println()
val va = longArrayOf(16758243290880L, 24959017348650L, 14593825548650L)
for (v in va) {
if (isVampiric(v, fl)) {
println("$v\t${showFangs(fl)}")
fl.clear()
} else {
println("$v\t = not vampiric")
}
}
}
- Output:
The first 25 vampire numbers and their fangs are: 1 : 1260 = 21 x 60 2 : 1395 = 15 x 93 3 : 1435 = 35 x 41 4 : 1530 = 30 x 51 5 : 1827 = 21 x 87 6 : 2187 = 27 x 81 7 : 6880 = 80 x 86 8 : 102510 = 201 x 510 9 : 104260 = 260 x 401 10 : 105210 = 210 x 501 11 : 105264 = 204 x 516 12 : 105750 = 150 x 705 13 : 108135 = 135 x 801 14 : 110758 = 158 x 701 15 : 115672 = 152 x 761 16 : 116725 = 161 x 725 17 : 117067 = 167 x 701 18 : 118440 = 141 x 840 19 : 120600 = 201 x 600 20 : 123354 = 231 x 534 21 : 124483 = 281 x 443 22 : 125248 = 152 x 824 23 : 125433 = 231 x 543 24 : 125460 = 204 x 615 = 246 x 510 25 : 125500 = 251 x 500 16758243290880 = 1982736 x 8452080 = 2123856 x 7890480 = 2751840 x 6089832 = 2817360 x 5948208 24959017348650 = 2947050 x 8469153 = 2949705 x 8461530 = 4125870 x 6049395 = 4129587 x 6043950 = 4230765 x 5899410 14593825548650 = not vampiric
Mathematica /Wolfram Language
ClearAll[VampireQ]
VampireQ[num_Integer] := Module[{poss, divs},
divs = Select[Divisors[num], # <= Sqrt[num] &];
poss = {#, num/#} & /@ divs;
If[Length[poss] > 0,
poss = Select[poss, Mod[#, 10] =!= {0, 0} &];
If[Length[poss] > 0,
poss = Select[poss, Length[IntegerDigits[First[#]]] == Length[IntegerDigits[Last[#]]] &];
If[Length[poss] > 0,
poss = Select[poss, Sort[IntegerDigits[num]] == Sort[Join @@ (IntegerDigits /@ #)] &];
If[Length[poss] > 0
,
Sow[{num, poss}];
True
,
False
]
,
False
]
,
False
]
,
False
]
]
Testing out the function:
Reap[Scan[VampireQ,Range[126027]]][[2,1]]//Grid
Reap[VampireQ[#]] & /@ {16758243290880, 24959017348650, 14593825548650} // Grid
- Output:
1260 {{21,60}}
1395 {{15,93}}
1435 {{35,41}}
1530 {{30,51}}
1827 {{21,87}}
2187 {{27,81}}
6880 {{80,86}}
102510 {{201,510}}
104260 {{260,401}}
105210 {{210,501}}
105264 {{204,516}}
105750 {{150,705}}
108135 {{135,801}}
110758 {{158,701}}
115672 {{152,761}}
116725 {{161,725}}
117067 {{167,701}}
118440 {{141,840}}
120600 {{201,600}}
123354 {{231,534}}
124483 {{281,443}}
125248 {{152,824}}
125433 {{231,543}}
125460 {{204,615},{246,510}}
125500 {{251,500}}
True {{{16758243290880,{{1982736,8452080},{2123856,7890480},{2751840,6089832},{2817360,5948208}}}}}
True {{{24959017348650,{{2947050,8469153},{2949705,8461530},{4125870,6049395},{4129587,6043950},{4230765,5899410}}}}}
False {}
Nim
import algorithm, math, sequtils, strformat, strutils, sugar
const Pow10 = collect(newSeq, for n in 0..18: 10 ^ n)
template isOdd(n: int): bool = (n and 1) != 0
proc fangs(n: Positive): seq[(int, int)] =
## Return the list fo fangs of "n" (empty if "n" is not vampiric).
let nDigits = sorted($n)
if nDigits.len.isOdd: return @[]
let fangLen = nDigits.len div 2
let inf = Pow10[fangLen - 1]
let sup = inf * 10 - 1
for d in inf..sup:
if n mod d != 0: continue
let q = n div d
if q < d: return
let dDigits = $d
let qDigits = $q
if qDigits.len > fangLen: continue
if qDigits.len < fangLen: return
if nDigits != sorted(dDigits & qDigits): continue
if dDigits[^1] != '0' or qDigits[^1] != '0':
# Finally, "n" is vampiric. Add the fangs to the result.
result.add (d, q)
echo "First 25 vampire numbers with their fangs:"
var count = 0
var n = 10
var limit = 100
while count != 25:
let fangList = n.fangs
if fangList.len != 0:
inc count
echo &"{count:2}: {n:>6} = ", fangList.mapIt(&"{it[0]:3} × {it[1]:3}").join(" = ")
inc n
if n == limit:
n *= 10
limit *= 10
echo()
for n in [16_758_243_290_880, 24_959_017_348_650, 14_593_825_548_650]:
let fangList = n.fangs
if fangList.len == 0:
echo &"{n} is not vampiric."
else:
echo &"{n} = ", fangList.mapIt(&"{it[0]} × {it[1]}").join(" = ")
- Output:
First 25 vampire numbers with their fangs: 1: 1260 = 21 × 60 2: 1395 = 15 × 93 3: 1435 = 35 × 41 4: 1530 = 30 × 51 5: 1827 = 21 × 87 6: 2187 = 27 × 81 7: 6880 = 80 × 86 8: 102510 = 201 × 510 9: 104260 = 260 × 401 10: 105210 = 210 × 501 11: 105264 = 204 × 516 12: 105750 = 150 × 705 13: 108135 = 135 × 801 14: 110758 = 158 × 701 15: 115672 = 152 × 761 16: 116725 = 161 × 725 17: 117067 = 167 × 701 18: 118440 = 141 × 840 19: 120600 = 201 × 600 20: 123354 = 231 × 534 21: 124483 = 281 × 443 22: 125248 = 152 × 824 23: 125433 = 231 × 543 24: 125460 = 204 × 615 = 246 × 510 25: 125500 = 251 × 500 16758243290880 = 1982736 × 8452080 = 2123856 × 7890480 = 2751840 × 6089832 = 2817360 × 5948208 24959017348650 = 2947050 × 8469153 = 2949705 × 8461530 = 4125870 × 6049395 = 4129587 × 6043950 = 4230765 × 5899410 14593825548650 is not vampiric.
PARI/GP
fang(n)=my(v=digits(n),u=List());if(#v%2,return([]));fordiv(n,d,if(#Str(d)==#v/2 && #Str(n/d)==#v/2 && vecsort(v)==vecsort(concat(digits(d),digits(n/d))) && (d%10 || (n/d)%10), if(d^2>n,return(Vec(u))); listput(u, d))); Vec(u)
k=25;forstep(d=4,6,2,for(n=10^(d-1),10^d-1,f=fang(n); for(i=1,#f,print(n" "f[i]" "n/f[i]); if(i==#f && k--==0,return))))
print();v=[16758243290880, 24959017348650, 14593825548650];
for(i=1,#v,f=fang(v[i]); for(j=1,#f, print(v[i]" "f[j]" "v[i]/f[j])))Output:
1260 21 60 1395 15 93 1435 35 41 1530 30 51 1827 21 87 2187 27 81 6880 80 86 102510 201 510 104260 260 401 105210 210 501 105264 204 516 105750 150 705 108135 135 801 110758 158 701 115672 152 761 116725 161 725 117067 167 701 118440 141 840 120600 201 600 123354 231 534 124483 281 443 125248 152 824 125433 231 543 125460 204 615 125460 246 510 125500 251 500 16758243290880 1982736 8452080 16758243290880 2123856 7890480 16758243290880 2751840 6089832 16758243290880 2817360 5948208 24959017348650 2947050 8469153 24959017348650 2949705 8461530 24959017348650 4125870 6049395 24959017348650 4129587 6043950 24959017348650 4230765 5899410
Perl
The trailing zeros condition is first triggered when searching for the 26th vampire number.
