# 算法设计：hoax数字介绍和代码实现

## 本文概述

``````Input : 22
Output : A Hoax Number
Explanation : The distinct prime factors of 22
are 2 and 11. The sum of their digits are 4, i.e 2 + 1 + 1 and sum of digits of 22 is also 4.

Input : 84
Output : A Hoax Number
Explanation : The distinct prime factors of 84
are 2, 3 and 7. The sum of their digits are 12, i.e 2 + 3 + 4 and sum of digits of 84 is also 12.

Input : 19
Output : Not a Hoax Number
Explanation : By definition, a hoax number is
a composite number.``````

hoax数字的定义与史密斯数字。实际上, 有些hoax数字也是史密斯数字。显然, 那些在素数分解中没有重复因素的hoax数字, 即方形免费电话也是符合条件的史密斯数字。

1)首先生成数字” n”的所有唯一质数。

2)如果”n”不是质数, 请找到在步骤1中获得的因子的数字总和。

3)找到数字”n”的总和。

4)检查在步骤2和3中获得的总和是否相等。

5)如果总和相等, 则” n”是一个hoax数字。

## C ++

``````// CPP code to check if a number is a hoax
// number or not.
#include <bits/stdc++.h>
using namespace std;
// Function to find distinct prime factors
// of given number n
vector< int > primeFactors( int n)
{
vector< int > res;
if (n % 2 == 0) {
while (n % 2 == 0)
n = n / 2;
res.push_back(2);
}

// n is odd at this point, since it is no
// longer divisible by 2. So we can test
// only for the odd numbers, whether they
// are factors of n
for ( int i = 3; i <= sqrt (n); i = i + 2) {

// Check if i is prime factor
if (n % i == 0) {
while (n % i == 0)
n = n / i;
res.push_back(i);
}
}

// This condition is to handle the case
// when n is a prime number greater than 2
if (n > 2)
res.push_back(n);
return res;
}

// Function to calculate sum of digits of
// distinct prime factors of given number n
// and sum of digits of number n and compare
// the sums obtained
bool isHoax( int n)
{
// Distinct prime factors of n are being
// stored in vector pf
vector< int > pf = primeFactors(n);

// If n is a prime number, it cannot be a
// hoax number
if (pf == n)
return false ;

// Finding sum of digits of distinct prime
// factors of the number n
int all_pf_sum = 0;
for ( int i = 0; i < pf.size(); i++) {

// Finding sum of digits in current
// prime factor pf[i].
int pf_sum;
for (pf_sum = 0; pf[i] > 0;
pf_sum += pf[i] % 10, pf[i] /= 10)
;

all_pf_sum += pf_sum;
}

// Finding sum of digits of number n
int sum_n;
for (sum_n = 0; n > 0; sum_n += n % 10, n /= 10)
;

// Comparing the two calculated sums
return sum_n == all_pf_sum;
}

// Driver Method
int main()
{
int n = 84;
if (isHoax(n))
cout << "A Hoax Number\n" ;
else
cout << "Not a Hoax Number\n" ;
return 0;
}``````

## Java

``````// Java code to check if a number is
// a hoax number or not.
import java.io.*;
import java.util.*;

public class GFG {

// Function to find distinct
// prime factors of given
// number n
static List<Integer> primeFactors( int n)
{
List<Integer> res = new ArrayList<Integer>();
if (n % 2 == 0 )
{
while (n % 2 == 0 )
n = n / 2 ;
}

// n is odd at this point, // since it is no longer
// divisible by 2. So we
// can test only for the
// odd numbers, whether they
// are factors of n
for ( int i = 3 ; i <= Math.sqrt(n);
i = i + 2 )
{

// Check if i is prime factor
if (n % i == 0 )
{
while (n % i == 0 )
n = n / i;
}
}

// This condition is to
// handle the case when
// n is a prime number
// greater than 2
if (n > 2 )
return res;
}

// Function to calculate
// sum of digits of distinct
// prime factors of given
// number n and sum of
// digits of number n and
// compare the sums obtained
static boolean isHoax( int n)
{

// Distinct prime factors
// of n are being
// stored in vector pf
List<Integer> pf = primeFactors(n);

// If n is a prime number, // it cannot be a hoax number
if (pf.get( 0 ) == n)
return false ;

// Finding sum of digits of distinct
// prime factors of the number n
int all_pf_sum = 0 ;
for ( int i = 0 ; i < pf.size(); i++)
{

// Finding sum of digits in current
// prime factor pf[i].
int pf_sum;
for (pf_sum = 0 ; pf.get(i) > 0 ;
pf_sum += pf.get(i) % 10 , pf.set(i, pf.get(i) / 10 ));

all_pf_sum += pf_sum;
}

// Finding sum of digits of number n
int sum_n;
for (sum_n = 0 ; n > 0 ; sum_n += n % 10 , n /= 10 )
;

// Comparing the two calculated sums
return sum_n == all_pf_sum;
}

// Driver Code
public static void main(String args[])
{
int n = 84 ;
if (isHoax(n))
System.out.print( "A Hoax Number\n" );
else
System.out.print( "Not a Hoax Number\n" );
}
}

// This code is contributed by
// Manish Shaw (manishshaw1)``````

## Python3

``````# Python3 code to check if a number is a hoax
# number or not.
import math

# Function to find distinct prime factors
# of given number n
def primeFactors(n) :
res = []
if (n % 2 = = 0 ) :
while (n % 2 = = 0 ) :
n = int (n / 2 )
res.append( 2 )

# n is odd at this point, since it is no
# longer divisible by 2. So we can test
# only for the odd numbers, whether they
# are factors of n
for i in range ( 3 , int (math.sqrt(n)), 2 ):
# Check if i is prime factor
if (n % i = = 0 ) :
while (n % i = = 0 ) :
n = int (n / i)
res.append(i)

