Experimental Mathematics 1 (2010)
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#contents
* Á°²ó¤Î²ÝÂê¤Ë¤Ä¤¤¤Æ [#na54261f]
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+ ¼¡¸µ¤Î°ã¤¤¤Î¥Á¥§¥Ã¥¯¤Ï¤·¤Ê¤¯¤Æ¤â¤è¤¤(¤â¤Á¤í¤ó¤·¤Æ¤â¤è¤¤)
+ (¾åµé¼Ô¸þ¤±)¾å¤ÇÄêµÁ¤·¤¿ ''inner_product'' ´Ø¿ô¤òÍѤ¤¤Æ...
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&br;
** Á´Âι½Â¤¤ò¹Í¤¨¤ë [#i25568de]
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// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
include Math
# ¹ÔÎóƱ»Î¤ÎÀÑ: ¹ÔÎóÆó¤Ä¤¬°ú¿ô
def mtx_product_mtx(m_a, m_b)
# ½ÐÎϤϹÔÎ󡥡֤Ȥꤢ¤¨¤ºÆ°¤¯¤è¤¦¤Ë¡×ºÇ½é¤Î°ú¿ô¤òÊÖ¤·...
return m_a
end
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ: ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤¬°ú¿ô
def mtx_product_vec(m_a, v_x)
# ½ÐÎϤϥ٥¯¥È¥ë¡¥¡Ö¤È¤ê¤¢¤¨¤ºÆ°¤¯¤è¤¦¤Ë¡×°ú¿ô¥Ù¥¯¥È¥ë...
return v_x
end
# ¹ÔÎó¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_mtx(m_a)
end
# ¥Ù¥¯¥È¥ë¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_vec(v_x)
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# ¥µ¥ó¥×¥ë¤Î 2 x 2 ÌäÂêÍѥǡ¼¥¿
a = [[1,2],
[3,4]]
b = [[5,6],
[7,8]]
x = [10,11]
# ¹ÔÎóƱ»Î¤ÎÀѤò·×»»
c = mtx_product_mtx(a,b)
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤò·×»»
y = mtx_product_vec(a,x)
# ²èÌ̤˽ÐÎÏ
print_mtx(c)
print_vec(y)
}}
&br;
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// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
def print_vec(v_x)
print("[ ")
for i in 1..v_x.size do
print(v_x[i-1]," ")
end
print("]\n")
end
}}
¤³¤Î´Ø¿ô¤¬¤Ç¤¤ì¤Ð¡¤¹ÔÎó¤Îɽ¼¨¤Ë¤Ï¤³¤ì¤òÍøÍѤ¹¤ë¤Î¤¬¿¿¤Ã...
// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
def print_mtx(m_a)
for i in 1..m_a.size do
print_vec(m_a[i-1])
end
end
}}
¤³¤ÎÎã¤Ç¤Ï ''print_vec'' ´Ø¿ô¤ò»È¤¨¤Ð ''print_mtx'' ´Ø¿ô...
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// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
# ¥Ù¥¯¥È¥ë¤ÎÆâÀÑ¡¥Á°²ó¤Î¥³¥Ô¡¼
def inner_product(v_a, v_b)
sum = 0.0
for i in 1..v_a.size do
sum += v_a[i-1]*v_b[i-1]
end
return sum
end
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
# ¤µ¤¢¤É¤¦¤¹¤ë?
end
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ: ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤¬°ú¿ô
def mtx_product_vec(m_a, v_x)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = inner_product(m_a[i-1], v_x)
end
return v_y
end
}}
¤½¤·¤Æ¡¤·è¤á¤é¤ì¤¿¼¡¸µ¤Î¥Ù¥¯¥È¥ë¤Î¡Ö¤Ò¤Ê¤¬¤¿¡×¤òÍÑ°Õ¤¹¤ë...
#highlighter(language=ruby,number=off,cache=on){{
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
# ¤Þ¤ºÍ×ÁǤ¬¤Ò¤È¤Ä¤â¤Ê¤¤¡Ö¶õ½¸¹ç¡×¤òºî¤ë¡¥
a = []
# Í×ÁÇ 0.0 ¤ò n¸ÄÄɲ乤롥
n.times { a.push(0.0) }
# ½ÐÎÏ
return a
end
}}
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#highlighter(language=ruby,number=off,cache=on){{
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
return Array.new(n){0.0}
end
}}
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> [ 1 2 ]
> [ 3 4 ]
> [ 32.0 74.0 ]
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** µ¡Ç½¤òÁý¤ä¤·¤Æ¤¤¤¯: ¹ÔÎó¤È¹ÔÎó¤ÎÀÑ [#e7a15e78]
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// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
# Îó¥Ù¥¯¥È¥ë¤òÈ´¤½Ð¤¹
def col_vec(m_a, k)
v_y = make_vec(m_a.size)
# ¶ñÂÎŪ¤Êµ¡Ç½¤Ï¤¢¤È¤Ç¼ÂÁõ¤¹¤ë
return v_y
end
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
# ¤µ¤¢¤É¤¦¤¹¤ë?
end
# ¹ÔÎóƱ»Î¤ÎÀÑ: ¹ÔÎóÆó¤Ä¤¬°ú¿ô
def mtx_product_mtx(m_a, m_b)
m_c = make_mtx(m_a.size,m_a.size)
# ÆâÀѤò»È¤¨¤Ð¡¤¤¢¤È¤Ï¿ô³Ø¤ÎÄêµÁÄ̤ꡥ
for i in 1..m_a.size do
for j in 1..m_a.size do
m_c[i-1][j-1] = inner_product(m_a[i-1],col_vec(m_b,...
end
end
return m_c
end
}}
¤Ç¡¤¤³¤³¤ÇɬÍפˤʤä¿Æó¤Ä¤Î´Ø¿ô¤Îµ¡Ç½¤ò¼ÂÁõ¤¹¤ë¡¥
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// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
def col_vec(m_a, k)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = m_a[i-1][k-1]
end
return v_y
end
}}
»Ä¤Ã¤¿¡Ö¹ÔÎó¤Î¤Ò¤Ê¤¬¤¿¤òºî¤ë¡×µ¡Ç½¤Ï¡¤¥Ù¥¯¥È¥ë¤òºî¤ëµ¡Ç½...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
a = []
n.times { a.push( make_vec(m) ) }
return a
end
}}
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#highlighter(language=ruby,number=off,cache=on){{
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
return Array.new(n){ Array.new(m){0.0} }
end
}}
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> [ 19.0 22.0 ]
> [ 43.0 50.0 ]
> [ 32.0 74.0 ]
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** ÌäÂê¤òÂ礤á¤ËÊѹ¹: ºÇ½ªÃʳ¬¤Ø [#zfba35ec]
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// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# ¥Ù¥¯¥È¥ë¤ÎÆâÀÑ¡¥Á°²ó¤Î¥³¥Ô¡¼
def inner_product(v_a, v_b)
sum = 0.0
for i in 1..v_a.size do
sum += v_a[i-1]*v_b[i-1]
end
return sum
end
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
a = []
n.times { a.push(0.0) }
return a
end
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
a = []
n.times { a.push( make_vec(m) ) }
return a
end
# Îó¥Ù¥¯¥È¥ë¤òÈ´¤½Ð¤¹
def col_vec(m_a, k)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = m_a[i-1][k-1]
end
return v_y
end
# ¹ÔÎóƱ»Î¤ÎÀÑ: ¹ÔÎóÆó¤Ä¤¬°ú¿ô
def mtx_product_mtx(m_a, m_b)
m_c = make_mtx(m_a.size, m_a.size)
for i in 1..m_a.size do
for j in 1..m_a.size do
m_c[i-1][j-1] = inner_product(m_a[i-1],col_vec(m_b,...