#!/usr/bin/perl
use warnings;
use strict;
use feature qw(say);
sub fangs {
my $vampire = shift;
my $length = length 0 + $vampire;
return if $length % 2;
my $fang_length = $length / 2;
my $from = '1' . '0' x ($fang_length - 1);
my $to = '9' x $fang_length;
my $sorted = join q(), sort split //, $vampire;
my @fangs;
for my $f1 ($from .. 1 + sqrt $vampire) {
next if $vampire % $f1;
my $f2 = $vampire / $f1;
next if $sorted ne join q(), sort split //, $f1 . $f2;
next if 2 == grep '0' eq substr($_, -1 , 1), $f1, $f2; # Needed for the 26th number.
push @fangs, [$f1, $f2];
}
return @fangs;
}
my $count = 0;
my $i = 9;
while ($count < 25) {
$i++;
my @f = fangs($i);
$count++, say join ' ', "$count. $i:", map "[@$_]", @f if @f;
}
say join ' ', $_, map "[@$_]", fangs($_) for 16758243290880, 24959017348650, 14593825548650;
A faster version, using the `divisors()` function from the ntheory library.
use ntheory qw(sqrtint logint divisors);
sub is_vampire {
my ($n) = @_;
return if (length($n) % 2 or $n < 0);
my $l1 = 10**logint(sqrtint($n), 10);
my $l2 = sqrtint($n);
my $s = join('', sort split(//, $n));
my @fangs;
foreach my $d (divisors($n)) {
$d < $l1 and next;
$d > $l2 and last;
my $t = $n / $d;
next if ($d % 10 == 0 and $t % 10 == 0);
next if (join('', sort split(//, "$d$t")) ne $s);
push @fangs, [$d, $t];
}
return @fangs;
}
print "First 25 Vampire Numbers:\n";
for (my ($n, $i) = (1, 1) ; $i <= 25 ; ++$n) {
if (my @fangs = is_vampire($n)) {
printf("%2d. %6s : %s\n", $i++, $n, join(' ', map { "[@$_]" } @fangs));
}
}
print "\nIndividual tests:\n";
foreach my $n (16758243290880, 24959017348650, 14593825548650) {
my @fangs = is_vampire($n);
print("$n: ", (@fangs ? join(' ', map { "[@$_]" } @fangs)
: "is not a vampire number"), "\n");
}
- Output:
First 25 Vampire Numbers: 1. 1260 : [21 60] 2. 1395 : [15 93] 3. 1435 : [35 41] 4. 1530 : [30 51] 5. 1827 : [21 87] 6. 2187 : [27 81] 7. 6880 : [80 86] 8. 102510 : [201 510] 9. 104260 : [260 401] 10. 105210 : [210 501] 11. 105264 : [204 516] 12. 105750 : [150 705] 13. 108135 : [135 801] 14. 110758 : [158 701] 15. 115672 : [152 761] 16. 116725 : [161 725] 17. 117067 : [167 701] 18. 118440 : [141 840] 19. 120600 : [201 600] 20. 123354 : [231 534] 21. 124483 : [281 443] 22. 125248 : [152 824] 23. 125433 : [231 543] 24. 125460 : [204 615] [246 510] 25. 125500 : [251 500] Individual tests: 16758243290880: [1982736 8452080] [2123856 7890480] [2751840 6089832] [2817360 5948208] 24959017348650: [2947050 8469153] [2949705 8461530] [4125870 6049395] [4129587 6043950] [4230765 5899410] 14593825548650: is not a vampire number
Phix
with javascript_semantics requires("1.0.2") -- (for in) function vampire(atom v) sequence res = {} if v>=0 then string vs = sprintf("%d",v) if mod(length(vs),2)=0 then -- even length vs = sort(vs) for i=power(10,length(vs)/2-1) to floor(sqrt(v)) do if remainder(v,i)=0 then integer i2 = v/i string si = sprintf("%d",i), s2 = sprintf("%d",i2) if (si[$]!='0' or s2[$]!='0') and sort(si&s2)=vs then res = append(res,{i,i2}) end if end if end for end if end if return res end function integer found = 0 atom i = 0 sequence res puts(1,"The first 26 vampire numbers and their fangs:\n") while found<26 do res = vampire(i) if length(res) then found += 1 printf(1,"%d: %d: %v\n",{found,i,res}) end if i += 1 end while puts(1,"\n") for i in {16758243290880,24959017348650,14593825548650} do res = vampire(i) printf(1,"%d: %s\n",{i,iff(res={}?"not a vampire number":sprint(res))}) end for
- Output:
The first 26 vampire numbers and their fangs:
1: 1260: {{21,60}}
2: 1395: {{15,93}}
3: 1435: {{35,41}}
4: 1530: {{30,51}}
5: 1827: {{21,87}}
6: 2187: {{27,81}}
7: 6880: {{80,86}}
8: 102510: {{201,510}}
9: 104260: {{260,401}}
10: 105210: {{210,501}}
11: 105264: {{204,516}}
12: 105750: {{150,705}}
13: 108135: {{135,801}}
14: 110758: {{158,701}}
15: 115672: {{152,761}}
16: 116725: {{161,725}}
17: 117067: {{167,701}}
18: 118440: {{141,840}}
19: 120600: {{201,600}}
20: 123354: {{231,534}}
21: 124483: {{281,443}}
22: 125248: {{152,824}}
23: 125433: {{231,543}}
24: 125460: {{204,615},{246,510}}
25: 125500: {{251,500}}
26: 126027: {{201,627}}
16758243290880: {{1982736,8452080},{2123856,7890480},{2751840,6089832},{2817360,5948208}}
24959017348650: {{2947050,8469153},{2949705,8461530},{4125870,6049395},{4129587,6043950},{4230765,5899410}}
14593825548650: not a vampire number
PureBasic
EnableExplicit
DisableDebugger
Macro CheckVamp(CheckNum)
c=0 : i=CheckNum : Print(~"\nCheck number: "+Str(i)+~"\n")
Gosub VampireLoop : If c=0 : Print(Str(i)+" is not vampiric.") : EndIf : PrintN("")
EndMacro
Procedure.i Factor(number.i,counter.i)
If number>0 And number>=counter*counter And number%counter=0
ProcedureReturn counter
EndIf
ProcedureReturn 0
EndProcedure
Procedure.b IsVampire(f1.i,f2.i)
Define a.s=Str(f1*f2),
b.s=Str(f1),
c.s=Str(f2),
d.s=b+c,
i.i
If Len(a)=Len(d) And Len(b)=Len(c)
While Len(a)
i=FindString(d,Left(a,1))
If i
a=Mid(a,2)
d=RemoveString(d,Mid(d,i,1),#PB_String_NoCase,i,1)
Else
ProcedureReturn #False
EndIf
Wend
ProcedureReturn Bool(Len(d)=0)
EndIf
ProcedureReturn #False
EndProcedure
OpenConsole("Vampire number")
Define i.i,
j.i,
m.i,
c.i=0
PrintN("The first 25 Vampire numbers...")
