第十回講義メモ

!Mac OS X-10.15.7 !ruby-2.6.3p62

Recursion

例題

フィボナッチ数列を求める.

fib(n) = fib(n-1)+fib(n-2)
0 1 1 2 3 5 8 13 21 ...

fib(0) = 0

Fibonacci数列の初項は0まずは, 関数にしてしまう.

def fib(n)
  if n==0
    return 0
  end
end

前回作ったassert_equal.rbのassertionで出力と期待値が一致しているかどうか確認
#+begin_src ruby
require './assert_equal'
puts assert_equal(0, fib(0))

結果

expected :: 0
result   :: 0
succeeded in assert_equal.

fib(1) = 1

n = 1の時を確認.

require './assert_equal'

def fib(n)
  if n==0
    return 0
  end
  if n==1
    return 1
  end
end
assert_equal(0, fib(0))
assert_equal(1, fib(1))  

fib(2) = fib(1) + fib(0) = 1

require './assert_equal'

 def fib(n)
   if n==0
     return 0
   end
   if n<=2
     return 1
   end
 end
[[0,0],[1,1],[2,1]].each do |index, expected|
  puts assert_equal(expected, fib(index))
end

配列の受け取りをより明示的にする/.

index, expected = pair

と修正できるので,以下のように修正

[[0,0],[1,1],[2,1]].each do |index, expected|
  puts assert_equal(pair[1], fib(index))
end

fib(3) = 2 = fib(2) + fib(1)

以下コード.

def fib(n)
  return 0  if n==0
  return 1  if n<=2
  return fib(2) + fib(1)
end

最終形

fib(2) = fib(1) + fib(0) = 1 + 0

上記が抜けているため, if文の条件分岐をもう少し狭める.

最終的に,

require './assert_equal'

def fib(n)
  return 0 if n==0
  return 1 if n==1
  return fib(n-1) + fib(n-2)
end

[[0,0],[1,1],[2,1],[3,2],[4,3],
[5,5],[6,8],[7,13],[8,21]].each do |index, expected|
  puts assert_equal(expected, fib(index))
end

結果

> ruby fobonacci.rb
expected :: 0
result   :: 0
succeeded in assert_equal
expected :: 1
result   :: 1
succeeded in assert_equal
expected :: 1
result   :: 1
succeeded in assert_equal
expected :: 2
result   :: 2
succeeded in assert_equal
expected :: 3
result   :: 3
succeeded in assert_equal
expected :: 5
result   :: 5
succeeded in assert_equal
expected :: 8
result   :: 8
succeeded in assert_equal
expected :: 13
result   :: 13
succeeded in assert_equal
expected :: 21
result   :: 21
succeeded in assert_equal
expected :: 34
result   :: 34
succeeded in assert_equal

上手く動作したことがたしかめられた.

参考サイト

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• source ~/my_ruby/grad_members_20f/members/drop-sd/lectures/no10.org