end
end
return m_c
end
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ: ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤¬°ú¿ô
def mtx_product_vec(m_a, v_x)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = inner_product(m_a[i-1], v_x)
end
return v_y
end
# ¹ÔÎó¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_mtx(m_a)
for i in 1..m_a.size do
print_vec(m_a[i-1])
end
end
# ¥Ù¥¯¥È¥ë¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_vec(v_x)
print("[ ")
for i in 1..v_x.size do
print(v_x[i-1]," ")
end
print("]\n")
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
a = [[1,2,3,4],
[5,6,7,8],
[9,10,11,12],
[13,14,15,16]]
b = [[17,18,19,20],
[21,22,23,24],
[25,26,27,28],
[29,30,31,32]]
x = [3,4,5,6]
# ¹ÔÎóƱ»Î¤ÎÀѤò·×»»
c = mtx_product_mtx(a,b)
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤò·×»»
y = mtx_product_vec(a,x)
# °Ê²¼¡¤²èÌ̤˽ÐÎÏ
print("A = \n")
print_mtx(a)
print("\n")
print("B = \n")
print_mtx(b)
print("\n")
print("A B = \n")
print_mtx(c)
print("\n")
print("x = \n")
print_vec(x)
print("\n")
print("A x = \n")
print_vec(y)
}}
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> A =
> [ 1 2 3 4 ]
> [ 5 6 7 8 ]
> [ 9 10 11 12 ]
> [ 13 14 15 16 ]
> &br;
> B =
> [ 17 18 19 20 ]
> [ 21 22 23 24 ]
> [ 25 26 27 28 ]
> [ 29 30 31 32 ]
> &br;
> A B =
> [ 250.0 260.0 270.0 280.0 ]
> [ 618.0 644.0 670.0 696.0 ]
> [ 986.0 1028.0 1070.0 1112.0 ]
> [ 1354.0 1412.0 1470.0 1528.0 ]
> &br;
> x =
> [ 3 4 5 6 ]
>
> A x =
> [ 50.0 122.0 194.0 266.0 ]
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** ¥×¥í¥°¥é¥àÃæ¤ËƱ¤¸¤³¤È¤ò·«¤êÊÖ¤µ¤Ê¤¤ [#adc95422]
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&size(16)...
&size(16)...
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¤³¤Î¾ì¹ç¤Ï¡¤Î㤨¤Ð¼¡¤Î¤è¤¦¤Ê¥×¥í¥°¥é¥à¤Ë¤Ê¤ë¤À¤í¤¦¡¥
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# Ķ¤¨¤ë¤«¤É¤¦¤«Ä´¤Ù¤ë¿ô¤Ïµ¯Æ°»þ¤Ë¤â¤é¤¦
n = ARGV[0].to_i
# ¹ç·×¤Î½é´üÃͤϤâ¤Á¤í¤ó¥¼¥í¡¥
sum = 0
# ¤·¤Æ¤¤¤¯¿ô¡¥ ºÇ½é¤Ï 1 ¤«¤é¤À¤¬¡¤¤³¤ÎÃʳ¬¤Ç¤Î sum ¤ËÂÐ...
# ¥¼¥í¤Ë¤·¤Æ¤ª¤¯¤Î¤¬¹çÍýŪ¡¥
i = 0
# n ¤òĶ¤¨¤Æ¤Ê¤¤¤È while ¤ÎÃæ¿È¤¬¼Â¹Ô¤µ¤ì¡¤ºÆ¤Ó n ¤òĶ¤¨...
while (sum <= n) do
print("i = ", i, ", sum = ", sum, " <= ", n, "\n")
# Àè¤Ë½ÐÎÏ. ¤³¤ÎÃʳ¬¤Ê¤é³Î¼Â¤Ë sum <= n.
# while ¤Ç¤Ï¡¤·ë²Ì¤ËÂФ¹¤ëȽÃǤä½ÐÎϤϾò·ï¥Á¥§¥Ã¥¯¤Î¤¹...
i += 1 # i ¤ò 1Áý¤ä¤¹¡¥
sum += i # i ¤À¤±¹ç·×¤¹¤ë¡¥
end
# i ¤òÁý¤ä¤·¤Æ¤«¤é i ¤ò sum ¤Ë¤¹¤³¤È!
# sum ¤Ë¤·¤Æ¤«¤é i ¤òÁý¤ä¤¹¤È¡¤ºÇ¸å¤Ë¤Ä¤¸¤Ä¤Þ¤¬¹ç¤ï¤Ê¤¯...
# ¤è¤¯Ê¬¤«¤é¤Ê¤¤¿Í¤Ï¡¤sum ¤Ë¤·¤Æ¤«¤é i ¤òÁý¤ä¤¹¤è¤¦¤Ë¤·...
# ºÇ¸å¤Ë·ë²Ì¤ò½ÐÎÏ¡¥
print("i = ", i, ", sum = ", sum, " > ", n, "\n")
}}
¤³¤ì¤ò
ruby -w ./over.rb 100
¤Ê¤É¤È¤·¤Æµ¯Æ°¤¹¤ë¤È¡¤
> i = 0, sum = 0 <= 100
> i = 1, sum = 1 <= 100
> i = 2, sum = 3 <= 100
> i = 3, sum = 6 <= 100
> i = 4, sum = 10 <= 100
> i = 5, sum = 15 <= 100
> i = 6, sum = 21 <= 100
> i = 7, sum = 28 <= 100
> i = 8, sum = 36 <= 100
> i = 9, sum = 45 <= 100
> i = 10, sum = 55 <= 100
> i = 11, sum = 66 <= 100
> i = 12, sum = 78 <= 100
> i = 13, sum = 91 <= 100
> i = 14, sum = 105 > 100
¤È¤¤¤¦¤è¤¦¤Ë·ë²Ì¤¬ÆÀ¤é¤ì¤ë¡¥¤É¤¦¤À¤í¤¦¤«¡¥¼«Ê¬¤Ç¤Ç¤¤¿¤À...
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CENTER:&size(24){''while = æ½ÐȽÄê¤Ä¤Ìµ¸Â¥ë¡¼¥×¤Î°ì¼ï''};
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** Fizz Buzz ¤ËÄ©Àï [#w6428d88]
Fizz Buzz ¤È¤Ï¸ÀÍÕÍ·¤Ó¤Î°ì¼ï¤Ç¡¤1, 2,... ¤È½ç¤Ë¿ô»ú¤ò½Ò¤Ù...
- 3 ¤Ç³ä¤êÀÚ¤ì¤ë¤È¤¤Ï¤½¤Î¿ô»ú¤ÎÂå¤ï¤ê¤Ë ''Fizz'' ¤È¸À¤¦
- 5 ¤Ç³ä¤êÀÚ¤ì¤ë¤È¤¤Ï¤½¤Î¿ô»ú¤ÎÂå¤ï¤ê¤Ë ''Buzz'' ¤È¸À¤¦
- ¤¿¤À¤·¡¤3 ¤Ç¤â 5 ¤Ç¤â³ä¤êÀÚ¤ì¤ë¤È¤¤ÏÆÃÊ̤ˤ½¤Î¿ô»ú¤ÎÂå...
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- ¥×¥í¥°¥é¥àµ¯Æ°»þ¤Ë¤¢¤ëÄøÅÙÂ礤ʿô ''n'' (100 ¤°¤é¤¤?) ...
- 1,2,... ¤È¿ô¤ò¾å¤Î¥ë¡¼¥ë¤Ç½ÐÎϤ·¤Æ¤¤¤Ã¤Æ¡¤''Fizz'', ''B...
¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð
ruby -w fb.rb 10
¤È¤·¤Æ 10¸Ä¤Î¡ÖÂå¤ï¤ê¡×¤¬½Ð¤Æ¤¯¤ë¤Þ¤Ç¤ò½ÐÎϤµ¤»¤ë¤È¡¤
> 1
> 2
> Fizz
> 4
> Buzz
> Fizz
> 7
> 8
> Fizz
> Buzz
> 11
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> 13
> 14
> Fizz Buzz
> 16
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> Buzz
> Fizz
¤È¤Ê¤ë¡¥¤µ¤Æ¡¤¤ß¤Ê¤µ¤ó¤Ï¤¦¤Þ¤¯¤Ç¤¤ë¤À¤í¤¦¤«¡¥
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** (¾åµé¼Ô¸þ¤±) 3¤ÎÇÜ¿ô¤È3¤Î¤Ä¤¯¿ô¤Î¤È¤¤À¤±¥¢¥Û [#y02db8...
¡Ö3¤ÎÇÜ¿ô¤È3¤Î¤Ä¤¯¿ô¤Î¤È¤¤À¤±¥¢¥Û¤Ë¤Ê¤ë¡×¤È¤·¤Æ¾å¤ÈƱ¤¸...
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** Collatz ¤ÎͽÁÛ¤òÄ´¤Ù¤Æ¤ß¤è¤¦ [#a4adf91b]
''Collatz ¤ÎͽÁÛ'' ¤È¤¤¤¦Í½ÁÛ¤¬¤¢¤ë¡¥¤³¤ì¤ò ''while'' ¤ò...
¤Þ¤º¤³¤ÎͽÁۤˤĤ¤¤Æµ½Ò¤·¤è¤¦¡¥¤³¤ÎͽÁۤȤϡ¤ÀµÀ°¿ô ''n'...
- n ¤¬¶ö¿ô¤Î¾ì¹ç: f(n) = n / 2
- n ¤¬´ñ¿ô¤Î¾ì¹ç: f(n) = (3 * n) + 1
¤È¤¹¤ë¤È¡¤¡Ö¤¤¤«¤Ê¤ëÀµÀ°¿ô¤ËÂФ·¤Æ¤â¤³¤Î ''f'' ¤ò·«¤êÊÖ¤·...
&ref(/materials/notes.png); ¤³¤ÎͽÁÛ¤¬Í¿¤¨¤é¤ì¤¿¿ô¤Ë¤Ä¤¤...
¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð
ruby -w collatz.rb 100
¤È¤·¤ÆºÇ½é¤Ë "100" ¤«¤é¥¹¥¿¡¼¥È¤·¤¿¾ì¹ç¤ò¥Á¥§¥Ã¥¯¤µ¤»¤ë¤È
> 100 -> 50 -> 25 -> 76 -> 38 -> 19 -> 58 -> 29 -> 88 ->
> 44 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40
> -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 1.
¤È¤¤¤¦¤è¤¦¤Ê½ÐÎϤò½Ð¤¹¤è¤¦¤Ë¤·¤è¤¦¡¥
&ref(/materials/warning.png); ¡Ö''f'' ¤Î·ë²Ì¤¬ 1 ¤Ç¤Ê¤¤´Ö...
&br;
* º£Æü¤ÎÁí»Å¾å¤² [#be9b628a]
¾å¤Î Collatz ¤ÎͽÁÛ¤ò°Ê²¼¤Î¤è¤¦¤ËÄ´¤Ù¤ë¥×¥í¥°¥é¥à¤ò½ñ¤¤¤Æ...
¾ò·ï¤Ï°Ê²¼¤ÎÄ̤ê¤Ç¤¢¤ë¡¥
- ÀµÀ°¿ô ''k'' ¤ËÂФ·¤Æ¡¤Collatz ¤Î´Ø¿ô ''f'' ¤ò²¿²óŬÍÑ...
- ¥×¥í¥°¥é¥àµ¯Æ°»þ¤Ë¤¢¤ëÄøÅÙÂ礤ʿô ''n'' (100¤°¤é¤¤) ¤¬...
- 1 ¤«¤é»Ï¤á¤Æ¡¤''n'' ¤Þ¤Ç ''num_col'' ¤Î·ë²Ì¤ò½ÐÎϤ¹¤ë¡¥
&ref(/materials/warning.png); ''num_col(1)'' ¤¬ 3 ¤Ë¤Ê¤Ã...
¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð
ruby -w col_num.rb 30
¤È¤·¤Æ 30 ¤Þ¤Ç¤òÄ´¤Ù¤µ¤»¤ë¤È
> 1, 0
> 2, 1
> 3, 7
> 4, 2
> 5, 5
> 6, 8
> 7, 16
> 8, 3
> 9, 19
> 10, 6
> 11, 14
> 12, 9
> 13, 9
> 14, 17
> 15, 17
> 16, 4
> 17, 12
> 18, 20
> 19, 20
> 20, 7
> 21, 7
> 22, 15
> 23, 15
> 24, 10
> 25, 23
> 26, 10
> 27, 111
> 28, 18
> 29, 18
> 30, 18
¤È¤¤¤¦¤è¤¦¤Ê½ÐÎϤò½Ð¤¹¤è¤¦¤Ë¤È¤¤¤¦¤³¤È¤Ç¤¢¤ë¡¥
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&ref(./collatz.png,80%);
¤È¤¤¤¦¤è¤¦¤Ê¤â¤Î¤òºî¤í¤¦¤È¤¤¤¦¤³¤È¤Ë¤Ê¤ë¡¥
¤³¤ÎÎã¤Ç¤Ï 30¤Þ¤Ç¤À¤¬¡¤¤³¤ì¤ò 100 ¤°¤é¤¤¤ÎÃͤǼ¹Ԥ·¤Æ¡¤...
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* ¥ì¥Ý¡¼¥È [#z0c9dd1e]
ËÜÆü¼õ¤±¤¿¹ÖµÁ¤ª¤è¤Ó¹Ô¤Ã¤¿¼Â½¬¤Ë¤Ä¤¤¤Æ¡¤´Êñ¤Ë¤Þ¤È¤á¤¿Êó...
¤Þ¤¿¡¤Áí»Å¾å¤²¤ÎÉôʬ¤Ç¼«Ê¬¤Ç½ñ¤¤¤¿¥×¥í¥°¥é¥à¤òÊó¹ð¤»¤è.
¤â¤Á¤í¤ó³Æ¼«¤Î
+ ½ê°(³ØÉô¡¤³Ø²Ê)
+ ³ØÀÒÈÖ¹æ
+ ³Øǯ
+ »á̾
+ Æü»þ
+ ´Î¿´¤Î¥ì¥Ý¡¼¥ÈÆâÍÆ(ÆÀ¤¿Ãθ«¡¤ºî¶È¤Ë¤Ä¤¤¤Æµ¤¤Å¤¤¤¿¤³¤ÈÅù...
¤ò½ñ¤¯¤Î¤ò˺¤ì¤Ê¤¤¤è¤¦¤Ë.
* about Icons, ClipArts [#ubfbbb67]
Some icons in this page are downloadable at [[ICONFINDER:...
The "note" icon &ref(/materials/notes.png); designed by [...
the "warning" icon &ref(/materials/warning.png); designed...
and the "triangle" icon &ref(/materials/JNorth_arrow-righ...
Some clip arts used in this page are downloadable at [[Op...
We deeply appreciate their superb works. With licence, th...