While c<25 : i+1 : Gosub VampireLoop : Wend
PrintN("")
CheckVamp(16758243290880) : CheckVamp(24959017348650) : CheckVamp(14593825548650)
Input()
End
VampireLoop:
For j=1 To Int(Sqr(i))
If Factor(i,j)>0
m=i/j
Else
Continue
EndIf
If IsVampire(m,j)
c+1
PrintN(RSet(Str(c),3," ")+". "+RSet(Str(i),10," ")+": ["+Str(j)+", "+Str(m)+"]")
EndIf
Next
Return
- Output:
The first 25 Vampire numbers... 1. 1260: [21, 60] 2. 1395: [15, 93] 3. 1435: [35, 41] 4. 1530: [30, 51] 5. 1827: [21, 87] 6. 2187: [27, 81] 7. 6880: [80, 86] 8. 102510: [201, 510] 9. 104260: [260, 401] 10. 105210: [210, 501] 11. 105264: [204, 516] 12. 105750: [150, 705] 13. 108135: [135, 801] 14. 110758: [158, 701] 15. 115672: [152, 761] 16. 116725: [161, 725] 17. 117067: [167, 701] 18. 118440: [141, 840] 19. 120600: [201, 600] 20. 123354: [231, 534] 21. 124483: [281, 443] 22. 125248: [152, 824] 23. 125433: [231, 543] 24. 125460: [204, 615] 25. 125460: [246, 510] Check number: 16758243290880 1. 1675824329: [1982736, 8452080] 2. 1675824329: [2123856, 7890480] 3. 1675824329: [2751840, 6089832] 4. 1675824329: [2817360, 5948208] Check number: 24959017348650 1. 2495901734: [2947050, 8469153] 2. 2495901734: [2949705, 8461530] 3. 2495901734: [4125870, 6049395] 4. 2495901734: [4129587, 6043950] 5. 2495901734: [4230765, 5899410] Check number: 14593825548650 14593825548650 is not vampiric.
Python
This routine finds all the fangs for a number.
from __future__ import division
import math
from operator import mul
from itertools import product
from functools import reduce
def fac(n):
'''\
return the prime factors for n
>>> fac(600)
[5, 5, 3, 2, 2, 2]
>>> fac(1000)
[5, 5, 5, 2, 2, 2]
>>>
'''
step = lambda x: 1 + x*4 - (x//2)*2
maxq = int(math.floor(math.sqrt(n)))
d = 1
q = n % 2 == 0 and 2 or 3
while q <= maxq and n % q != 0:
q = step(d)
d += 1
res = []
if q <= maxq:
res.extend(fac(n//q))
res.extend(fac(q))
else: res=[n]
return res
def fact(n):
'''\
return the prime factors and their multiplicities for n
>>> fact(600)
[(2, 3), (3, 1), (5, 2)]
>>> fact(1000)
[(2, 3), (5, 3)]
>>>
'''
res = fac(n)
return [(c, res.count(c)) for c in set(res)]
def divisors(n):
'Returns all the divisors of n'
factors = fact(n) # [(primefactor, multiplicity), ...]
primes, maxpowers = zip(*factors)
powerranges = (range(m+1) for m in maxpowers)
powers = product(*powerranges)
return (
reduce(mul,
(prime**power for prime, power in zip(primes, powergroup)),
1)
for powergroup in powers)
def vampire(n):
fangsets = set( frozenset([d, n//d])
for d in divisors(n)
if (len(str(d)) == len(str(n))/2.
and sorted(str(d) + str(n//d)) == sorted(str(n))
and (str(d)[-1] == 0) + (str(n//d)[-1] == 0) <=1) )
return sorted(tuple(sorted(fangs)) for fangs in fangsets)
if __name__ == '__main__':
print('First 25 vampire numbers')
count = n = 0
while count <25:
n += 1
fangpairs = vampire(n)
if fangpairs:
count += 1
print('%i: %r' % (n, fangpairs))
print('\nSpecific checks for fangpairs')
for n in (16758243290880, 24959017348650, 14593825548650):
fangpairs = vampire(n)
print('%i: %r' % (n, fangpairs))
- Output:
First 25 vampire numbers 1260: [(21, 60)] 1395: [(15, 93)] 1435: [(35, 41)] 1530: [(30, 51)] 1827: [(21, 87)] 2187: [(27, 81)] 6880: [(80, 86)] 102510: [(201, 510)] 104260: [(260, 401)] 105210: [(210, 501)] 105264: [(204, 516)] 105750: [(150, 705)] 108135: [(135, 801)] 110758: [(158, 701)] 115672: [(152, 761)] 116725: [(161, 725)] 117067: [(167, 701)] 118440: [(141, 840)] 120600: [(201, 600)] 123354: [(231, 534)] 124483: [(281, 443)] 125248: [(152, 824)] 125433: [(231, 543)] 125460: [(204, 615), (246, 510)] 125500: [(251, 500)] Specific checks for fangpairs 16758243290880: [(1982736, 8452080), (2123856, 7890480), (2751840, 6089832), (2817360, 5948208)] 24959017348650: [(2947050, 8469153), (2949705, 8461530), (4125870, 6049395), (4129587, 6043950), (4230765, 5899410)] 14593825548650: []
This alternative solution is not fast but it's short:
from math import sqrt
from itertools import imap, ifilter, islice, count
def factor_pairs(n):
return ((x, n // x) for x in xrange(2, int(sqrt(n))) if n % x == 0)
def fangs(n):
dlen = lambda x: len(str(x))
half = dlen(n) // 2
digits = lambda (x, y): sorted(str(x) + str(y))
halvesQ = lambda xs: all(y == half for y in imap(dlen, xs))
dn = sorted(str(n))
return [p for p in factor_pairs(n) if halvesQ(p) and dn==digits(p)]
def vampiricQ(n):
fn = fangs(n)
return (n, fn) if fn else None
for v in islice(ifilter(None, imap(vampiricQ, count())), 0, 25):
print v
for n in [16758243290880, 24959017348650, 14593825548650]:
print vampiricQ(n) or str(n) + " is not vampiric."
- Output:
(1260, [(21, 60)]) (1395, [(15, 93)]) (1435, [(35, 41)]) (1530, [(30, 51)]) (1827, [(21, 87)]) (2187, [(27, 81)]) (6880, [(80, 86)]) (102510, [(201, 510)]) (104260, [(260, 401)]) (105210, [(210, 501)]) (105264, [(204, 516)]) (105750, [(150, 705)]) (108135, [(135, 801)]) (110758, [(158, 701)]) (115672, [(152, 761)]) (116725, [(161, 725)]) (117067, [(167, 701)]) (118440, [(141, 840)]) (120600, [(201, 600)]) (123354, [(231, 534)]) (124483, [(281, 443)]) (125248, [(152, 824)]) (125433, [(231, 543)]) (125460, [(204, 615), (246, 510)]) (125500, [(251, 500)]) (16758243290880L, [(1982736, 8452080L), (2123856, 7890480L), (2751840, 6089832L), (2817360, 5948208L)]) (24959017348650L, [(2947050, 8469153L), (2949705, 8461530L), (4125870, 6049395L), (4129587, 6043950L), (4230765, 5899410L)]) 14593825548650 is not vampiric.
Racket
Naive implementation, but notice the sequence-filter/sequence-map composition -- it's a good way to "find the first n numbers meeting predicate p?":
#lang racket
;; chock full of fun... including divisors
(require math/number-theory)
;; predicate to tell if n is a vampire number
(define (sub-vampire?-and-fangs n)
(define digit-count-n (add1 (order-of-magnitude n)))
(define (string-sort-characters s) (sort (string->list s) char<?))
