From 79e1f45b8eee18db5450e5c7e8cae4970f123773 Mon Sep 17 00:00:00 2001
From: Evan Hemsley <evan@moonside.games>
Date: Wed, 8 Jan 2020 12:51:45 -0800
Subject: [PATCH] more solutions in V

---
 v/euler/euler.v | 112 ++++++++++++++++++++++++++++++++++++++++++++++++
 v/euler005.v    |  26 +++++++++++
 v/euler006.v    |   9 ++++
 v/euler007.v    |   5 +++
 4 files changed, 152 insertions(+)
 create mode 100644 v/euler005.v
 create mode 100644 v/euler006.v
 create mode 100644 v/euler007.v

diff --git a/v/euler/euler.v b/v/euler/euler.v
index 645fb66..e4eee74 100644
--- a/v/euler/euler.v
+++ b/v/euler/euler.v
@@ -64,3 +64,115 @@ pub fn palindrome(n int) bool {
 	}
 	return true
 }
+
+fn check(n int, p int) []int {
+	mut result := []int
+	mut q := n / p
+	mut r := n % p
+	mut m := n
+	for r == 0 {
+		result << p
+		m = q
+		q = m / p
+		r = m % p
+	}
+	return result
+}
+
+fn trial_division(n int) []int {
+	mut factors := []int
+	factors << check(n, 2)
+	factors << check(n, 3)
+	mut p := 5
+	for p * p <= n {
+		factors << check(n, p)
+		p += 2
+		factors << check(n, p)
+		p += 4
+	}
+	if factors.len == 0 { factors << n }
+	return factors
+}
+
+pub fn prime_factorization(n int) map[string]int {
+	mut result := map[string]int
+	factors := trial_division(n)
+	for f in factors {
+		result[f.str()] = 0
+		mut num := n
+		for num % f == 0 {
+			result[f.str()] = result[f.str()] + 1
+			num /= f
+		}
+	}
+	return result
+}
+
+pub fn eratosthenes_sieve(n int) []bool {
+	mut sieve := [true].repeat(n + 1)
+	sieve[0] = false
+	sieve[1] = false
+
+	for i := 2; i <= int(math.sqrt(n)); i++ {
+		if (sieve[i]) {
+			for j := i * i; j <= n; j += i {
+				sieve[j] = false
+			}
+		}
+	}
+
+	return sieve
+}
+
+pub fn eratosthenes_sieve_expand(n int, sieve []bool) []bool
+{
+	mut new_sieve := sieve
+	for i := sieve.len + 1; i <= n + 1; i++ {
+		new_sieve << true
+	}
+
+	for i := 2; i <= int(math.sqrt(n)); i++ {
+		if (new_sieve[i]) {
+			mut start := i * i
+			if (i * i >= sieve.len) {
+				start = sieve.len + i - (sieve.len % i)
+			}
+			for j := start; j <= n; j += i {
+				new_sieve[j] = false
+			}
+		}
+	}
+
+	return new_sieve
+}
+
+pub fn primes_up_to(n int) []int {
+	return primes_from_sieve(eratosthenes_sieve(n))
+}
+
+fn count_primes_from_sieve(sieve []bool) int {
+	mut result := 0
+	for b in sieve { if b { result++ } }
+	return result
+}
+
+fn primes_from_sieve(sieve []bool) []int {
+	mut result := []int
+	for index, b in sieve {
+		if b { result << index }
+	}
+	return result
+}
+
+pub fn find_nth_prime(n int) int {
+	mut sieve_size := 16
+	mut sieve := eratosthenes_sieve(sieve_size)
+
+	for count_primes_from_sieve(sieve) < n {
+		sieve_size *= 2
+		sieve = eratosthenes_sieve_expand(sieve_size, sieve)
+	}
+
+	primes := primes_from_sieve(sieve)
+	return primes[n - 1]
+}
diff --git a/v/euler005.v b/v/euler005.v
new file mode 100644
index 0000000..eab3794
--- /dev/null
+++ b/v/euler005.v
@@ -0,0 +1,26 @@
+import euler
+import math
+
+fn factorization_of_integer_divisible_by_all_integers_up_to(n int) map[string]int {
+	mut result := map[string]int
+	for i in euler.range(2, n) {
+		for p, e in euler.prime_factorization(i) {
+			if !(p in result) || e > result[p] {
+				result[p] = e
+			}
+		}
+	}
+	return result
+}
+
+fn factors_to_int(factorization map[string]int) int {
+	mut result := 1
+	for p, e in factorization {
+		result *= int(math.pow(p.int(), e))
+	}
+	return result
+}
+
+fn main() {
+	println(factors_to_int(factorization_of_integer_divisible_by_all_integers_up_to(20)))
+}
diff --git a/v/euler006.v b/v/euler006.v
new file mode 100644
index 0000000..ba1cbde
--- /dev/null
+++ b/v/euler006.v
@@ -0,0 +1,9 @@
+import euler
+
+fn main() {
+	range := euler.range(1, 100)
+	sum := range.reduce(euler.add, 0)
+	square_of_sum := sum * sum
+	sum_of_squares := range.map(it * it).reduce(euler.add, 0)
+	println(square_of_sum - sum_of_squares)
+}
diff --git a/v/euler007.v b/v/euler007.v
new file mode 100644
index 0000000..928466e
--- /dev/null
+++ b/v/euler007.v
@@ -0,0 +1,5 @@
+import euler
+
+fn main() {
+	println(euler.find_nth_prime(10001))
+}