西电复试之——真题2008 Problems D
Smith数
对于一个正整数n,如果它的各位之和等于它的所有质因数的各位之和,则称该数为Smith
#include<iostream>
#include<math.h>
using namespace std;
//判断素数
bool isprime(int n) {
if (n <= 1) return 0;
//sqrt要求的参数为浮点数,所以用1.0*
int sqr = (int)sqrt(1.0 * n);
for (int i = 2; i <= sqr; i++) {
if (n % i == 0) return 0;
}
return 1;
}
const int maxn = 100010;
int prime[maxn], pNum = 0;
bool p[maxn] = { 0 };
//求素数表
void Find_Prime(int n) {
for (int i = 1; i < n; i++) {
if (isprime(i)) {
prime[pNum++] = i;
p[i] = true;
}
}
}
//存放质因子
struct factor {
int x, cnt;//x为质因子,cnt为其个数
}fac[10];
int a[8] = { 0 };
int main() {
int n;
cin >> n;
//计算各位之和
int temp = n, i = 0;//记录n
while (temp > 0) {
a[i++] = temp % 10;
temp /= 10;
}
int num = 0;
for (int j = 0; j < i; j++)
num += a[j];
//计算各位质因子和
Find_Prime(n + 1);//计算素数表
temp = n;
int j = 0;
for (i = 0; i < pNum; i++) {
if (temp % prime[i] == 0) {
fac[j].x = prime[i];
fac[j].cnt = 0;
while (temp % prime[i] == 0) {
fac[j].cnt++;
temp /= prime[i];
}
j++;
}
}
int num1 = 0;
for (i = 0; i < 10; i++) {
while (fac[i].x > 0)
{
num1 += (fac[i].x % 10) * fac[i].cnt;
fac[i].x /= 10;
}
}
if (num == num1)
cout << "yes";
else
cout << "no";
return 0;
}