// ¨¬¨¨®¨¯¨°¨±¨²¨³¨´¨µ¨¶
// ¥³¥Þ¥ó¥É¥é¥¤¥óÆþÎϤϡֹÔƬ¤ò¥Ö¥é¥ó¥¯¤Ç»Ï¤á¤ë¡×.
// ¥³¥Þ¥ó¥É¥é¥¤¥ó½ÐÎϤϡֹÔƬ¤ò > ¤Ç»Ï¤á¤ë¡×.
// ¼Â½¬¥¢¥¤¥³¥ó
// &ref(/materials/notes.png);
// Ãí°Õ¥¢¥¤¥³¥ó
// &ref(/materials/warning.png);
// Link ¥¢¥¤¥³¥ó
// &ref(/materials/JNorth_arrow-right-sm.png);
// Âçʸ»ú¤Ç¤Î¶¯Ä´
// CENTER:&size(24){''¤Û¤²¤Û¤²''};
// programu source ɽµ
// #highlighter(language=ruby,number=on,cache=on){{}}
½ªÎ»¹Ô:
#contents
* Á°²ó¤Î²ÝÂê¤Ë¤Ä¤¤¤Æ [#na54261f]
Á°²ó¤Î²ÝÂê¤Ï°Ê²¼¤Î¤è¤¦¤Ê¤â¤Î¤Ç¤¢¤Ã¤¿¡¥
¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ¡¤¹ÔÎó¤È¹ÔÎó¤ÎÀѤò·×»»¤¹¤ë´Ø¿ô¤ò¥×¥í¥°...
+ ¹ÔÎó¤ÏÀµÊý¹ÔÎó¤Î¤ß°·¤¦¤È¤·¤Æ¤ª¤¯
+ ¼¡¸µ¤Î°ã¤¤¤Î¥Á¥§¥Ã¥¯¤Ï¤·¤Ê¤¯¤Æ¤â¤è¤¤(¤â¤Á¤í¤ó¤·¤Æ¤â¤è¤¤)
+ (¾åµé¼Ô¸þ¤±)¾å¤ÇÄêµÁ¤·¤¿ ''inner_product'' ´Ø¿ô¤òÍѤ¤¤Æ...
¤½¤·¤Æ¡¤4 x 4 ¤Î¹ÔÎó¤òŬÅö¤ËÆó¤Ä¡¤4¼¡¸µ¥Ù¥¯¥È¥ë¤òŬÅö¤Ë°ì...
&ref(/materials/warning.png); ¤³¤Îʸ¾Ï¤òÆɤà¸Â¤ê ''°ìÈ̤Î...
&ref(/materials/warning.png); ¤À¤«¤é¡¤¾ò·ï¤òËþ¤¿¤·¤Æ¤¤¤Ê...
&br;
** Á´Âι½Â¤¤ò¹Í¤¨¤ë [#i25568de]
¤¤¤Ä¤â¤Î¤è¤¦¤ËÁ´Âι½Â¤¤ò¹Í¤¨¤ë¡¥
´ðËÜŪ¤Êµ¡Ç½¤È¤·¤Æ¹ÔÎóƱ»Î¤ÎÀѤȹÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤÎÆó¤Ä...
// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
include Math
# ¹ÔÎóƱ»Î¤ÎÀÑ: ¹ÔÎóÆó¤Ä¤¬°ú¿ô
def mtx_product_mtx(m_a, m_b)
# ½ÐÎϤϹÔÎ󡥡֤Ȥꤢ¤¨¤ºÆ°¤¯¤è¤¦¤Ë¡×ºÇ½é¤Î°ú¿ô¤òÊÖ¤·...
return m_a
end
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ: ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤¬°ú¿ô
def mtx_product_vec(m_a, v_x)
# ½ÐÎϤϥ٥¯¥È¥ë¡¥¡Ö¤È¤ê¤¢¤¨¤ºÆ°¤¯¤è¤¦¤Ë¡×°ú¿ô¥Ù¥¯¥È¥ë...
return v_x
end
# ¹ÔÎó¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_mtx(m_a)
end
# ¥Ù¥¯¥È¥ë¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_vec(v_x)
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# ¥µ¥ó¥×¥ë¤Î 2 x 2 ÌäÂêÍѥǡ¼¥¿
a = [[1,2],
[3,4]]
b = [[5,6],
[7,8]]
x = [10,11]
# ¹ÔÎóƱ»Î¤ÎÀѤò·×»»
c = mtx_product_mtx(a,b)
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤò·×»»
y = mtx_product_vec(a,x)
# ²èÌ̤˽ÐÎÏ
print_mtx(c)
print_vec(y)
}}
&br;
** µ¡Ç½¤òÁý¤ä¤·¤Æ¤¤¤¯: ·ë²Ì¤ò¤¹¤°¥Á¥§¥Ã¥¯¤Ç¤¤ë¤è¤¦¤Ë¡¤É½...
º£²ó¤Î²ÝÂê¤Ï¹ÔÎó¤Îź»ú¤Î¥º¥ì¤Ê¤É¤Î¤¢¤Á¤³¤Á¤Ë´Ö°ã¤¤¤¬È¯À¸...
¤Þ¤º¤Ï¡¤¥Ù¥¯¥È¥ë¤Îɽ¼¨¤«¤é¼ê¤òÉÕ¤±¤ë¤Î¤¬´Êñ¤À¤í¤¦¡¥Î㤨...
// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
def print_vec(v_x)
print("[ ")
for i in 1..v_x.size do
print(v_x[i-1]," ")
end
print("]\n")
end
}}
¤³¤Î´Ø¿ô¤¬¤Ç¤¤ì¤Ð¡¤¹ÔÎó¤Îɽ¼¨¤Ë¤Ï¤³¤ì¤òÍøÍѤ¹¤ë¤Î¤¬¿¿¤Ã...
// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
def print_mtx(m_a)
for i in 1..m_a.size do
print_vec(m_a[i-1])
end
end
}}
¤³¤ÎÎã¤Ç¤Ï ''print_vec'' ´Ø¿ô¤ò»È¤¨¤Ð ''print_mtx'' ´Ø¿ô...
&ref(/materials/warning.png);¤³¤Î¤è¤¦¤Ë¡¤¡Ö´û¤Ë¥×¥í¥°¥é¥à...
+ Ʊ¤¸¤è¤¦¤Ê¤³¤È¤ò²¿ÅÙ¤â½ñ¤«¤Ê¤¯¤ÆÎɤ¤¤Î¤Ç¡¤¥ß¥¹¤¬Æþ¤ê¹þ...
+ ½¤Àµ¤¹¤ë»þ¤Ë¡¤½¤Àµ²Õ½ê¤¬É¬Í׺Ǿ®¸Â¤ÇºÑ¤à
+ ¥×¥í¥°¥é¥à¤ÎÃê¾ÝÅÙ¤¬¾å¤¬¤ê¡¤¤è¤ê¤¤Á¤ó¤È¤·¤¿¤â¤Î¤Ë¤Ê¤ë...
¤«¤é¤Ç¤¢¤ë(Don't Repeat Yourself = ''DRY ¸¶Â§''¤Ë¶á¤¤¤«)...
CENTER:&size(24){''¥×¥í¥°¥é¥à¤Ç¤ÏƱÅù¤Î½èÍý¤ò½ÅÊ£¤·¤Æ½ñ¤¯...
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** µ¡Ç½¤òÁý¤ä¤·¤Æ¤¤¤¯: ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ [#h04340c6]
¼¡¤Ë´Êñ¤Ê¤Î¤Ï¡¤¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤμÂÁõ¤À¤í¤¦¡¥¤³¤ì¤ÏÆâ...