# This condition is to handle the case
# when n is a prime number greater than 2
if (n > 2 ) :
res.append(n)
return res

# Function to calculate sum of digits of
# distinct prime factors of given number n
# and sum of digits of number n and compare
# the sums obtained
def isHoax(n) :
# Distinct prime factors of n are being
# stored in vector pf
pf = primeFactors(n)

# If n is a prime number, it cannot be a
# hoax number
if (pf[ 0 ] = = n) :
return False

# Finding sum of digits of distinct prime
# factors of the number n
all_pf_sum = 0
for i in range ( 0 , len (pf)):

# Finding sum of digits in current
# prime factor pf[i].
pf_sum = 0
while (pf[i] > 0 ):
pf_sum + = pf[i] % 10
pf[i] = int (pf[i] / 10 )

all_pf_sum + = pf_sum

# Finding sum of digits of number n
sum_n = 0 ;
while (n > 0 ):
sum_n + = n % 10
n = int (n / 10 )

# Comparing the two calculated sums
return sum_n = = all_pf_sum

# Driver Method
n = 84 ;
if (isHoax(n)):
print ( "A Hoax Number\n" )
else :
print ( "Not a Hoax Number\n" )

# This code is contributed by Manish Shaw
# (manishshaw1)``````

## C#

``````// C# code to check if a number is
// a hoax number or not.
using System;
using System.Collections.Generic;

class GFG {

// Function to find distinct
// prime factors of given
// number n
static List< int > primeFactors( int n)
{
List< int > res = new List< int >();
if (n % 2 == 0)
{
while (n % 2 == 0)
n = n / 2;
}

// n is odd at this point, // since it is no longer
// divisible by 2. So we
// can test only for the
// odd numbers, whether they
// are factors of n
for ( int i = 3; i <= Math.Sqrt(n);
i = i + 2)
{

// Check if i is prime factor
if (n % i == 0)
{
while (n % i == 0)
n = n / i;
}
}

// This condition is to
// handle the case when
// n is a prime number
// greater than 2
if (n > 2)
return res;
}

// Function to calculate
// sum of digits of distinct
// prime factors of given
// number n and sum of
// digits of number n and
// compare the sums obtained
static bool isHoax( int n)
{

// Distinct prime factors
// of n are being
// stored in vector pf
List< int > pf = primeFactors(n);

// If n is a prime number, // it cannot be a hoax number
if (pf == n)
return false ;

// Finding sum of digits of distinct
// prime factors of the number n
int all_pf_sum = 0;
for ( int i = 0; i < pf.Count; i++)
{

// Finding sum of digits in current
// prime factor pf[i].
int pf_sum;
for (pf_sum = 0; pf[i] > 0;
pf_sum += pf[i] % 10, pf[i] /= 10);

all_pf_sum += pf_sum;
}

// Finding sum of digits of number n
int sum_n;
for (sum_n = 0; n > 0; sum_n += n % 10, n /= 10)
;

// Comparing the two calculated sums
return sum_n == all_pf_sum;
}

// Driver Code
public static void Main()
{
int n = 84;
if (isHoax(n))
Console.Write( "A Hoax Number\n" );
else
Console.Write( "Not a Hoax Number\n" );
}
}

// This code is contributed by
// Manish Shaw (manishshaw1)``````

## 的PHP

``````<?php
// PHP code to check if a number
// is a hoax number or not.

// Function to find distinct prime
// factors of given number n
function primeFactors( \$n )
{
\$res = array ();
if ( \$n % 2 == 0)
{
while ( \$n % 2 == 0)
\$n = (int) \$n / 2;
array_push ( \$res , 2);
}

// n is odd at this point, since
// it is no longer divisible by 2.
// So we can test only for the odd
// numbers, whether they are factors of n
for ( \$i = 3; \$i <= sqrt( \$n ); \$i = \$i + 2)
{

// Check if i is prime factor
if ( \$n % \$i == 0)
{
while ( \$n % \$i == 0)
\$n = (int) \$n / \$i ;
array_push ( \$res , \$i );
}
}

// This condition is to handle
// the case when n is a prime
// number greater than 2
if ( \$n > 2)
array_push ( \$res , \$n );
return \$res ;
}

// Function to calculate sum
// of digits of distinct prime
// factors of given number n
// and sum of digits of number
// n and compare the sums obtained
function isHoax( \$n )
{
// Distinct prime factors
// of n are being stored
// in vector pf
\$pf = primeFactors( \$n );

// If n is a prime number, // it cannot be a hoax number
if ( \$pf  == \$n )
return false;

// Finding sum of digits of distinct
// prime factors of the number n
\$all_pf_sum = 0;
for ( \$i = 0; \$i < count ( \$pf ); \$i ++)
{

// Finding sum of digits in
// current prime factor pf[i].
\$pf_sum ;
for ( \$pf_sum = 0; \$pf [ \$i ] > 0;
\$pf_sum += \$pf [ \$i ] % 10, \$pf [ \$i ] /= 10)
;

\$all_pf_sum += \$pf_sum ;
}

// Finding sum of digits of number n
for ( \$sum_n = 0; \$n > 0;
\$sum_n += \$n % 10, \$n /= 10)
;

// Comparing the two calculated sums
return \$sum_n == \$all_pf_sum ;
}

// Driver Code
\$n = 84;
if (isHoax( \$n ))
echo ( "A Hoax Number\n" );
else
echo ( "Not a Hoax Number\n" );

// This code is contributed by
// Manish Shaw(manishshaw1)
?>``````

``A Hoax Number``

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