Smith Number | C ++ program to check whether a number is Smith Number or not . ; array to store all prime less than and equal to 10 ^ 6 ; utility function for sieve of sundaram ; In general Sieve of Sundaram , produces primes smaller than ( 2 * x + 2 ) for a number given number x . Since we want primes smaller than MAX , we reduce MAX to half This array is used to separate numbers of the form i + j + 2 ij from others where 1 <= i <= j ; Main logic of Sundaram . Mark all numbers which do not generate prime number by doing 2 * i + 1 ; Since 2 is a prime number ; Print other primes . Remaining primes are of the form 2 * i + 1 such that marked [ i ] is false . ; Returns true if n is a Smith number , else false . ; Find sum the digits of prime factors of n ; If primes [ i ] is a prime factor , add its digits to pDigitSum . ; If n != 1 then one prime factor still to be summed up ; ; All prime factors digits summed up Now sum the original number digits ; If sum of digits in prime factors and sum of digits in original number are same , then return true . Else return false . ; Driver code ; Finding all prime numbers before limit . These numbers are used to find prime factors .
#include <bits/stdc++.h> NEW_LINE using namespace std ; const int MAX = 10000 ; vector < int > primes ; void sieveSundaram ( ) { bool marked [ MAX / 2 + 100 ] = { 0 } ; for ( int i = 1 ; i <= ( sqrt ( MAX ) - 1 ) / 2 ; i ++ ) for ( int j = ( i * ( i + 1 ) ) << 1 ; j <= MAX / 2 ; j = j + 2 * i + 1 ) marked [ j ] = true ; primes . push_back ( 2 ) ; for ( int i = 1 ; i <= MAX / 2 ; i ++ ) if ( marked [ i ] == false ) primes . push_back ( 2 * i + 1 ) ; } bool isSmith ( int n ) { int original_no = n ; int pDigitSum = 0 ; for ( int i = 0 ; primes [ i ] <= n / 2 ; i ++ ) { while ( n % primes [ i ] == 0 ) { int p = primes [ i ] ; n = n / p ; while ( p > 0 ) { pDigitSum += ( p % 10 ) ; p = p / 10 ; } } } if ( n != 1 && n != original_no ) { while ( n > 0 ) { pDigitSum = pDigitSum + n % 10 ; n = n / 10 ; } } int sumDigits = 0 ; while ( original_no > 0 ) { sumDigits = sumDigits + original_no % 10 ; original_no = original_no / 10 ; } return ( pDigitSum == sumDigits ) ; } int main ( ) { sieveSundaram ( ) ; cout << " Printing ▁ first ▁ few ▁ Smith ▁ Numbers " " ▁ using ▁ isSmith ( ) n " ; for ( int i = 1 ; i < 500 ; i ++ ) if ( isSmith ( i ) ) cout << i << " ▁ " ; return 0 ; }