¤¿¤À¡¤·è¤á¤é¤ì¤¿¼¡¸µ¤Î¥Ù¥¯¥È¥ë¤Î¡Ö¤Ò¤Ê¤¬¤¿¡×¤òÍÑ°Õ¤¹¤ëÊý...
&ref(/materials/warning.png); ¿Í´Ö¤ÎǾ¤ß¤½¤Ï¤¢¤ëÄøÅٰʾå...
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Ç¡²¿¤ËÊ£»¨¤µ¤òʬ²ò¤¹¤ë¤«¤¬¥×¥í¥°¥é¥ß¥ó¥°¤Î¡Ö¥¥â¡×¤Ç¤¢¤ë¡¥
// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
# ¥Ù¥¯¥È¥ë¤ÎÆâÀÑ¡¥Á°²ó¤Î¥³¥Ô¡¼
def inner_product(v_a, v_b)
sum = 0.0
for i in 1..v_a.size do
sum += v_a[i-1]*v_b[i-1]
end
return sum
end
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
# ¤µ¤¢¤É¤¦¤¹¤ë?
end
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ: ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤¬°ú¿ô
def mtx_product_vec(m_a, v_x)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = inner_product(m_a[i-1], v_x)
end
return v_y
end
}}
¤½¤·¤Æ¡¤·è¤á¤é¤ì¤¿¼¡¸µ¤Î¥Ù¥¯¥È¥ë¤Î¡Ö¤Ò¤Ê¤¬¤¿¡×¤òÍÑ°Õ¤¹¤ë...
#highlighter(language=ruby,number=off,cache=on){{
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
# ¤Þ¤ºÍ×ÁǤ¬¤Ò¤È¤Ä¤â¤Ê¤¤¡Ö¶õ½¸¹ç¡×¤òºî¤ë¡¥
a = []
# Í×ÁÇ 0.0 ¤ò n¸ÄÄɲ乤롥
n.times { a.push(0.0) }
# ½ÐÎÏ
return a
end
}}
&ref(/materials/warning.png); (¾åµé¼Ô¸þ¤±) Ruby ¤Îµ¡Ç½¤ò...
#highlighter(language=ruby,number=off,cache=on){{
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
return Array.new(n){0.0}
end
}}
¤È¤¤¤¦´¶¤¸¤Ë¤Ê¤ë¤À¤í¤¦¡¥
¤µ¤Æ¡¤¤³¤¦¤¹¤ë¤³¤È¤Ç¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤϤ¤Á¤ó¤È·×»»¤Ç¤...
> [ 1 2 ]
> [ 3 4 ]
> [ 32.0 74.0 ]
¤È¤¤¤¦½ÐÎϤ¬ÆÀ¤é¤ì¡¤³Î¤«¤Ë 2 x 2 ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤ¬·×»»...
&br;
** µ¡Ç½¤òÁý¤ä¤·¤Æ¤¤¤¯: ¹ÔÎó¤È¹ÔÎó¤ÎÀÑ [#e7a15e78]
¤µ¤Æ¡¤ºÇ¸å¤Ï¹ÔÎó¤È¹ÔÎó¤ÎÀѤǤ¢¤ë¡¥¤³¤ì¤â¡¤¹ÔÎó¤ò¥Ù¥¯¥È¥ë...
¤¢¤È¤Ï¡¤¹ÔÎ󤫤é¹Ô¥Ù¥¯¥È¥ë¡¤Îó¥Ù¥¯¥È¥ë¤òÈ´¤½Ð¤¹Áàºî¤ò¤·...
¤À¤«¤é¡¤Î㤨¤Ð¼¡¤Î¤è¤¦¤Ë¤Ê¤ë¤À¤í¤¦¡¥
// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
# Îó¥Ù¥¯¥È¥ë¤òÈ´¤½Ð¤¹
def col_vec(m_a, k)
v_y = make_vec(m_a.size)
# ¶ñÂÎŪ¤Êµ¡Ç½¤Ï¤¢¤È¤Ç¼ÂÁõ¤¹¤ë
return v_y
end
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
# ¤µ¤¢¤É¤¦¤¹¤ë?
end
# ¹ÔÎóƱ»Î¤ÎÀÑ: ¹ÔÎóÆó¤Ä¤¬°ú¿ô
def mtx_product_mtx(m_a, m_b)
m_c = make_mtx(m_a.size,m_a.size)
# ÆâÀѤò»È¤¨¤Ð¡¤¤¢¤È¤Ï¿ô³Ø¤ÎÄêµÁÄ̤ꡥ
for i in 1..m_a.size do
for j in 1..m_a.size do
m_c[i-1][j-1] = inner_product(m_a[i-1],col_vec(m_b,...
end
end
return m_c
end
}}
¤Ç¡¤¤³¤³¤ÇɬÍפˤʤä¿Æó¤Ä¤Î´Ø¿ô¤Îµ¡Ç½¤ò¼ÂÁõ¤¹¤ë¡¥
¤Þ¤º¤Ï¡Ö¹ÔÎ󤫤éÎó¥Ù¥¯¥È¥ë¤òÈ´¤½Ð¤¹¡×µ¡Ç½¤À¤¬¡¤¤³¤ì¤Ï´Ê...
// programu source ɽµ
#highlighter(language=ruby,number=off,cache=on){{
def col_vec(m_a, k)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = m_a[i-1][k-1]
end
return v_y
end
}}
»Ä¤Ã¤¿¡Ö¹ÔÎó¤Î¤Ò¤Ê¤¬¤¿¤òºî¤ë¡×µ¡Ç½¤Ï¡¤¥Ù¥¯¥È¥ë¤òºî¤ëµ¡Ç½...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
a = []
n.times { a.push( make_vec(m) ) }
return a
end
}}
¤È¤¹¤ì¤Ð¤è¤¤¡¥´Êñ¤¹¤®¤ÆÇϼ¯¤Ë¤µ¤ì¤Æ¤¤¤ëµ¤Ê¬¤âͤ뤫¤â¤·...
&ref(/materials/warning.png); (¾åµé¼Ô¸þ¤±) Ruby ¤Îµ¡Ç½¤ò...
#highlighter(language=ruby,number=off,cache=on){{
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
return Array.new(n){ Array.new(m){0.0} }
end
}}
¤È¤¤¤¦´¶¤¸¤Ë¤Ê¤ë¤À¤í¤¦¡¥
¤µ¤Æ¡¤¤³¤ì¤Ç¤³¤Îµ¡Ç½¤â´°À®¤·¤¿¡¥»î¤·¤ËÆ°¤«¤·¤Æ¤ß¤ë¤È¡¤
> [ 19.0 22.0 ]
> [ 43.0 50.0 ]
> [ 32.0 74.0 ]
¤È¤Ê¤ê¡¤³Î¤«¤ËÀµ¤·¤¯Æ°¤¤¤Æ¤¤¤ë¤³¤È¤¬Ê¬¤«¤ë¡¥
&br;
** ÌäÂê¤òÂ礤á¤ËÊѹ¹: ºÇ½ªÃʳ¬¤Ø [#zfba35ec]
¤µ¤Æ¡¤¤¤Á¤ó¤ÈÆ°¤¤¤Æ¤¤¤ë¤è¤¦¤Ë¸«¤¨¤ë¤Î¤Ç¡¤ÌäÂê¤ò»Ø¼¨¤µ¤ì...
