problem 8 9 10 in julia

3 files changed, 111 insertions, 0 deletions

diff --git a/julia/008-largest_product_in_a_series.jl b/julia/008-largest_product_in_a_series.jl
new file mode 100644
index 0000000..7a67206
--- /dev/null
+++ b/julia/008-largest_product_in_a_series.jl
@@ -0,0 +1,61 @@
+###
+# Largest product in a series
+# Problem 8
+#
+# The four adjacent digits in the 1000-digit number that have the greatest product are 9 ×
+# 9 × 8 × 9 = 5832.
+# 73167176531330624919225119674426574742355349194934
+# 96983520312774506326239578318016984801869478851843
+# 85861560789112949495459501737958331952853208805511
+# 12540698747158523863050715693290963295227443043557
+# 66896648950445244523161731856403098711121722383113
+# 62229893423380308135336276614282806444486645238749
+# 30358907296290491560440772390713810515859307960866
+# 70172427121883998797908792274921901699720888093776
+# 65727333001053367881220235421809751254540594752243
+# 52584907711670556013604839586446706324415722155397
+# 53697817977846174064955149290862569321978468622482
+# 83972241375657056057490261407972968652414535100474
+# 82166370484403199890008895243450658541227588666881
+# 16427171479924442928230863465674813919123162824586
+# 17866458359124566529476545682848912883142607690042
+# 24219022671055626321111109370544217506941658960408
+# 07198403850962455444362981230987879927244284909188
+# 84580156166097919133875499200524063689912560717606
+# 05886116467109405077541002256983155200055935729725
+# 71636269561882670428252483600823257530420752963450
+# Find the thirteen adjacent digits in the 1000-digit number that have the greatest
+# product. What is the value of this product?
+###
+
+
+const NUMBER_STRING = join(split("
+    73167176531330624919225119674426574742355349194934
+    96983520312774506326239578318016984801869478851843
+    85861560789112949495459501737958331952853208805511
+    12540698747158523863050715693290963295227443043557
+    66896648950445244523161731856403098711121722383113
+    62229893423380308135336276614282806444486645238749
+    30358907296290491560440772390713810515859307960866
+    70172427121883998797908792274921901699720888093776
+    65727333001053367881220235421809751254540594752243
+    52584907711670556013604839586446706324415722155397
+    53697817977846174064955149290862569321978468622482
+    83972241375657056057490261407972968652414535100474
+    82166370484403199890008895243450658541227588666881
+    16427171479924442928230863465674813919123162824586
+    17866458359124566529476545682848912883142607690042
+    24219022671055626321111109370544217506941658960408
+    07198403850962455444362981230987879927244284909188
+    84580156166097919133875499200524063689912560717606
+    05886116467109405077541002256983155200055935729725
+    71636269561882670428252483600823257530420752963450
+"))
+
+const CHUNK_SIZE = 13
+
+const NUMBERS       = [parse(Int, c) for c in NUMBER_STRING]
+const NUMBER_CHUNKS = zip([NUMBERS[start:end] for start in 1:CHUNK_SIZE]...)
+const RESULT        = maximum(cumprod(chunk)[end] for chunk in NUMBER_CHUNKS)
+
+println(RESULT)
diff --git a/julia/009-special_pythagorean_triplet.jl b/julia/009-special_pythagorean_triplet.jl
new file mode 100644
index 0000000..65404be
--- /dev/null
+++ b/julia/009-special_pythagorean_triplet.jl
@@ -0,0 +1,27 @@
+###
+# Special Pythagorean triplet
+# Problem 9
+#
+# A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
+#  a2 + b2 = c2
+# For example, 32 + 42 = 9 + 16 = 25 = 52.
+# There exists exactly one Pythagorean triplet for which a + b + c = 1000.Find the product
+# abc.
+###
+
+
+using Base.Iterators
+
+
+for c in countfrom(1)
+    for b in 1:(c - 1)
+        for a in 1:(b - 1)
+            if  a ^ 2 + b ^ 2 == c ^ 2 && a + b + c == 1000
+                println(a * b * c)
+                exit(0)
+            end
+        end
+    end
+end
+
+
diff --git a/julia/010-summation_of_primes.jl b/julia/010-summation_of_primes.jl
new file mode 100644
index 0000000..1e93a4f
--- /dev/null
+++ b/julia/010-summation_of_primes.jl
@@ -0,0 +1,23 @@
+###
+# Summation of primes
+# Problem 10
+#
+# The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
+# Find the sum of all the primes below two million.
+###
+
+function eratosthenes_sieve(stop)
+    ns = Array(reverse(2:stop))
+    primes = []
+    while true
+        prime = pop!(ns)
+        push!(primes, prime)
+        if prime > ceil(sqrt(stop))
+            return append!(primes, ns)
+            break
+        end
+        ns = filter(n -> n % prime != 0, ns)
+    end
+end
+
+println(sum(eratosthenes_sieve(2_000_000 - 1)))