Solution to problem 57 in julia

src/Julia/Problem057.jl

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+#=
+Created on 11 Oct 2021
+
+@author: David Doblas Jiménez
+@email: daviddoji@pm.me
+
+Solution for Problem 57 of Project Euler
+https://projecteuler.net/problem=57
+=#
+
+using BenchmarkTools
+
+function Problem57()
+    #=
+    It is possible to show that the square root of two can be expressed
+    as an infinite continued fraction.
+
+    By expanding this for the first four iterations, we get:
+
+        1 +  1/2 = 3/2 = 1.5
+        1 + 1/2+1/2 = 7/5 = 1.4
+        1 + 1/2+1/2+1/2 = 17/12 = 1.41666...
+        1 + 1/2+1/2+1/2+1/2 = 41/29 = 1.41379...
+
+    The next three expansions are 99/70, 239/169, and 577/408, but the eighth
+    expansion, 1393/985, is the first example where the number of digits in
+    the numerator exceeds the number of digits in the denominator.
+
+    In the first one-thousand expansions, how many fractions contain a numerator
+    with more digits than the denominator
+    =#
+
+    ans = 0
+    f = 1 // 2
+    for i in 1:1000
+        f = big(1) / (2 + f)
+        result = 1 + f
+        if length(digits(numerator(result))) > length(digits(denominator(result)))
+            ans += 1
+        end
+    end
+
+    return ans
+end
+
+
+println("Time to evaluate Problem 57:")
+@btime Problem57()
+println("")
+println("Result for Problem 57: ", Problem57())