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  1. def sum(n)
  2.   if (n == 1) then
  3.       return 1
  4.     else
  5.       return sum(n-1) + n
  6.   end
  7. end



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  1. def gcd(n,m)
  2.   # Ç°¤Î¤¿¤á¡¤n >= m ¤ò³Î¼Â¤Ë¤·¤Æ¤ª¤¯.
  3.   if (n < m) then
  4.     n,m = m,n
  5.   end
  6.  
  7.   # ¤¢¤È¤ÏºÆµ¢ÄêµÁ¤Î¼°¤ÎÄ̤ê.
  8.   if (n % m == 0) then
  9.       return m
  10.     else
  11.       return gcd(m, (n % m) )
  12.   end
  13.  
  14. end



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  1. include Math
  2.  
  3. # ºÇÂç¸øÌó¿ô¤òµá¤á¤ë´Ø¿ô
  4. def gcd(n,m)
  5.   # Ç°¤Î¤¿¤á¡¤n >= m ¤ò³Î¼Â¤Ë¤·¤Æ¤ª¤¯.
  6.   if (n < m) then
  7.     n,m = m,n
  8.   end
  9.  
  10.   # ¸½ºß ÂоݤȤ·¤Æ¤¤¤ë¤ÎÆó¤Ä¤Î¿ô»ú¤È¡¤¤½¤Î mod ¤ò½ÐÎÏ.
  11.   print(n," mod ",m, " = ",n % m,"\n")
  12.  
  13.   # ¤¢¤È¤ÏºÆµ¢ÄêµÁ¤Î¼°¤ÎÄ̤ê.
  14.   if (n % m == 0) then
  15.       # ·×»»½ªÎ»
  16.       print("Finished. \n")
  17.       return m
  18.     else
  19.       return gcd(m, (n % m) )
  20.   end
  21. end
  22.  
  23. # °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
  24. n = 1071
  25. m = 1029
  26.  
  27. # ºÇÂç¸øÌó¿ô¤ò´Ø¿ô¤ò»È¤Ã¤Æ·×»»¤·¤Æɽ¼¨
  28. print("gcd(",n,", ",m,") = ",gcd(n,m),"\n")



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  1. notes.png ³¬¾è´Ø¿ô(factorial) n! ¤òºÆµ¢ÄêµÁ¤ò»È¤Ã¤Æ´Ø¿ô¤È¤·¤Æ¥×¥í¥°¥é¥à¤·¤è¤¦¡¥
    ¤¿¤À¤·¡¤°Ê²¼¤Î¾ò·ï¤ò¤ß¤¿¤¹¤è¤¦¤Ë¤·¤è¤¦¡¥
    1. 0! = 1, 1! = 1 ¤È¤¹¤ë¡¥
    2. µ¯Æ°»þ¤ËÀµÀ°¿ô¥Ñ¥é¥á¡¼¥¿ n (30¤°¤é¤¤¤òÁÛÄê)¤¬Í¿¤¨¤é¤ì¡¤0!, 1!, 2!,... n! ¤Þ¤Ç¤ò½ÐÎϤ¹¤ë¤â¤Î¤È¤¹¤ë¡¥
    3. ¥×¥í¥°¥é¥à¤Ï¡¤ºÆµ¢ÄêµÁ¤òÍѤ¤¤Æ·×»»¤¹¤ë¤È¤¹¤ë¡¥

      ¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð¥×¥í¥°¥é¥à¤Î¥Õ¥¡¥¤¥ë̾¤¬ factorial.rb ¤À¤È¤¹¤ë¤È¡¤

      ruby -w factorial.rb 20



      ¤È¤·¤Æ¼Â¹Ô¤¹¤ë¤È¡¤
       0! = 1
       1! = 1
       2! = 2
       3! = 6
       4! = 24
       5! = 120
       6! = 720
       7! = 5040
       8! = 40320
       9! = 362880
       10! = 3628800
       11! = 39916800
       12! = 479001600
       13! = 6227020800
       14! = 87178291200
       15! = 1307674368000
       16! = 20922789888000
       17! = 355687428096000
       18! = 6402373705728000
       19! = 121645100408832000
       20! = 2432902008176640000
      ¤È¤¤¤¦·ë²Ì¤¬¤Ç¤ë¤è¤¦¤Ë¤·¤í¡¤¤È¤¤¤¦¤³¤È¤Ë¤Ê¤ë¡¥

  2. notes.png Fibonacci ¿ôÎó F_0, F_1, F_2, ... ¤ò·×»»¤·¤Æ½ÐÎϤ¹¤ë¥×¥í¥°¥é¥à¤òºÆµ¢ÄêµÁ¤Ç½ñ¤³¤¦(Fibonacci ¿ôÎó¤ÎÄêµÁ¤òÃΤé¤Ê¤¤¿Í¤ÏÄ´¤Ù¤è¤¦)¡¥ ¤¿¤À¤·¡¤°Ê²¼¤Î¾ò·ï¤òËþ¤¿¤¹¤â¤Î¤È¤¹¤ë¡¥
  1. F_0 = 0, F_1 = 1 ¤È¤¹¤ë.
  2. µ¯Æ°»þ¤ËÀµÀ°¿ô¥Ñ¥é¥á¡¼¥¿ n (30¤°¤é¤¤¤òÁÛÄê)¤¬Í¿¤¨¤é¤ì¡¤F_0, F_1, F_2,... F_n ¤Þ¤Ç¤ò½ÐÎϤ¹¤ë¤â¤Î¤È¤¹¤ë¡¥
  3. ¥×¥í¥°¥é¥à¤Ï¡¤ºÆµ¢ÄêµÁ¤òÍѤ¤¤Æ·×»»¤¹¤ë¤È¤¹¤ë¡¥

    ¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð¥×¥í¥°¥é¥à¤Î¥Õ¥¡¥¤¥ë̾¤¬ fibonacci.rb ¤À¤È¤¹¤ë¤È¡¤

    ruby -w fibonacci.rb 30



    ¤È¤·¤Æ¼Â¹Ô¤¹¤ë¤È¡¤
      F_0 = 0
      F_1 = 1
      F_2 = 1
      F_3 = 2
      F_4 = 3
      F_5 = 5
      F_6 = 8
      F_7 = 13
      F_8 = 21
      F_9 = 34
      F_10 = 55
      F_11 = 89
      F_12 = 144
      F_13 = 233
      F_14 = 377
      F_15 = 610
      F_16 = 987
      F_17 = 1597
      F_18 = 2584
      F_19 = 4181
      F_20 = 6765
      F_21 = 10946
      F_22 = 17711
      F_23 = 28657
      F_24 = 46368
      F_25 = 75025
      F_26 = 121393
      F_27 = 196418
      F_28 = 317811
      F_29 = 514229
      F_30 = 832040
    ¤È¤¤¤¦·ë²Ì¤¬¤Ç¤ë¤è¤¦¤Ë¤·¤í¡¤¤È¤¤¤¦¤³¤È¤Ë¤Ê¤ë¡¥

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