(define digits-in-order-n (string-sort-characters (number->string n)))
(define (fangs-of-n? d e)
(and (<= d e) ; avoid duplication
(= (add1 (order-of-magnitude d)) (add1 (order-of-magnitude e)) (/ digit-count-n 2))
(not (= 0 (modulo d 10) (modulo e 10)))
(equal? digits-in-order-n
(string-sort-characters (string-append (number->string d) (number->string e))))))
(let* ((fangses (for*/list ((d (in-list (divisors n))) #:when (fangs-of-n? d (/ n d)))
(list d (/ n d)))))
(and (not (null? fangses)) (cons n fangses))))
(define (vampire?-and-fangs n)
(and (odd? (order-of-magnitude n)) ; even number of digits - else not even worth looking!
(sub-vampire?-and-fangs n)))
(displayln "First 25 vampire numbers:")
(for ((vmp (sequence-filter identity (sequence-map vampire?-and-fangs (in-naturals 1))))
(cnt (in-range 1 (add1 25))))
(printf "#~a ~a~%" cnt vmp))
(displayln "Test the big numbers:")
(displayln (vampire?-and-fangs 16758243290880))
(displayln (vampire?-and-fangs 24959017348650))
(displayln (vampire?-and-fangs 14593825548650))
Output:
First 25 vampire numbers: #1 (1260 (21 60)) #2 (1395 (15 93)) #3 (1435 (35 41)) #4 (1530 (30 51)) #5 (1827 (21 87)) #6 (2187 (27 81)) #7 (6880 (80 86)) #8 (102510 (201 510)) #9 (104260 (260 401)) #10 (105210 (210 501)) #11 (105264 (204 516)) #12 (105750 (150 705)) #13 (108135 (135 801)) #14 (110758 (158 701)) #15 (115672 (152 761)) #16 (116725 (161 725)) #17 (117067 (167 701)) #18 (118440 (141 840)) #19 (120600 (201 600)) #20 (123354 (231 534)) #21 (124483 (281 443)) #22 (125248 (152 824)) #23 (125433 (231 543)) #24 (125460 (204 615) (246 510)) #25 (125500 (251 500)) Test the big numbers: (16758243290880 (1982736 8452080) (2123856 7890480) (2751840 6089832) (2817360 5948208)) (24959017348650 (2947050 8469153) (2949705 8461530) (4125870 6049395) (4129587 6043950) (4230765 5899410)) #f
Raku
(formerly Perl 6)
sub is_vampire (Int $num) {
my $digits = $num.comb.sort;
my @fangs;
(10**$num.sqrt.log(10).floor .. $num.sqrt.ceiling).map: -> $this {
next if $num % $this;
my $that = $num div $this;
next if $this %% 10 && $that %% 10;
@fangs.push("$this x $that") if ($this ~ $that).comb.sort eq $digits;
}
@fangs
}
constant @vampires = flat (3..*).map: -> $s, $e {
(10**$s .. 10**$e).hyper.map: -> $n {
next unless my @fangs = is_vampire($n);
"$n: { @fangs.join(', ') }"
}
}
say "\nFirst 25 Vampire Numbers:\n";
.say for @vampires[^25];
say "\nIndividual tests:\n";
.say for (16758243290880, 24959017348650, 14593825548650).hyper(:1batch).map: {
"$_: " ~ (is_vampire($_).join(', ') || 'is not a vampire number.')
}
First 25 Vampire Numbers: 1260: 21 x 60 1395: 15 x 93 1435: 35 x 41 1530: 30 x 51 1827: 21 x 87 2187: 27 x 81 6880: 80 x 86 102510: 201 x 510 104260: 260 x 401 105210: 210 x 501 105264: 204 x 516 105750: 150 x 705 108135: 135 x 801 110758: 158 x 701 115672: 152 x 761 116725: 161 x 725 117067: 167 x 701 118440: 141 x 840 120600: 201 x 600 123354: 231 x 534 124483: 281 x 443 125248: 152 x 824 125433: 231 x 543 125460: 204 x 615, 246 x 510 125500: 251 x 500 Individual tests: 16758243290880: 1982736 x 8452080, 2123856 x 7890480, 2751840 x 6089832, 2817360 x 5948208 24959017348650: 2947050 x 8469153, 2949705 x 8461530, 4125870 x 6049395, 4129587 x 6043950, 4230765 x 5899410 14593825548650: is not a vampire number.
REXX
Note: if the argument is negative, its absolute value is used to test if that single number is vampiric.
/*REXX program displays N vampire numbers, or verifies if a number is vampiric. */
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N= 25 /*Not specified? Then use the default.*/
!.0= 1260; !.1= 11453481; !.2= 115672; !.3= 124483; !.4= 105264 /*lowest #, dig*/
!.5= 1395; !.6= 126846; !.7= 1827; !.8= 110758; !.9= 156289 /* " " " */
L= length(N); aN= abs(N) /*L: length of N; aN: absolute value*/
numeric digits max(9, length(aN) ) /*be able to handle ginormus numbers. */
# = 0 /*#: count of vampire numbers (so far)*/
if N>0 then do j=1260 until # >= N /*search until N vampire numbers found.*/
if length(j) // 2 then do; j= j*10 - 1; iterate /*bump J to even length*/
end /* [↑] check if odd. */
parse var j '' -1 _ /*obtain the last decimal digit of J. */
if j<!._ then iterate /*is number tenable based on last dig? */
f= vampire(j) /*obtain the fangs of J. */
if f=='' then iterate /*Are fangs null? Yes, not vampire. */
#= # + 1 /*bump the vampire count, Vlad. */
say right('vampire number', 20) right(#, L) "is: " right(j, 9)', fangs=' f
end /*j*/ /* [↑] process a range of numbers. */
else do; f= vampire(aN) /* [↓] process a number; obtain fangs.*/
if f=='' then say aN " isn't a vampire number."
else say aN " is a vampire number, fangs=" f
end
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
vampire: procedure; parse arg x,, $. a bot; L= length(x) /*get arg; compute len of X*/
if L//2 then return '' /*is L odd? Then ¬vampire.*/
do k=1 for L; _= substr(x, k, 1); $._= $._ || _
end /*k*/
w= L % 2 /*%: is REXX's integer ÷ */
do m=0 for 10; bot= bot || $.m
end /*m*/
top= left( reverse(bot), w)
bot= left(bot, w) /*determine limits of search*/
inc= x // 2 + 1 /*X is odd? INC=2. No? INC=1*/
beg= max(bot, 10 ** (w-1) ) /*calculate where to begin.*/
if inc==2 then if beg//2==0 then beg= beg + 1 /*possibly adjust the begin.*/
/* [↑] odd BEG if odd INC*/
do d=beg to min(top, 10**w - 1) by inc /*use smart BEG, END, INC. */
if x // d \==0 then iterate /*X not ÷ by D? Then skip,*/
q= x % d; if d>q then iterate /*is D > Q " " */
if length(q) \== w then iterate /*Len of Q ¬= W? Then skip.*/
if q*d//9 \== (q+d)//9 then iterate /*modulo 9 congruence test. */
parse var q '' -1 _ /*get last decimal dig. of Q*/
if _== 0 then if right(d, 1) == 0 then iterate
dq= d || q
t= x; do i=1 for L; p= pos( substr(dq, i, 1), t)
if p==0 then iterate d; t= delstr(t, p, 1)
end /*i*/
a= a '['d"∙"q'] ' /*construct formatted fangs.*/
end /*d*/ /* [↑] ∙ is a round bullet*/
return a /*return formatted fangs.*/
- output when using the default input:
vampire number 1 is: 1260, fangs= [21∙60]
vampire number 2 is: 1395, fangs= [15∙93]
vampire number 3 is: 1435, fangs= [35∙41]
vampire number 4 is: 1530, fangs= [30∙51]
vampire number 5 is: 1827, fangs= [21∙87]
vampire number 6 is: 2187, fangs= [27∙81]
vampire number 7 is: 6880, fangs= [80∙86]
vampire number 8 is: 102510, fangs= [201∙510]
vampire number 9 is: 104260, fangs= [260∙401]
vampire number 10 is: 105210, fangs= [210∙501]
vampire number 11 is: 105264, fangs= [204∙516]
vampire number 12 is: 105750, fangs= [150∙705]
vampire number 13 is: 108135, fangs= [135∙801]
vampire number 14 is: 110758, fangs= [158∙701]
vampire number 15 is: 115672, fangs= [152∙761]
vampire number 16 is: 116725, fangs= [161∙725]
vampire number 17 is: 117067, fangs= [167∙701]
vampire number 18 is: 118440, fangs= [141∙840]
vampire number 19 is: 120600, fangs= [201∙600]
vampire number 20 is: 123354, fangs= [231∙534]
vampire number 21 is: 124483, fangs= [281∙443]
vampire number 22 is: 125248, fangs= [152∙824]
vampire number 23 is: 125433, fangs= [231∙543]
vampire number 24 is: 125460, fangs= [204∙615] [246∙510]
vampire number 25 is: 125500, fangs= [251∙500]
- output when using the input of: -16758243290880
16758243290880 is a vampire number, fangs= [1982736∙8452080] [2123856∙7890480] [2751840∙6089832] [2817360∙5948208]
- output when using the input of: -24959017348650
24959017348650 is a vampire number, fangs= [2947050∙8469153] [2949705∙8461530] [4125870∙6049395] [4129587∙6043950] [4230765∙5899410]
- output when using the input of: -14593825548650
14593825548650 isn't a vampire number.
