day2_part2.go

// returns a list of integer factors sorted descending, since we don't care about pairs.
func maximalProperDivisors(n int) (divisors []int) {
	primes := constructPrimes(int(math.Sqrt(float64(n))))
	for _, p := range primeFactors(n, primes) {
		divisors = append(divisors, n/p)
	}
	return divisors
}

// find prime numbers up to SQRT of N
func buildPrimes(n int) {
	n = int(math.Sqrt(float64(n)))
	for i := range n {
		if isPrime(i) {
			PRIMES = append(PRIMES, i)
		}
	}
}

func isPrime(n int) bool {
	if n < 2 {
		return false
	}
	if n == 2 {
		return true
	}
	if n%2 == 0 {
		return false
	}

	for i := 3; i*i <= n; i += 2 {
		if n%i == 0 {
			return false
		}
	}

	return true
}

func maxId(ids []string) (max int) {
	for _, id := range ids {
		idRange := strings.Split(id, "-")
		end := toi(idRange[1])
		if end > max {
			max = end
		}
	}
	return max

}

// primes is sorted smallest to largest
func primeFactors(n int, primes []int) (factors []int) {
	max := int(math.Sqrt(float64(n)))
	for _, p := range primes {
		if p > max {
			break
		}
		if n%p == 0 {
			factors = append(factors, p)
		}
	}
	return factors
}

// return prime numbers <= n
func constructPrimes(n int) []int {
	for i, p := range PRIMES {
		if p > n {
			return PRIMES[0:i]
		}
	}
	return []int{}
}