// problem 4

int IsPerfect(int num)
// precondition: 0 < num
// postcondition: returns 1 if num is perfect, else returns 0
{
    int sum = 1;                 // sum of proper divisors
    int k;
    for(k=2; k <= num/2; k++)    // 1 must be divisor, last is num/2
    {
	if (num % k == 0){
	    sum += k;
	}
    }
    return (sum ==num);
}

// problem 5 (part A)

String day;
int period;

AceCourse course(129244);   // polysci 110
course.Meeting(day,period);

cout << course.Instructor() << end;
cout << "meets at " << day << " " << period << endl;


// problem 5 (part B)

void KnowledgeArea(String distrib)
// postcondition: titles of all courses with area of knowledge = distrib
//                printed with a count of the number of such courses
{
    int count = 0;
    AceCourse course(1);      // dummy number here
    int num;
    for(num = 100000; num <= 160000; num++)
    {
	course.SetNumber(num);   // alternatively: AceCourse course(num);
	if(course.IsValid() && couse.Area() == distrib)
	{
	    count++;
	    cout << course.Title() << endl;
	}
    }
    cout << "# of courses with " << distrib
	 << " designation = " << count << endl;
}

// extra credit

bool IsArmstrong(int num)
// precondition: 0 < num
// postcondition: returns true if num is an Armstrong number
//                otherwise returns false
{
    int numDigits = NumDigits(num);
    int sum = 0;
    int k;
    for(k=0; k < numDigits; k++){
	sum += int(Pow(num % 10, numDigits));  // last digit^numDigits
	num /= 10;                             // chop off last digit
    }
    return (sum == num);
}

int
NumDigits(int num)
// precondition: 0 < num
// postcondition: returns # of digits in num     
{
    // return int(log10(num)) + 1;
    
    int count = 0;
    while (num != 0)
    {
	count++;
	num /= 10;
    }
    return count;

    
}