Ring
# Project : Vampire number
for p = 10 to 127000
vampire(p)
next
func vampire(listnum)
sum = 0
flag = 1
list = list(len(string(listnum)))
total = newlist(len(list),2)
for n = 1 to len(string(listnum))
liststr = string(listnum)
list[n] = liststr[n]
next
for perm = 1 to fact(len(list))
numstr = substr(list2str(list), nl, "")
num1 = number(left(numstr,len(numstr)/2))
num2 = number(right(numstr,len(numstr)/2))
if (listnum = num1 * num2)
for n = 1 to len(total)
if (num1 = total[n][2] and num2 = total[n][1]) or
(num1 = total[n][1] and num2 = total[n][2])
flag = 0
ok
next
if flag = 1
sum = sum + 1
total[sum][1] = num1
total[sum][2] = num2
see "" + listnum + ": [" + num1 + "," + num2 + "]" + nl
ok
ok
nextPermutation(list)
next
func nextPermutation(a)
elementcount = len(a)
if elementcount < 1 then return ok
pos = elementcount-1
while a[pos] >= a[pos+1]
pos -= 1
if pos <= 0 permutationReverse(a, 1, elementcount)
return ok
end
last = elementcount
while a[last] <= a[pos]
last -= 1
end
temp = a[pos]
a[pos] = a[last]
a[last] = temp
permutationReverse(a, pos+1, elementcount)
func permutationReverse a, first, last
while first < last
temp = a[first]
a[first] = a[last]
a[last] = temp
first += 1
last -= 1
end
func fact(nr)
if nr = 1
return 1
else
return nr * fact(nr-1)
ok
func newlist(x,y)
if isstring(x) x=0+x ok
if isstring(y) y=0+y ok
alist = list(x)
for t in alist
t = list(y)
next
return alistOutput:
1260: [21,60] 1395: [15,93] 1435: [35,41] 1530: [30,51] 1827: [21,87] 2187: [27,81] 6880: [80,86] 102510: [201,510] 104260: [260,401] 105210: [210,501] 105264: [204,516] 105750: [150,705] 108135: [135,801] 110758: [158,701] 115672: [152,761] 116725: [161,725] 117067: [167,701] 118440: [141,840] 123354: [231,534] 124483: [281,443] 125248: [152,824] 125433: [231,543] 125460: [204,615] [246,510] 125500: [251,500] 126027: [201,627]
RPL
« 0 10 NDPUN →LIST
WHILE OVER REPEAT
SWAP 10 IDIV2 1 +
ROT SWAP DUP2 GET 1 + PUT
END NIP
» 'DIGCNT' STO
« DUP XPON LASTARG DIGCNT 2 / IP { } DUP
→ n digc fangsize result divs
« n DIVIS SORT
DUP « XPON » MAP
DUP fangsize POS
IF DUP THEN
SWAP fangsize 1 + POS 1 - PICK3 SIZE MIN FOR j
DUP j GET
CASE
divs OVER POS THEN DROP END
n OVER /
DUP XPON fangsize ≠ THEN DROP2 END
2 →LIST
DUP 10 MOD { 0 0 } == THEN DROP END
DUP « →STR » MAP ∑LIST STR→ DIGCNT digc ≠ THEN DROP END
DUP 2 GET 'divs' STO+
'result' STO+
END
NEXT
ELSE DROP2 END
DROP result
» » 'VAMPIRE?' STO
« IF OVER SIZE THEN
1 PICK3 SIZE FOR j
" = " +
OVER j GET +
"*" + OVER j 1 + GET +
2 STEP NIP
ELSE DROP2 "Not vampiric" END
» 'V→STR' STO @ ( { (d1,d2) } n → "n = d1*d2" )
« { } 10
WHILE OVER SIZE 8 < REPEAT
DUP VAMPIRE?
IF DUP SIZE THEN
OVER V→STR
ROT SWAP + SWAP
ELSE DROP END
1 +
IF DUP XPON 2 MOD NOT THEN 10 * END
END DROP
{ 16758243290880 24959017348650 14593825548650 }
1 « DUP VAMPIRE? SWAP V→STR » DOLIST
» 'TASK' STO
Since the search is very slow, it has been limited to the first eight numbers:
- Output:
2: { "1260 = 60*21" "1395 = 15*93" "1435 = 35*41" "1530 = 30*51" "1827 = 21*87" "2187 = 27*81" "6880 = 80*86" "102510 = 510*201" }
1: { "16758243290880 = 2817360*5948208 = 2751840*6089832 = 2123856*7890480 = 1982736*8452080"
"24959017348650 = 4230765*5899410 = 4129587*6043950 = 4125870*6049395 = 2949705*8461530 = 2947050*8469153"
"Not vampiric" }
Ruby
def factor_pairs n
first = n / (10 ** (n.to_s.size / 2) - 1)
(first .. n ** 0.5).map { |i| [i, n / i] if n % i == 0 }.compact
end
def vampire_factors n
return [] if n.to_s.size.odd?
half = n.to_s.size / 2
factor_pairs(n).select do |a, b|
a.to_s.size == half && b.to_s.size == half &&
[a, b].count {|x| x%10 == 0} != 2 &&
"#{a}#{b}".chars.sort == n.to_s.chars.sort
end
end
i = vamps = 0
until vamps == 25
vf = vampire_factors(i += 1)
unless vf.empty?
puts "#{i}:\t#{vf}"
vamps += 1
end
end
[16758243290880, 24959017348650, 14593825548650].each do |n|
if (vf = vampire_factors n).empty?
puts "#{n} is not a vampire number!"
else
puts "#{n}:\t#{vf}"
end
end
- Output:
1260: [[21, 60]] 1395: [[15, 93]] 1435: [[35, 41]] 1530: [[30, 51]] 1827: [[21, 87]] 2187: [[27, 81]] 6880: [[80, 86]] 102510: [[201, 510]] 104260: [[260, 401]] 105210: [[210, 501]] 105264: [[204, 516]] 105750: [[150, 705]] 108135: [[135, 801]] 110758: [[158, 701]] 115672: [[152, 761]] 116725: [[161, 725]] 117067: [[167, 701]] 118440: [[141, 840]] 120600: [[201, 600]] 123354: [[231, 534]] 124483: [[281, 443]] 125248: [[152, 824]] 125433: [[231, 543]] 125460: [[204, 615], [246, 510]] 125500: [[251, 500]] 16758243290880: [[1982736, 8452080], [2123856, 7890480], [2751840, 6089832], [2817360, 5948208]] 24959017348650: [[2947050, 8469153], [2949705, 8461530], [4125870, 6049395], [4129587, 6043950], [4230765, 5899410]] 14593825548650 is not a vampire number!
