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