160925

Ruby


倍数判定法(1)

tsujimotter さんの記事（http://tsujimotter.hatenablog.com/entry/multiple-of-29）を見て、

倍数判定法が正しいことを確認してみた。

以下で何をしているかは元の記事を読んでほしいのだが、

例えば、19 の倍数判定法は次のことを行う。

n = 2014 のとき、

2014 → 201 + 4 × 2 = 209 → 20 + 9 × 2 = 38

38 は19 の倍数なので、2014 は19 の倍数。

n = 2016 のとき、

2016 → 201 + 6 × 2 = 213 → 21 + 3 × 2 = 27

27 は19 の倍数ではないので、2016 は19 の倍数ではない。

# -*- coding: cp932 -*-

require 'prime'
require 'OpenSSL'

# 1の桁をcp倍して足すことを繰り返す
def f(pr, cp, n)
  m = n / 10 + (n % 10) * cp
  return n % pr if m >= n
  f(pr, cp, m)
end

n = 100
p Prime.each(n).select{|pr| 10 % pr != 0}.map{|pr| OpenSSL::BN.new("10").mod_inverse(pr).to_i}
p 'これだと使いにくいので、下を使用'
ary = []
Prime.each(n).select{|pr| 10 % pr != 0}.each{|pr|
  cp = OpenSSL::BN.new("10").mod_inverse(pr).to_i
  cp -= pr if cp > pr / 2
  ary << cp
}
p ary
p ''

Prime.each(n).select{|pr| 10 % pr != 0}.each{|pr|
  cp = OpenSSL::BN.new("10").mod_inverse(pr).to_i
  cp -= pr if cp > pr / 2
  p [pr, cp, (1..n).map{|i| [i, f(pr, cp, i)]}]
}

出力結果
[1, 5, 10, 4, 12, 2, 7, 3, 28, 26, 37, 13, 33, 16, 6, 55, 47, 64, 22, 8, 25, 9, 68]
"これだと使いにくいので、下を使用"
[1, -2, -1, 4, -5, 2, 7, 3, -3, -11, -4, 13, -14, 16, 6, -6, -20, -7, 22, 8, 25, 9, -29]
""
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