Rust
use std::cmp::{max, min};
static TENS: [u64; 20] = [
1,
10,
100,
1000,
10000,
100000,
1000000,
10000000,
100000000,
1000000000,
10000000000,
100000000000,
1000000000000,
10000000000000,
100000000000000,
1000000000000000,
10000000000000000,
100000000000000000,
1000000000000000000,
10000000000000000000,
];
/// Get the number of digits present in x
fn ndigits(mut x: u64) -> u64 {
let mut n = 0;
while x != 0 {
n += 1;
x /= 10;
}
n
}
fn dtally(mut x: u64) -> u64 {
let mut t = 0;
while x != 0 {
t += 1 << ((x % 10) * 6);
x /= 10;
}
t
}
/// Get a list of all fangs of x. Get only the first divider of each fang. The second one can be found simply with x / fang.
fn fangs(x: u64) -> Vec<u64> {
let mut nd = ndigits(x) as usize;
let mut fangs = vec![];
if nd & 1 != 1 {
nd /= 2;
let lo = max(TENS[nd - 1], (x + TENS[nd] - 2) / (TENS[nd] - 1));
let hi = min(x / lo, (x as f64).sqrt() as u64);
let t = dtally(x);
for a in lo..(hi + 1) {
let b = x / a;
if a * b == x && ((a % 10) > 0 || b % 10 > 0) && t == dtally(a) + dtally(b) {
fangs.push(a);
}
}
}
fangs
}
/// Pretty print the fangs of x
fn print_fangs(x: u64, fangs: Vec<u64>) {
print!("{} = ", x);
if fangs.is_empty() {
print!("is not vampiric");
} else {
for fang in fangs {
print!("{} x {}, ", fang, x / fang);
}
}
print!("\n");
}
fn main() {
println!("The first 25 vampire numbers are :");
let mut nfangs = 0;
let mut x = 1;
while nfangs < 25 {
let fangs = fangs(x);
if !fangs.is_empty() {
nfangs += 1;
print_fangs(x, fangs);
}
x += 1;
}
println!("\nSpecial requests :");
print_fangs(16758243290880, fangs(16758243290880));
print_fangs(24959017348650, fangs(24959017348650));
print_fangs(14593825548650, fangs(14593825548650));
}
#[test]
fn test() {
assert_eq!(
fangs(16758243290880),
vec![1982736, 2123856, 2751840, 2817360]
);
assert_eq!(
fangs(24959017348650),
vec![2947050, 2949705, 4125870, 4129587, 4230765]
);
assert_eq!(fangs(14593825548650), vec![]);
}
Scala
import Stream._
import math._
import scala.collection.mutable.ListBuffer
object VampireNumbers extends App {
val elapsed: (=> Unit) => Long = f => {val s = System.currentTimeMillis; f; (System.currentTimeMillis - s)/1000}
val sexp = from(1, 2) // stream of integer: 1,3,5,7, ...
val rs: Stream[Int] => Stream[Pair[Long,Long]] = exps => Pair(pow(10,exps.head).toLong,(pow(10,exps.head)*10-1).toLong)#::rs(exps.tail)
val srs = rs(sexp) // stream of ranges: [10..99], [1000..9999], [100000..999999], ...
val cs: Stream[Pair[Long,Long]] => Stream[Long] = rs => (rs.head._1 to rs.head._2).toStream#:::cs(rs.tail)
val scs = cs(srs) // stream of candidates: 10,11,..,99,1000,1001,..,9999, ...
val it = scs.iterator
val checkVN: Long => Pair[Long,Seq[Pair[Long,Long]]] = n => {
val check: Pair[Long,Long] => Pair[Long,Long] = p => {
val len: Long => Int = n => n.toString.size
val (a,b) = p
if ((a%10==0)&&(b%10==0)) Pair(0,0) else
if (len(a) != len(b)) Pair(0,0) else
if (n.toString.toList.diff(a.toString.toList++b.toString.toList)!=Nil) Pair(0,0) else p
}
Pair(n,(pow(10,log10(sqrt(n).toLong).toLong).toLong+1 to sqrt(n).toLong).filter{i=>n%i==0}
.map {fac =>Pair(fac,n/fac)}.map {p => check(p)}.filter {p => p._1 != 0})
}
val et = elapsed {
val lb = new ListBuffer[Pair[Long,Seq[Pair[Long,Long]]]]
while ((lb.size<25)&&(it.hasNext)) {
checkVN(it.next) match {
case (n, Seq()) =>
case p => lb += p
}
}
lb.toList.zipWithIndex.foreach {p =>
println(p._2+1+": "+p._1._1+(p._1._2:\"")((x,y)=>" = "+x._1+" x "+x._2+y))
}
println
List(16758243290880L, 24959017348650L, 14593825548650L)
.map {checkVN(_)}
.foreach {
case (n, Seq()) => println(n+" is not vampiric")
case p => println(p._1+(p._2:\"")((x,y)=>" = "+x._1+" x "+x._2+y))
}
}
println("\n"+"elapsed time: "+et+" seconds")
}
Output:
1: 1260 = 21 x 60 2: 1395 = 15 x 93 3: 1435 = 35 x 41 4: 1530 = 30 x 51 5: 1827 = 21 x 87 6: 2187 = 27 x 81 7: 6880 = 80 x 86 8: 102510 = 201 x 510 9: 104260 = 260 x 401 10: 105210 = 210 x 501 11: 105264 = 204 x 516 12: 105750 = 150 x 705 13: 108135 = 135 x 801 14: 110758 = 158 x 701 15: 115672 = 152 x 761 16: 116725 = 161 x 725 17: 117067 = 167 x 701 18: 118440 = 141 x 840 19: 120600 = 201 x 600 20: 123354 = 231 x 534 21: 124483 = 281 x 443 22: 125248 = 152 x 824 23: 125433 = 231 x 543 24: 125460 = 204 x 615 = 246 x 510 25: 125500 = 251 x 500 16758243290880 = 1982736 x 8452080 = 2123856 x 7890480 = 2751840 x 6089832 = 2817360 x 5948208 24959017348650 = 2947050 x 8469153 = 2949705 x 8461530 = 4125870 x 6049395 = 4129587 x 6043950 = 4230765 x 5899410 14593825548650 is not vampiric elapsed time: 11 seconds
Sidef
func is_vampire (n) {
return [] if n.ilog10.is_even
var l1 = n.isqrt.ilog10.ipow10
var l2 = n.isqrt
var s = n.digits.sort.join
gather {
n.divisors.each { |d|
d < l1 && next
d > l2 && break
var t = n/d
next if (d%%10 && t%%10)
next if ("#{d}#{t}".sort != s)
take([d, t])
}
}
}
say "First 25 Vampire Numbers:"
with (1) { |i|
for (var n = 1; i <= 25; ++n) {
var fangs = is_vampire(n)
printf("%2d. %6s : %s\n", i++, n, fangs.join(' ')) if fangs
}
}
say "\nIndividual tests:"
[16758243290880, 24959017348650, 14593825548650].each { |n|
var fangs = is_vampire(n)
say "#{n}: #{fangs ? fangs.join(', ') : 'is not a vampire number'}"
}
- Output:
First 25 Vampire Numbers: 1. 1260 : [21, 60] 2. 1395 : [15, 93] 3. 1435 : [35, 41] 4. 1530 : [30, 51] 5. 1827 : [21, 87] 6. 2187 : [27, 81] 7. 6880 : [80, 86] 8. 102510 : [201, 510] 9. 104260 : [260, 401] 10. 105210 : [210, 501] 11. 105264 : [204, 516] 12. 105750 : [150, 705] 13. 108135 : [135, 801] 14. 110758 : [158, 701] 15. 115672 : [152, 761] 16. 116725 : [161, 725] 17. 117067 : [167, 701] 18. 118440 : [141, 840] 19. 120600 : [201, 600] 20. 123354 : [231, 534] 21. 124483 : [281, 443] 22. 125248 : [152, 824] 23. 125433 : [231, 543] 24. 125460 : [204, 615] [246, 510] 25. 125500 : [251, 500] Individual tests: 16758243290880: [1982736, 8452080], [2123856, 7890480], [2751840, 6089832], [2817360, 5948208] 24959017348650: [2947050, 8469153], [2949705, 8461530], [4125870, 6049395], [4129587, 6043950], [4230765, 5899410] 14593825548650: is not a vampire number
Swift
import Foundation
func vampire<T>(n: T) -> [(T, T)] where T: BinaryInteger, T.Stride: SignedInteger {
let strN = String(n).sorted()
let fangLength = strN.count / 2
let start = T(pow(10, Double(fangLength - 1)))
let end = T(Double(n).squareRoot())
var fangs = [(T, T)]()
for i in start...end where n % i == 0 {
let quot = n / i
guard i % 10 != 0 || quot % 10 != 0 else {
continue
}
if "\(i)\(quot)".sorted() == strN {
fangs.append((i, quot))
}
}
return fangs
}
var count = 0
var i = 1.0
while count < 25 {
let start = Int(pow(10, i))
let end = start * 10
for num in start...end {
let fangs = vampire(n: num)
guard !fangs.isEmpty else { continue }
count += 1
print("\(num) is a vampire number with fangs: \(fangs)")
guard count != 25 else { break }
}
i += 2
}
for (vamp, fangs) in [16758243290880, 24959017348650, 14593825548650].lazy.map({ ($0, vampire(n: $0)) }) {
if fangs.isEmpty {
print("\(vamp) is not a vampire number")
} else {
print("\(vamp) is a vampire number with fangs: \(fangs)")
}
}
- Output:
1260 is a vampire number with fangs: [(21, 60)] 1395 is a vampire number with fangs: [(15, 93)] 1435 is a vampire number with fangs: [(35, 41)] 1530 is a vampire number with fangs: [(30, 51)] 1827 is a vampire number with fangs: [(21, 87)] 2187 is a vampire number with fangs: [(27, 81)] 6880 is a vampire number with fangs: [(80, 86)] 102510 is a vampire number with fangs: [(201, 510)] 104260 is a vampire number with fangs: [(260, 401)] 105210 is a vampire number with fangs: [(210, 501)] 105264 is a vampire number with fangs: [(204, 516)] 105750 is a vampire number with fangs: [(150, 705)] 108135 is a vampire number with fangs: [(135, 801)] 110758 is a vampire number with fangs: [(158, 701)] 115672 is a vampire number with fangs: [(152, 761)] 116725 is a vampire number with fangs: [(161, 725)] 117067 is a vampire number with fangs: [(167, 701)] 118440 is a vampire number with fangs: [(141, 840)] 120600 is a vampire number with fangs: [(201, 600)] 123354 is a vampire number with fangs: [(231, 534)] 124483 is a vampire number with fangs: [(281, 443)] 125248 is a vampire number with fangs: [(152, 824)] 125433 is a vampire number with fangs: [(231, 543)] 125460 is a vampire number with fangs: [(204, 615), (246, 510)] 125500 is a vampire number with fangs: [(251, 500)] 16758243290880 is a vampire number with fangs: [(1982736, 8452080), (2123856, 7890480), (2751840, 6089832), (2817360, 5948208)] 24959017348650 is a vampire number with fangs: [(2947050, 8469153), (2949705, 8461530), (4125870, 6049395), (4129587, 6043950), (4230765, 5899410)] 14593825548650 is not a vampire number
Tcl
proc factorPairs {n {from 2}} {
set result [list 1 $n]
if {$from<=1} {set from 2}
for {set i $from} {$i<=sqrt($n)} {incr i} {
if {$n%$i} {} {lappend result $i [expr {$n/$i}]}
}
return $result
}
proc vampireFactors {n} {
if {[string length $n]%2} return
set half [expr {[string length $n]/2}]
set digits [lsort [split $n ""]]
set result {}
foreach {a b} [factorPairs $n [expr {10**$half/10}]] {
if {
[string length $a]==$half && [string length $b]==$half &&
($a%10 || $b%10) && $digits eq [lsort [split $a$b ""]]
} then {
lappend result [list $a $b]
}
}
return $result
}
Demonstrating:
# A nicer way to print the evidence of vampire-ness
proc printVampire {n pairs} {
set out "${n}:"
foreach p $pairs {
append out " \[[join $p {, }]\]"
}
puts $out
}
set n 0
for {set i 0} {$i < 25} {incr i} {
while 1 {
if {[llength [set vamps [vampireFactors [incr n]]]]} {
printVampire $n $vamps
break
}
}
}
puts ""
foreach n {16758243290880 24959017348650 14593825548650} {
if {[llength [set vamps [vampireFactors $n]]]} {
printVampire $n $vamps
} else {
puts "$n is not a vampire number"
}
}
- Output:
1260: [21, 60] 1395: [15, 93] 1435: [35, 41] 1530: [30, 51] 1827: [21, 87] 2187: [27, 81] 6880: [80, 86] 102510: [201, 510] 104260: [260, 401] 105210: [210, 501] 105264: [204, 516] 105750: [150, 705] 108135: [135, 801] 110758: [158, 701] 115672: [152, 761] 116725: [161, 725] 117067: [167, 701] 118440: [141, 840] 120600: [201, 600] 123354: [231, 534] 124483: [281, 443] 125248: [152, 824] 125433: [231, 543] 125460: [204, 615] [246, 510] 125500: [251, 500] 16758243290880: [1982736, 8452080] [2123856, 7890480] [2751840, 6089832] [2817360, 5948208] 24959017348650: [2947050, 8469153] [2949705, 8461530] [4125870, 6049395] [4129587, 6043950] [4230765, 5899410] 14593825548650 is not a vampire number
V (Vlang)
import math
fn max(a u64, b u64) u64 {
if a > b {
return a
}
return b
}
fn min(a u64, b u64) u64 {
if a < b {
return a
}
return b
}
fn ndigits(xx u64) int {
mut n:=0
mut x := xx
for ; x > 0; x /= 10 {
n++
}
return n
}
fn dtally(xx u64) u64 {
mut t := u64(0)
mut x := xx
for ; x > 0; x /= 10 {