¤Þ¤¿¡¤½ÐÎϤ⾯¤·Æɤߤ䤹¤¯¤·¤¿¤¤¡¥
¤È¤¤¤¦¤³¤È¤Ç¡¤Î㤨¤Ð°Ê²¼¤Î¤è¤¦¤Ë¤Ê¤ë¤À¤í¤¦¡¥
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# ¥Ù¥¯¥È¥ë¤ÎÆâÀÑ¡¥Á°²ó¤Î¥³¥Ô¡¼
def inner_product(v_a, v_b)
sum = 0.0
for i in 1..v_a.size do
sum += v_a[i-1]*v_b[i-1]
end
return sum
end
# n ¼¡¸µ¥Ù¥¯¥È¥ë¤òºî¤ë
def make_vec(n)
a = []
n.times { a.push(0.0) }
return a
end
# n x m ¹ÔÎó¤òºî¤ë
def make_mtx(n,m)
a = []
n.times { a.push( make_vec(m) ) }
return a
end
# Îó¥Ù¥¯¥È¥ë¤òÈ´¤½Ð¤¹
def col_vec(m_a, k)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = m_a[i-1][k-1]
end
return v_y
end
# ¹ÔÎóƱ»Î¤ÎÀÑ: ¹ÔÎóÆó¤Ä¤¬°ú¿ô
def mtx_product_mtx(m_a, m_b)
m_c = make_mtx(m_a.size, m_a.size)
for i in 1..m_a.size do
for j in 1..m_a.size do
m_c[i-1][j-1] = inner_product(m_a[i-1],col_vec(m_b,...
end
end
return m_c
end
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀÑ: ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤¬°ú¿ô
def mtx_product_vec(m_a, v_x)
v_y = make_vec(m_a.size)
for i in 1..m_a.size do
v_y[i-1] = inner_product(m_a[i-1], v_x)
end
return v_y
end
# ¹ÔÎó¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_mtx(m_a)
for i in 1..m_a.size do
print_vec(m_a[i-1])
end
end
# ¥Ù¥¯¥È¥ë¤ò¿Í´ÖÍѤ˽ÐÎϤ¹¤ë
def print_vec(v_x)
print("[ ")
for i in 1..v_x.size do
print(v_x[i-1]," ")
end
print("]\n")
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
a = [[1,2,3,4],
[5,6,7,8],
[9,10,11,12],
[13,14,15,16]]
b = [[17,18,19,20],
[21,22,23,24],
[25,26,27,28],
[29,30,31,32]]
x = [3,4,5,6]
# ¹ÔÎóƱ»Î¤ÎÀѤò·×»»
c = mtx_product_mtx(a,b)
# ¹ÔÎó¤È¥Ù¥¯¥È¥ë¤ÎÀѤò·×»»
y = mtx_product_vec(a,x)
# °Ê²¼¡¤²èÌ̤˽ÐÎÏ
print("A = \n")
print_mtx(a)
print("\n")
print("B = \n")
print_mtx(b)
print("\n")
print("A B = \n")
print_mtx(c)
print("\n")
print("x = \n")
print_vec(x)
print("\n")
print("A x = \n")
print_vec(y)
}}
¤½¤·¤Æ¡¤¤³¤ì¤òÆ°¤«¤¹¤È¼¡¤Î¤è¤¦¤Ë¤Ê¤ë¡¥
¼ê·×»»¤Ê¤É¤Ç¡¤³Î¤«¤ËÀµ¤·¤¤·ë²Ì¤Ç¤¢¤ë¤³¤È¤¬³Î¤«¤á¤é¤ì¤ë¡¥
> A =
> [ 1 2 3 4 ]
> [ 5 6 7 8 ]
> [ 9 10 11 12 ]
> [ 13 14 15 16 ]
> &br;
> B =
> [ 17 18 19 20 ]
> [ 21 22 23 24 ]
> [ 25 26 27 28 ]
> [ 29 30 31 32 ]
> &br;
> A B =
> [ 250.0 260.0 270.0 280.0 ]
> [ 618.0 644.0 670.0 696.0 ]
> [ 986.0 1028.0 1070.0 1112.0 ]
> [ 1354.0 1412.0 1470.0 1528.0 ]
> &br;
> x =
> [ 3 4 5 6 ]
>
> A x =
> [ 50.0 122.0 194.0 266.0 ]
&ref(/materials/warning.png); ´°À®¤·¤¿¥×¥í¥°¥é¥à¤ÏŤ¤¤¬...
º£²ó¤Î²ÝÂ꤬Æñ¤·¤¤¤È»×¤Ã¤¿¿Í¤Ï¡¤Á´Âι½Â¤¤ò¹Í¤¨¤º¤Ë¤Ê¤ó¤È...
+ Ê£»¨¤Ê¤â¤Î¤ËÂФ¹¤ëÂнè¤ò¤¤¤¤Ê¤ê¡Ö»×¤¤¤Ä¤¯¡×¤Û¤ÉÉáÄ̤Î...
+ ¥×¥í¥°¥é¥à¤Ï¡ÖÂоݤòʬ²ò¤·¤Æµ¡Ç½¤òµ½Ò¤¹¤ëÁàºî¤ò·«¤êÊÖ...
¤³¤ì¤Ï¤ª¤½¤é¤¯¡¤¡ÖÊ£»¨¤µ¤òʬ²ò¤¹¤ë¤³¤È¤ÎËܼÁ¤µ¡¤½ÅÍ×À¤ò...
&br;
// CENTER:&size(24){''¥×¥í¥°¥é¥ß¥ó¥°¤Ï»×¤¤¤Ä¤¯¤â¤Î¤Ç¤Ï¤Ê...
// CENTER:&size(24){''ÂоݤÎÊ£»¨¤µ¤òʬ²ò¤·¤Æ¤«¤éµ¡Ç½¤ò¼Â...
CENTER:&size(24){''¥×¥í¥°¥é¥ß¥ó¥°¤Ç¤Ï¥Æ¥¯¥Ë¥«¥ë¤Êµ¡Ç½¼ÂÁõ...
CENTER:&size(24){''¤à¤·¤í¡ÖÌäÂê¤ò¤É¤¦Ê¬²ò¤¹¤ë¤«¡×¤ËÃíÎϤ¹...
&br;
&ref(/materials/warning.png); ¡ÖÆñ¤·¤«¤Ã¤¿¡×¡Ö»×¤¤¤Ä¤«¤Ê...
&br;
** ¥×¥í¥°¥é¥àÃæ¤ËƱ¤¸¤³¤È¤ò·«¤êÊÖ¤µ¤Ê¤¤ [#adc95422]
Àè¤Ë½ñ¤¤¤¿¤¬¡¤Æ±ÍͤνèÍý¤ò¤Ê¤ó¤É¤â½ñ¤«¤º¤Ë¡Ö´û¤Ë¥×¥í¥°¥é...
&ref(/materials/warning.png); ¼ÂºÝ¤Ë¡¤¾å¤Î¥µ¥ó¥×¥ë¤Ç¤Ï¡Ö...
&br;
* ¾ò·ï¤¬Ëþ¤¿¤µ¤ì¤Æ¤¤¤ë´Ö¤Ï¥ë¡¼¥×¤¹¤ë : while Ì¿Îá [#d2fc2...
¾ò·ï¤¬Ëþ¤¿¤µ¤ì¤Æ¤¤¤ë´Ö¤Ï¥ë¡¼¥×¤¹¤ë¤È¤¤¤¦À©¸æ¤ò³Ø¤Ü¤¦¡¥
¤Þ¤º¤Ïʸˡ¤ò½ñ¤¤¤Æ¤ª¤³¤¦¡¥
&br;
&size(24){''while (&color(blue){¾ò·ï};) do''};
&size(16)...
&size(16)...
&size(16)...
&size(24){''end''};
&br;
&ref(/materials/warning.png); ''for'' ¤È ''if'' ¤òÁȤ߹ç...
