more solutions in crystal

crystal/euler.cr

@@ -1,23 +1,59 @@
 # miscellaneous stuff
 
+require "big"
+
 module Euler
-  def self.eratosthenes_sieve(n)
-    sieve = Array.new(n + 1, true)
-    sieve[0] = false
-    sieve[1] = false
+  alias NumType = Int32 | Int64 | UInt32 | UInt64 | BigInt
 
-    2.step(to: Math.sqrt(n)) do |i|
-      if sieve[i]
-        (i * i).step(to: n, by: i) do |j|
-          sieve[j] = false
+  def self.trial_division(n : NumType)
+    factors = [] of NumType
+    check = ->(p: NumType) {
+      q, r = n.divmod(p)
+      while r.zero?
+        factors << p
+        n = q
+        q, r = n.divmod(p)
       end
+    }
+
+    check.call(2)
+    check.call(3)
+    p = 5
+    while p * p <= n
+      check.call(p)
+      p += 2
+      check.call(p)
+      p += 4
+    end
+    factors << n if n > 1
+    factors
+  end
+
+  def self.prime_factorization(n : NumType)
+    result = {} of NumType => NumType
+    factors = self.trial_division(n)
+
+    factors.each do |f|
+      result[f] = 0
+      num = n
+      while num % f == 0
+        result[f] += 1
+        num /= f
       end
     end
 
-    result = sieve.map_with_index { |b, i| b ? i : nil }.compact
+    result
   end
 
   def self.palindrome?(x)
     x.to_s.reverse == x.to_s
   end
+
+  def self.to_digit_list(n : NumType)
+    n.to_s.chars.map { |d| d.to_i }
+  end
+
+  def self.to_big_ints(num_list : Array(NumType))
+    num_list.map { |n| BigInt.new(n) }
+  end
 end

crystal/euler003.cr

@@ -1,27 +1,3 @@
-alias NumType = Int32 | Int64 | UInt32 | UInt64
+require "./euler"
 
-def trial_division(n : NumType)
-  factors = [] of NumType
-  check = ->(p: NumType) {
-    q, r = n.divmod(p)
-    while r.zero?
-      factors << p
-      n = q
-      q, r = n.divmod(p)
-    end
-  }
-
-  check.call(2)
-  check.call(3)
-  p = 5
-  while p * p <= n
-    check.call(p)
-    p += 2
-    check.call(p)
-    p += 4
-  end
-  factors << n if n > 1
-  factors
-end
-
-puts trial_division(600851475143).max
+puts Euler.trial_division(600851475143).max

crystal/euler005.cr

@@ -0,0 +1,19 @@
+require "./euler"
+
+def integer_factorization_divisible_by_all_up_to(n)
+  result = {} of Euler::NumType => Euler::NumType
+  (2..n).map do |i|
+    Euler.prime_factorization(i).each do |prime, exponent|
+      if !result.has_key?(prime) || (exponent > result[prime])
+        result[prime] = exponent
+      end
+    end
+  end
+  result
+end
+
+def factors_to_int(factorization : Hash(Euler::NumType, Euler::NumType))
+  factorization.map { |prime, exponent| prime ** exponent }.product
+end
+
+puts factors_to_int(integer_factorization_divisible_by_all_up_to(20))

crystal/euler006.cr

@@ -0,0 +1 @@
+puts (1..100).sum ** 2 - (1..100).map { |n| n * n }.sum

crystal/euler007.cr

@@ -0,0 +1,3 @@
+require "./euler"
+
+puts Euler.eratosthenes_sieve(1000000)[10000]

crystal/euler008.cr

@@ -0,0 +1,27 @@
+require "./euler"
+
+def largest_consecutive_product(n, adjacent)
+  Euler.to_big_ints(Euler.to_digit_list(n)).each_cons(adjacent).map { |x| x.product }.max
+end
+
+puts largest_consecutive_product(
+BigInt.new("73167176531330624919225119674426574742355349194934
+96983520312774506326239578318016984801869478851843
+85861560789112949495459501737958331952853208805511
+12540698747158523863050715693290963295227443043557
+66896648950445244523161731856403098711121722383113
+62229893423380308135336276614282806444486645238749
+30358907296290491560440772390713810515859307960866
+70172427121883998797908792274921901699720888093776
+65727333001053367881220235421809751254540594752243
+52584907711670556013604839586446706324415722155397
+53697817977846174064955149290862569321978468622482
+83972241375657056057490261407972968652414535100474
+82166370484403199890008895243450658541227588666881
+16427171479924442928230863465674813919123162824586
+17866458359124566529476545682848912883142607690042
+24219022671055626321111109370544217506941658960408
+07198403850962455444362981230987879927244284909188
+84580156166097919133875499200524063689912560717606
+05886116467109405077541002256983155200055935729725
+71636269561882670428252483600823257530420752963450"), 13)

crystal/euler009.cr

@@ -0,0 +1,14 @@
+require "./euler"
+
+def generate_pythagorean_triples(upper_bound)
+  ([] of Array(Euler::NumType)).tap do |triples|
+    (2..upper_bound).each do |a|
+      (a..upper_bound).each do |b|
+        c = Math.sqrt(a**2 + b**2)
+        triples << [a, b, c.to_i] if c % 1 == 0
+      end
+    end
+  end
+end
+
+puts generate_pythagorean_triples(500).find([-1]) { |x| x.sum == 1000 }.product

crystal/euler010.cr

@@ -0,0 +1,4 @@
+require "./prime"
+
+prime = Euler::Prime.new
+puts prime.take_while { |x| x < 2000000 }.sum

crystal/prime.cr

@@ -0,0 +1,68 @@
+require "./euler"
+
+module Euler
+  class Prime
+    include Iterator(NumType)
+
+    def initialize()
+      @sieve_size = 16
+      @sieved_up_to = 0
+
+      @primes = Array(Bool).new(@sieve_size, true)
+      @primes[0] = false
+      @primes[1] = false
+
+      @index = 0
+      iterative_eratosthenes_sieve
+    end
+
+    private def check_and_increase_sieve
+      if @index > @primes.size - 1
+        @sieve_size *= 2
+        until @primes.size == @sieve_size
+          @primes << true
+        end
+      end
+
+      iterative_eratosthenes_sieve
+    end
+
+    private def iterative_eratosthenes_sieve
+      2.step(to: Math.sqrt(@sieve_size)) do |i|
+        if @primes[i]
+          (i * i >= @sieved_up_to ? i * i : @sieved_up_to + i - (@sieved_up_to % i)).step(to: @sieve_size-1, by: i) do |j|
+            @primes[j] = false
+          end
+        end
+      end
+      @sieved_up_to = @sieve_size-1
+    end
+
+    def next
+      @index += 1
+      check_and_increase_sieve
+
+      until @primes[@index]
+        @index += 1
+        check_and_increase_sieve
+      end
+      @index
+    end
+
+    def self.eratosthenes_sieve(n)
+      sieve = Array.new(n + 1, true)
+      sieve[0] = false
+      sieve[1] = false
+
+      2.step(to: Math.sqrt(n)) do |i|
+        if sieve[i]
+          (i * i).step(to: n, by: i) do |j|
+            sieve[j] = false
+          end
+        end
+      end
+
+      result = sieve.map_with_index { |b, i| b ? i : nil }.compact
+    end
+  end
+end