t += 1 << (x % 10 * 6)
}
return t
}
__global (
tens [20]u64
)
fn init() {
tens[0] = 1
for i := 1; i < 20; i++ {
tens[i] = tens[i-1] * 10
}
}
fn fangs(x u64) []u64 {
mut f := []u64{}
mut nd := ndigits(x)
if nd&1 == 1 {
return f
}
nd /= 2
lo := max(tens[nd-1], (x+tens[nd]-2)/(tens[nd]-1))
hi := min(x/lo, u64(math.sqrt(f64(x))))
t := dtally(x)
for a := lo; a <= hi; a++ {
b := x / a
if a*b == x &&
(a%10 > 0 || b%10 > 0) &&
t == dtally(a)+dtally(b) {
f << a
}
}
return f
}
fn show_fangs(x u64, f []u64) {
print(x)
if f.len > 1 {
println('')
}
for a in f {
println(" = $a × ${x/a}")
}
}
fn main() {
for x, n := u64(1), 0; n < 26; x++ {
f := fangs(x)
if f.len > 0 {
n++
print("${n:2}: ")
show_fangs(x, f)
}
}
println('')
for x in [u64(16758243290880), 24959017348650, 14593825548650] {
f := fangs(x)
if f.len > 0 {
show_fangs(x, f)
} else {
println("$x is not vampiric")
}
}
}- Output:
1: 1260 = 21 × 60 2: 1395 = 15 × 93 3: 1435 = 35 × 41 4: 1530 = 30 × 51 5: 1827 = 21 × 87 6: 2187 = 27 × 81 7: 6880 = 80 × 86 8: 102510 = 201 × 510 9: 104260 = 260 × 401 10: 105210 = 210 × 501 11: 105264 = 204 × 516 12: 105750 = 150 × 705 13: 108135 = 135 × 801 14: 110758 = 158 × 701 15: 115672 = 152 × 761 16: 116725 = 161 × 725 17: 117067 = 167 × 701 18: 118440 = 141 × 840 19: 120600 = 201 × 600 20: 123354 = 231 × 534 21: 124483 = 281 × 443 22: 125248 = 152 × 824 23: 125433 = 231 × 543 24: 125460 = 204 × 615 = 246 × 510 25: 125500 = 251 × 500 26: 126027 = 201 × 627 16758243290880 = 1982736 × 8452080 = 2123856 × 7890480 = 2751840 × 6089832 = 2817360 × 5948208 24959017348650 = 2947050 × 8469153 = 2949705 × 8461530 = 4125870 × 6049395 = 4129587 × 6043950 = 4230765 × 5899410 14593825548650 is not vampiric
Wren
import "./fmt" for Fmt
var ndigits = Fn.new { |x|
var n = 0
while (x > 0) {
n = n + 1
x = (x/10).floor
}
return n
}
var dtally = Fn.new { |x|
var t = 0
while (x > 0) {
t = t + 2.pow((x%10) * 6)
x = (x/10).floor
}
return t
}
var tens = List.filled(15, 0)
var init = Fn.new {
tens[0] = 1
for (i in 1..14) tens[i] = tens[i-1] * 10
}
var fangs = Fn.new { |x|
var f = []
var nd = ndigits.call(x)
if ((nd&1) == 1) return f
nd = (nd/2).floor
var lo = tens[nd-1].max(((x + tens[nd] - 2) / (tens[nd] - 1)).floor)
var hi = (x/lo).floor.min(x.sqrt.floor)
var t = dtally.call(x)
var a = lo
while (a <= hi) {
var b = (x/a).floor
if (a*b == x && ((a%10) > 0 || (b%10) > 0) && t == dtally.call(a) + dtally.call(b)) {
f.add(a)
}
a = a + 1
}
return f
}
var showFangs = Fn.new { |x, f|
Fmt.write("$6d", x)
if (f.count > 1) System.print()
for (a in f) Fmt.print(" = $3d x $3d", a, (x/a).floor)
}
init.call()
var x = 1
var n = 0
while (n < 25) {
var f = fangs.call(x)
if (f.count > 0) {
n = n + 1
Fmt.write("$2d: ", n)
showFangs.call(x, f)
}
x = x + 1
}
System.print()
for (x in [16758243290880, 24959017348650, 14593825548650]) {
var f = fangs.call(x)
if (f.count > 0) {
showFangs.call(x, f)
} else {
Fmt.print("$d is not vampiric", x)
}
}
- Output:
1: 1260 = 21 x 60 2: 1395 = 15 x 93 3: 1435 = 35 x 41 4: 1530 = 30 x 51 5: 1827 = 21 x 87 6: 2187 = 27 x 81 7: 6880 = 80 x 86 8: 102510 = 201 x 510 9: 104260 = 260 x 401 10: 105210 = 210 x 501 11: 105264 = 204 x 516 12: 105750 = 150 x 705 13: 108135 = 135 x 801 14: 110758 = 158 x 701 15: 115672 = 152 x 761 16: 116725 = 161 x 725 17: 117067 = 167 x 701 18: 118440 = 141 x 840 19: 120600 = 201 x 600 20: 123354 = 231 x 534 21: 124483 = 281 x 443 22: 125248 = 152 x 824 23: 125433 = 231 x 543 24: 125460 = 204 x 615 = 246 x 510 25: 125500 = 251 x 500 16758243290880 = 1982736 x 8452080 = 2123856 x 7890480 = 2751840 x 6089832 = 2817360 x 5948208 24959017348650 = 2947050 x 8469153 = 2949705 x 8461530 = 4125870 x 6049395 = 4129587 x 6043950 = 4230765 x 5899410 14593825548650 is not vampiric
zkl
fcn fangs(N){ //-->if Vampire number: (N,(a,b,c,...)), where a*x==N
var [const] tens=[0 .. 18].pump(List,(10.0).pow,"toInt");
(half:=N.numDigits) : if (_.isOdd) return(T);;
half/=2; digits:=N.toString().sort();
lo:=tens[half-1].max((N+tens[half])/(tens[half]));
hi:=(N/lo).min(N.toFloat().sqrt());
fs:=[lo .. hi].filter('wrap(n){
N%n==0 and (n%10!=0 or (N/n)%10!=0) and
(n.toString()+(N/n).toString()).sort()==digits
});
fs and T(N,fs) or T;
}fcn vampiric(fangs,n=Void){
if(not fangs) return(n,"Not a Vampire number");
v:=fangs[0]; T(v,fangs[1].apply('wrap(n){T(n,v/n)})) }
T(16758243290880, 24959017348650, 14593825548650)
.pump(Console.println,fcn(n){"%d: %s".fmt(vampiric(fangs(n),n).xplode())});
(0).walker(*).tweak(fangs).filter(26)
.pump(Console.println,vampiric);- Output:
16758243290880: L(L(1982736,8452080),L(2123856,7890480),L(2751840,6089832),L(2817360,5948208)) 24959017348650: L(L(2947050,8469153),L(2949705,8461530),L(4125870,6049395),L(4129587,6043950),L(4230765,5899410)) 14593825548650: Not a Vampire number L(1260,L(L(21,60))) L(1395,L(L(15,93))) L(1435,L(L(35,41))) L(1530,L(L(30,51))) L(1827,L(L(21,87))) L(2187,L(L(27,81))) L(6880,L(L(80,86))) L(102510,L(L(201,510))) L(104260,L(L(260,401))) L(105210,L(L(210,501))) L(105264,L(L(204,516))) L(105750,L(L(150,705))) L(108135,L(L(135,801))) L(110758,L(L(158,701))) L(115672,L(L(152,761))) L(116725,L(L(161,725))) L(117067,L(L(167,701))) L(118440,L(L(141,840))) L(120600,L(L(201,600))) L(123354,L(L(231,534))) L(124483,L(L(281,443))) L(125248,L(L(152,824))) L(125433,L(L(231,543))) L(125460,L(L(204,615),L(246,510))) L(125500,L(L(251,500))) L(126027,L(L(201,627)))