Narcissistic decimal number: Difference between revisions
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A [http://mathworld.wolfram.com/NarcissisticNumber.html Narcissistic decimal number] is a positive decimal number, <math>n</math> in which if there are <math>m</math> digits in the number then the sum of all the individual digits of the number raised to the power <math>m</math> is equal to <math>n</math>.
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Revision as of 07:58, 7 March 2014
You are encouraged to solve this task according to the task description, using any language you may know.
A Narcissistic decimal number is a positive decimal number, in which if there are digits in the number then the sum of all the individual digits of the number raised to the power is equal to .
For example, if is 153 then , the number of digits is 3 and we have and so 153 is a narcissistic decimal number.
The task is to generate and show here, the first 25 narcissistic numbers.
C
<lang c>#include <stdio.h>
typedef long long xint;
- define MAX_LEN 16
xint dpow[MAX_LEN + 1][11];
void init(void) { int i, p; for (p = 0; p <= MAX_LEN; p++) for (i = 0; i <= 10; i++) dpow[p][i] = p ? dpow[p-1][i] * i : 1; }
void narc(int power, int pos, xint value, xint dsum) { xint i, ds, v, ten;
if (!pos) { if (value == dsum) printf(" %lld", value); return; }
ten = dpow[pos - 1][10]; for (i = (pos == power); i < 10; i++) { ds = dsum + dpow[power][i]; v = value + i * ten;
if (ds >= v + ten) break;
if (v <= ds + dpow[power][9] * (pos - 1)) narc(power, pos - 1, v, ds); } }
int main(void) { int i; init();
for (i = 1; i <= 16; i++) { printf("length %d:", i); narc(i, i, 0, 0); putchar('\n'); }
return 0; }</lang>
- Output:
length 1: 1 2 3 4 5 6 7 8 9 length 2: length 3: 153 370 371 407 length 4: 1634 8208 9474 length 5: 54748 92727 93084 length 6: 548834 length 7: 1741725 4210818 9800817 9926315 length 8: 24678050 24678051 88593477 length 9: 146511208 472335975 534494836 912985153 ^C
Perl 6
Here is a straightforward, naive implementation. It works but takes ages. <lang perl6>sub is-narcissistic(Int $n) { $n == [+] $n.comb »**» $n.chars }
for 0 .. * {
if .&is-narcissistic {
.say; last if ++state$ >= 25;
}
}</lang>
- Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 Ctrl-C
Here the program was interrupted but if you're patient enough you'll see all the 25 numbers.
Python
This solution pre-computes the powers once.
<lang python>from __future__ import print_function from itertools import count, islice
def narcissists():
for digits in count(0): digitpowers = [i**digits for i in range(10)] for n in range(int(10**(digits-1)), 10**digits): div, digitpsum = n, 0 while div: div, mod = divmod(div, 10) digitpsum += digitpowers[mod] if n == digitpsum: yield n
for i, n in enumerate(islice(narcissists(), 25), 1):
print(n, end=' ') if i % 5 == 0: print()
print()</lang>
- Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315
REXX
<lang rexx>/*REXX program to generate and display a number of narcissistic numbers.*/ numeric digits 20 /*just in case more are wanted. */ parse arg N .; if N== then N=25 /*get number of narcissistic #'s.*/
- =0 /*number of narcissistic # so far*/
do j=1 until #==N; L=length(j) /*get the length of the J number.*/ s=left(j,1)**L /*sum of the J digits to L power.*/ /* [↑] calculate partial sum. */ do k=2 for L-1 /*perform for each digit in J. */ s=s+substr(j,k,1)**L /*add digit raised to pow to sum.*/ if s>j then iterate j /*perform a short-circuit test. */ end /*k*/ /* [↑] calculate the rest of sum*/ /* [↓] perform final "sum" test.*/ if s\==j then iterate /*does sum equal to J? No ∙∙∙ */ #=#+1 /*bump the narcissistic num count*/ say right(#,9) ' narcissistic:' j /*display index & narcissistic #.*/ end /*j*/ /* [↑] this list starts at 1. */ /*stick a fork in it, we're done.*/</lang>
output when using the default input:
1 narcissistic: 1 2 narcissistic: 2 3 narcissistic: 3 4 narcissistic: 4 5 narcissistic: 5 6 narcissistic: 6 7 narcissistic: 7 8 narcissistic: 8 9 narcissistic: 9 10 narcissistic: 153 11 narcissistic: 370 12 narcissistic: 371 13 narcissistic: 407 14 narcissistic: 1634 15 narcissistic: 8208 16 narcissistic: 9474 17 narcissistic: 54748 18 narcissistic: 92727 19 narcissistic: 93084 20 narcissistic: 548834 21 narcissistic: 1741725 22 narcissistic: 4210818 23 narcissistic: 9800817 24 narcissistic: 9926315 25 narcissistic: 24678050