Merge pull request #57 from anubhav8421/add-solution-to-project-euler-problem-21

Add solution to project euler problem 21

Project Euler/Problem 21/problem21_sol1.rb

@@ -0,0 +1,57 @@
+# frozen_string_literal: true
+
+# Let d(n) be defined as the sum of proper divisors of n
+# (numbers less than n which divide evenly into n).
+# If d(a) = b and d(b) = a, where a & b, then a and b are an amicable pair.
+# and each of a and b are called amicable numbers.
+#
+# For example,
+#
+# The proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110;
+# therefore d(220) = 284.
+#
+# The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
+#
+# Evaluate the sum of all the amicable numbers under 10000.
+
+# get list of all divisors of `number`
+def get_divisors(number)
+  divisors = []
+  (1..(Math.sqrt(number).to_i)).each do |num|
+    if (number % num).zero?
+      divisors << num
+      divisors << number / num
+    end
+  end
+  divisors
+end
+
+# get list of all proper divisors of `number` i.e. removing `number` from
+# the list of divisors
+def get_proper_divisors(number)
+  divisors = get_divisors(number)
+  divisors.delete(number)
+  divisors
+end
+
+# implementation of a method `d` as mentioned in the question
+# i.e. finding sum of all proper divisors of `number`
+def d(number)
+  get_proper_divisors(number).sum
+end
+
+# given an upper `limit`, this method finds all amicable numbers
+# under this `limit`
+def find_amicable_numbers(limit)
+  result = []
+  (1...limit).each do |a|
+    b = d(a)
+    res = d(b)
+    result.push(a) if (a == res) && (a != b)
+  end
+  result
+end
+
+# calling `find_amicable_numbers` method and finding sum of all such numbers
+# below 10000, and printing the result on the console
+puts find_amicable_numbers(10_000).sum