void primeFactorization(const bignum &bn, vector<bignum> &factors)
{
if (bn.getDecimalCount() > 0)
throw error_handler(__FILE__, __LINE__, "Cannot find the prime factorization of a decimal");
//converts to base 10 first for faster prime checks, then converts base of all prime factors in the list
if (bn.getBase() != 10)
{
bignum converted(bn);
converted.convertBase(10);
primeFactorization(converted, factors);
for (vector<bignum>::iterator i = factors.begin(); i != factors.end(); i++)
i->convertBase(bn.getBase());
return;
}
if (bn < 0)
{
factors.push_back(-1);
if (bn.absolute().isPrime())
{
factors.push_back(bn.absolute());
return;
}
else return primeFactorization(bn.absolute(), factors);
}
if (bn.isPrime())
{
factors.push_back(1);
factors.push_back(bn);
return;
}
bignum temp(2);
while (bn % temp != 0)
temp++;
if (!(bn / temp).isPrime())
primeFactorization(bn / temp, factors);
else factors.push_back(bn / temp);
if (!temp.isPrime())
primeFactorization(temp, factors);
else factors.push_back(temp);
}
/* solve the problem */
int main (int argc, char *argv[]) {
int elements[MAX_SIZE];
int primes[MAX_PRIMES], instancesCount[MAX_PRIMES], primesUsed[MAX_PRIMES];
int maxPrimeDefined, primesUsedCount;
int numberOfDivisors, loop;
#ifdef debug_on
printf("\nP25 - Brave Balloonists:\n");
#endif
primes[0] = 2;
primes[1] = 3; /* necessary to be defined for currentPrime+=2 logic to work */
maxPrimeDefined = 1;
primesUsedCount = 0;
/* read program arguments */
for (loop=0; loop<MAX_SIZE; loop++) {
scanf("%d", &elements[loop]);
primeFactorization(elements[loop],primes,instancesCount,primesUsed,&maxPrimeDefined,&primesUsedCount);
}
#ifdef debug_on
printArgs(elements);
printf("\nProblem Solution:\n");
#endif
/* solution */
numberOfDivisors = 1;
for (loop=0; loop<primesUsedCount; loop++) {
numberOfDivisors = numberOfDivisors * (instancesCount[primesUsed[loop]] + 1);
}
#ifdef debug_on
printf("result: %d MOD 10 = ", numberOfDivisors);
#endif
printf("%d\n",numberOfDivisors%10);
#ifdef debug_on
printf("\n--------------------\n");
#endif
return 0;
}