&ref(/materials/notes.png); ¤³¤Î ''while'' Ì¿Îá¤ò»È¤Ã¤Æ¡¤...
&br;
¤³¤Î¾ì¹ç¤Ï¡¤Î㤨¤Ð¼¡¤Î¤è¤¦¤Ê¥×¥í¥°¥é¥à¤Ë¤Ê¤ë¤À¤í¤¦¡¥
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# Ķ¤¨¤ë¤«¤É¤¦¤«Ä´¤Ù¤ë¿ô¤Ïµ¯Æ°»þ¤Ë¤â¤é¤¦
n = ARGV[0].to_i
# ¹ç·×¤Î½é´üÃͤϤâ¤Á¤í¤ó¥¼¥í¡¥
sum = 0
# ¤·¤Æ¤¤¤¯¿ô¡¥ ºÇ½é¤Ï 1 ¤«¤é¤À¤¬¡¤¤³¤ÎÃʳ¬¤Ç¤Î sum ¤ËÂÐ...
# ¥¼¥í¤Ë¤·¤Æ¤ª¤¯¤Î¤¬¹çÍýŪ¡¥
i = 0
# n ¤òĶ¤¨¤Æ¤Ê¤¤¤È while ¤ÎÃæ¿È¤¬¼Â¹Ô¤µ¤ì¡¤ºÆ¤Ó n ¤òĶ¤¨...
while (sum <= n) do
print("i = ", i, ", sum = ", sum, " <= ", n, "\n")
# Àè¤Ë½ÐÎÏ. ¤³¤ÎÃʳ¬¤Ê¤é³Î¼Â¤Ë sum <= n.
# while ¤Ç¤Ï¡¤·ë²Ì¤ËÂФ¹¤ëȽÃǤä½ÐÎϤϾò·ï¥Á¥§¥Ã¥¯¤Î¤¹...
i += 1 # i ¤ò 1Áý¤ä¤¹¡¥
sum += i # i ¤À¤±¹ç·×¤¹¤ë¡¥
end
# i ¤òÁý¤ä¤·¤Æ¤«¤é i ¤ò sum ¤Ë¤¹¤³¤È!
# sum ¤Ë¤·¤Æ¤«¤é i ¤òÁý¤ä¤¹¤È¡¤ºÇ¸å¤Ë¤Ä¤¸¤Ä¤Þ¤¬¹ç¤ï¤Ê¤¯...
# ¤è¤¯Ê¬¤«¤é¤Ê¤¤¿Í¤Ï¡¤sum ¤Ë¤·¤Æ¤«¤é i ¤òÁý¤ä¤¹¤è¤¦¤Ë¤·...
# ºÇ¸å¤Ë·ë²Ì¤ò½ÐÎÏ¡¥
print("i = ", i, ", sum = ", sum, " > ", n, "\n")
}}
¤³¤ì¤ò
ruby -w ./over.rb 100
¤Ê¤É¤È¤·¤Æµ¯Æ°¤¹¤ë¤È¡¤
> i = 0, sum = 0 <= 100
> i = 1, sum = 1 <= 100
> i = 2, sum = 3 <= 100
> i = 3, sum = 6 <= 100
> i = 4, sum = 10 <= 100
> i = 5, sum = 15 <= 100
> i = 6, sum = 21 <= 100
> i = 7, sum = 28 <= 100
> i = 8, sum = 36 <= 100
> i = 9, sum = 45 <= 100
> i = 10, sum = 55 <= 100
> i = 11, sum = 66 <= 100
> i = 12, sum = 78 <= 100
> i = 13, sum = 91 <= 100
> i = 14, sum = 105 > 100
¤È¤¤¤¦¤è¤¦¤Ë·ë²Ì¤¬ÆÀ¤é¤ì¤ë¡¥¤É¤¦¤À¤í¤¦¤«¡¥¼«Ê¬¤Ç¤Ç¤¤¿¤À...
&br;
&ref(/materials/warning.png); ´ª¤ÎÎɤ¤¿Í¤Ï¤â¤¦µ¤¤Å¤¤¤Æ¤¤...
CENTER:&size(24){''while = æ½ÐȽÄê¤Ä¤Ìµ¸Â¥ë¡¼¥×¤Î°ì¼ï''};
¤Ç¤¢¤ë¡¥
&br;
** Fizz Buzz ¤ËÄ©Àï [#w6428d88]
Fizz Buzz ¤È¤Ï¸ÀÍÕÍ·¤Ó¤Î°ì¼ï¤Ç¡¤1, 2,... ¤È½ç¤Ë¿ô»ú¤ò½Ò¤Ù...
- 3 ¤Ç³ä¤êÀÚ¤ì¤ë¤È¤¤Ï¤½¤Î¿ô»ú¤ÎÂå¤ï¤ê¤Ë ''Fizz'' ¤È¸À¤¦
- 5 ¤Ç³ä¤êÀÚ¤ì¤ë¤È¤¤Ï¤½¤Î¿ô»ú¤ÎÂå¤ï¤ê¤Ë ''Buzz'' ¤È¸À¤¦
- ¤¿¤À¤·¡¤3 ¤Ç¤â 5 ¤Ç¤â³ä¤êÀÚ¤ì¤ë¤È¤¤ÏÆÃÊ̤ˤ½¤Î¿ô»ú¤ÎÂå...
¤È¤¤¤¦¤â¤Î¤Ç¤¢¤ë¡¥¤½¤³¤Ç¡¤¤³¤ì¤ò°Ê²¼¤Î¤è¤¦¤Ë¥×¥í¥°¥é¥à¤·...
- ¥×¥í¥°¥é¥àµ¯Æ°»þ¤Ë¤¢¤ëÄøÅÙÂ礤ʿô ''n'' (100 ¤°¤é¤¤?) ...
- 1,2,... ¤È¿ô¤ò¾å¤Î¥ë¡¼¥ë¤Ç½ÐÎϤ·¤Æ¤¤¤Ã¤Æ¡¤''Fizz'', ''B...
¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð
ruby -w fb.rb 10
¤È¤·¤Æ 10¸Ä¤Î¡ÖÂå¤ï¤ê¡×¤¬½Ð¤Æ¤¯¤ë¤Þ¤Ç¤ò½ÐÎϤµ¤»¤ë¤È¡¤
> 1
> 2
> Fizz
> 4
> Buzz
> Fizz
> 7
> 8
> Fizz
> Buzz
> 11
> Fizz
> 13
> 14
> Fizz Buzz
> 16
> 17
> Fizz
> 19
> Buzz
> Fizz
¤È¤Ê¤ë¡¥¤µ¤Æ¡¤¤ß¤Ê¤µ¤ó¤Ï¤¦¤Þ¤¯¤Ç¤¤ë¤À¤í¤¦¤«¡¥
&ref(/materials/warning.png); ¤½¤ì¤Ã¤Ý¤¤Æ°ºî¤¬ÆÀ¤é¤ì¤Æ¤â...
&br;
** (¾åµé¼Ô¸þ¤±) 3¤ÎÇÜ¿ô¤È3¤Î¤Ä¤¯¿ô¤Î¤È¤¤À¤±¥¢¥Û [#y02db8...
¡Ö3¤ÎÇÜ¿ô¤È3¤Î¤Ä¤¯¿ô¤Î¤È¤¤À¤±¥¢¥Û¤Ë¤Ê¤ë¡×¤È¤·¤Æ¾å¤ÈƱ¤¸...
¤¿¤À¤·¡¤¡Ö3¤Î¤Ä¤¯¡×¤È¤¤¤¦¾ò·ï¤Ëʸ»úÎó½èÍý¤¬É¬Íפǡ¤¤³¤ì¤Ï...
&br;
** Collatz ¤ÎͽÁÛ¤òÄ´¤Ù¤Æ¤ß¤è¤¦ [#a4adf91b]
''Collatz ¤ÎͽÁÛ'' ¤È¤¤¤¦Í½ÁÛ¤¬¤¢¤ë¡¥¤³¤ì¤ò ''while'' ¤ò...
¤Þ¤º¤³¤ÎͽÁۤˤĤ¤¤Æµ½Ò¤·¤è¤¦¡¥¤³¤ÎͽÁۤȤϡ¤ÀµÀ°¿ô ''n'...
- n ¤¬¶ö¿ô¤Î¾ì¹ç: f(n) = n / 2
- n ¤¬´ñ¿ô¤Î¾ì¹ç: f(n) = (3 * n) + 1
¤È¤¹¤ë¤È¡¤¡Ö¤¤¤«¤Ê¤ëÀµÀ°¿ô¤ËÂФ·¤Æ¤â¤³¤Î ''f'' ¤ò·«¤êÊÖ¤·...
&ref(/materials/notes.png); ¤³¤ÎͽÁÛ¤¬Í¿¤¨¤é¤ì¤¿¿ô¤Ë¤Ä¤¤...
¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð
ruby -w collatz.rb 100
¤È¤·¤ÆºÇ½é¤Ë "100" ¤«¤é¥¹¥¿¡¼¥È¤·¤¿¾ì¹ç¤ò¥Á¥§¥Ã¥¯¤µ¤»¤ë¤È
> 100 -> 50 -> 25 -> 76 -> 38 -> 19 -> 58 -> 29 -> 88 ->
> 44 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40
> -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 1.
¤È¤¤¤¦¤è¤¦¤Ê½ÐÎϤò½Ð¤¹¤è¤¦¤Ë¤·¤è¤¦¡¥
&ref(/materials/warning.png); ¡Ö''f'' ¤Î·ë²Ì¤¬ 1 ¤Ç¤Ê¤¤´Ö...
&br;
* º£Æü¤ÎÁí»Å¾å¤² [#be9b628a]
¾å¤Î Collatz ¤ÎͽÁÛ¤ò°Ê²¼¤Î¤è¤¦¤ËÄ´¤Ù¤ë¥×¥í¥°¥é¥à¤ò½ñ¤¤¤Æ...
¾ò·ï¤Ï°Ê²¼¤ÎÄ̤ê¤Ç¤¢¤ë¡¥
- ÀµÀ°¿ô ''k'' ¤ËÂФ·¤Æ¡¤Collatz ¤Î´Ø¿ô ''f'' ¤ò²¿²óŬÍÑ...
- ¥×¥í¥°¥é¥àµ¯Æ°»þ¤Ë¤¢¤ëÄøÅÙÂ礤ʿô ''n'' (100¤°¤é¤¤) ¤¬...
- 1 ¤«¤é»Ï¤á¤Æ¡¤''n'' ¤Þ¤Ç ''num_col'' ¤Î·ë²Ì¤ò½ÐÎϤ¹¤ë¡¥
&ref(/materials/warning.png); ''num_col(1)'' ¤¬ 3 ¤Ë¤Ê¤Ã...
¶ñÂÎŪ¤Ë¤Ï¡¤Î㤨¤Ð
ruby -w col_num.rb 30
¤È¤·¤Æ 30 ¤Þ¤Ç¤òÄ´¤Ù¤µ¤»¤ë¤È
> 1, 0
> 2, 1
> 3, 7
> 4, 2
> 5, 5
> 6, 8
> 7, 16
> 8, 3
> 9, 19
> 10, 6
> 11, 14
> 12, 9
> 13, 9
> 14, 17
> 15, 17
> 16, 4
> 17, 12
> 18, 20
> 19, 20
> 20, 7
> 21, 7
> 22, 15
> 23, 15
> 24, 10
> 25, 23
> 26, 10
> 27, 111
> 28, 18
> 29, 18
> 30, 18
¤È¤¤¤¦¤è¤¦¤Ê½ÐÎϤò½Ð¤¹¤è¤¦¤Ë¤È¤¤¤¦¤³¤È¤Ç¤¢¤ë¡¥
¤½¤·¤Æ¡¤¤³¤Î½ÐÎϥǡ¼¥¿¤ò¥Õ¥¡¥¤¥ë¤ËÊݸ¤·¤Æ¤ª¤¤¤ÆŬÅö¤Ê¥Ä...
&ref(./collatz.png,80%);
¤È¤¤¤¦¤è¤¦¤Ê¤â¤Î¤òºî¤í¤¦¤È¤¤¤¦¤³¤È¤Ë¤Ê¤ë¡¥
¤³¤ÎÎã¤Ç¤Ï 30¤Þ¤Ç¤À¤¬¡¤¤³¤ì¤ò 100 ¤°¤é¤¤¤ÎÃͤǼ¹Ԥ·¤Æ¡¤...
&br;
* ¥ì¥Ý¡¼¥È [#z0c9dd1e]
ËÜÆü¼õ¤±¤¿¹ÖµÁ¤ª¤è¤Ó¹Ô¤Ã¤¿¼Â½¬¤Ë¤Ä¤¤¤Æ¡¤´Êñ¤Ë¤Þ¤È¤á¤¿Êó...
¤Þ¤¿¡¤Áí»Å¾å¤²¤ÎÉôʬ¤Ç¼«Ê¬¤Ç½ñ¤¤¤¿¥×¥í¥°¥é¥à¤òÊó¹ð¤»¤è.
¤â¤Á¤í¤ó³Æ¼«¤Î
+ ½ê°(³ØÉô¡¤³Ø²Ê)
+ ³ØÀÒÈÖ¹æ
+ ³Øǯ
+ »á̾
+ Æü»þ
+ ´Î¿´¤Î¥ì¥Ý¡¼¥ÈÆâÍÆ(ÆÀ¤¿Ãθ«¡¤ºî¶È¤Ë¤Ä¤¤¤Æµ¤¤Å¤¤¤¿¤³¤ÈÅù...
¤ò½ñ¤¯¤Î¤ò˺¤ì¤Ê¤¤¤è¤¦¤Ë.
* about Icons, ClipArts [#ubfbbb67]
Some icons in this page are downloadable at [[ICONFINDER:...
The "note" icon &ref(/materials/notes.png); designed by [...
the "warning" icon &ref(/materials/warning.png); designed...
and the "triangle" icon &ref(/materials/JNorth_arrow-righ...
Some clip arts used in this page are downloadable at [[Op...
We deeply appreciate their superb works. With licence, th...
// ¨¬¨¨®¨¯¨°¨±¨²¨³¨´¨µ¨¶
// ¥³¥Þ¥ó¥É¥é¥¤¥óÆþÎϤϡֹÔƬ¤ò¥Ö¥é¥ó¥¯¤Ç»Ï¤á¤ë¡×.
// ¥³¥Þ¥ó¥É¥é¥¤¥ó½ÐÎϤϡֹÔƬ¤ò > ¤Ç»Ï¤á¤ë¡×.
// ¼Â½¬¥¢¥¤¥³¥ó
// &ref(/materials/notes.png);
// Ãí°Õ¥¢¥¤¥³¥ó
// &ref(/materials/warning.png);
// Link ¥¢¥¤¥³¥ó
// &ref(/materials/JNorth_arrow-right-sm.png);
// Âçʸ»ú¤Ç¤Î¶¯Ä´
// CENTER:&size(24){''¤Û¤²¤Û¤²''};
// programu source ɽµ
// #highlighter(language=ruby,number=on,cache=on){{}}
¥Ú¡¼¥¸Ì¾: