1.59M

Category:

informatics

算法设计与分

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January 26, 2021

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44.

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50.

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56.

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– 5. Ž{L«µ–è
Algorithm 1 Power algorithm
Input: n ≥ 0 {// Ñ\˜‡Œu0
Output: y = xn
1: y ← 1
2: X ← x
3: N ← n
4: while N 6= 0 do
5:
if N is even then
6:
X ←X ×X
7:
N ← N/2
8:
else {N is odd}
9:
y ←y×X
10:
N ←N −1
11:
end if
12: end while
ê}

57.

Y
擌
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– 5. Ž{L«µ–è
Algorithm 2 Power algorithm
Input: n ≥ 0 {// Ñ\˜‡Œu0
Output: y = xn
1: y ← 1
2: X ← x
3: N ← n
4: while N 6= 0 do
5:
if N is even then
6:
X ←X ×X
7:
N ← N/2
8:
else {N is odd}
9:
y ←y×X
10:
N ←N −1
11:
end if
12: end while
ê}

58.

Y
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– 5. Ž{L«µ–è
Algorithm 3 Power algorithm
Input: n ≥ 0 {// Ñ\˜‡Œu0
Output: y = xn
1: y ← 1
2: X ← x
3: N ← n
4: while N 6= 0 do
5:
if N is even then
6:
X ←X ×X
7:
N ← N/2
8:
else {N is odd}
9:
y ←y×X
10:
N ←N −1
11:
end if
12: end while
ê}

59.

Y
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– 5. Ž{L«µ–è
Algorithm 4 Power algorithm
Input: n ≥ 0 {// Ñ\˜‡Œu0
Output: y = xn
1: y ← 1
2: X ← x
3: N ← n
4: while N 6= 0 do
5:
if N is even then
6:
X ←X ×X
7:
N ← N/2
8:
else {N is odd}
9:
y ←y×X
10:
N ←N −1
11:
end if
12: end while
ê}

60.

Y
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– 5. Ž{L«µ–è
Algorithm 5 Power algorithm
Input: n ≥ 0 {// Ñ\˜‡Œu0
Output: y = xn
1: y ← 1
2: X ← x
3: N ← n
4: while N 6= 0 do
5:
if N is even then
6:
X ←X ×X
7:
N ← N/2
8:
else {N is odd}
9:
y ←y×X
10:
N ←N −1
11:
end if
12: end while
ê}

61.

Y
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ng
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tel
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Y
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ognitive C
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– 5. Ž{L«µ–è
Algorithm 6 Power algorithm
Input: n ≥ 0 {// Ñ\˜‡Œu0
Output: y = xn
1: y ← 1
2: X ← x
3: N ← n
4: while N 6= 0 do
5:
if N is even then
6:
X ←X ×X
7:
N ← N/2
8:
else {N is odd}
9:
y ←y×X
10:
N ←N −1
11:
end if
12: end while
ê}

62.

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ng
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– 5. Ž{L«µ–è
Algorithm 7 Power algorithm
Input: n ≥ 0 {// Ñ\˜‡Œu0
Output: y = xn
1: y ← 1
2: X ← x
3: N ← n
4: while N 6= 0 do
5:
if N is even then
6:
X ←X ×X
7:
N ← N/2
8:
else {N is odd}
9:
y ←y×X
10:
N ←N −1
11:
end if
12: end while
ê}

63.

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tel
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Y
Y
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OŽÅŽ{¦)¯K Ú½
– 5. Ž{L«µ–è `":
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OŽÅŽ{¦)¯K Ú½
– 7. §SNÁ
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OŽÅŽ{¦)¯K Ú½
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Ž{©Û¶
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5‰“è¶
éX‡"
ÿÁ(J¶
¦^•H"

78.

79.

80.

81.

82.

83.

84.

Y
敧
擌
䕏嚎
摿
呀
sted Artificial In
tel
Tru
lig
e
α COT A I
Y
e
nc
A
ng
Y
Y
Y 䞌怦吼䋳撜兕
Ž{ ½Â
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
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éX‡"
Ž{Ò´é)û8I¯K
•{ÚÚ½9Ù£ã"

85.

Y
敧
擌
䕏嚎
摿
呀
sted Artificial In
tel
Tru
lig
e
α COT A I
Y
e
nc
A
ng
Y
Y
Y 䞌怦吼䋳撜兕
Ž{ ‡ƒ
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
Ž{döŠ!››( !êâ( n‡ƒ|¤§
Ù¥öŠÌ‡kµ
Žâ$Žµ\!~!¦!Ø¶
˜‡«~
'X' µŒu!
u! u!Ø u¶
‘ g
Ü6$Žµ†!½!š¶
éX‡"
êâDxµÑ\!ÑÑ!DŠ"

86.

87.

88.

89.

90.

91.

Y
敧
擌
䕏嚎
摿
呀
sted Artificial In
tel
Tru
lig
e
α COT A I
Y
e
nc
A
ng
Y
Y
Y 䞌怦吼䋳撜兕
Ž{ /
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
Ž{´OŽÅÆ‰¥•äk•{Ø5Ÿ Ø%Vg§
• ™•OŽÅÆ‰ (µ"

92.

Y
敧
擌
䕏嚎
摿
呀
sted Artificial In
tel
Tru
lig
e
α COT A I
Y
e
nc
A
ng
Y
Y
Y 䞌怦吼䋳撜兕
Ž{ A
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
Ì‡kµ
¯K¦)
Ñ\¶
Ž{Ä:
ÑÑ¶
O•{
˜‡«~
k¡5¶
‘ g
(½5¶
éX‡"
Œ15"

93.

94.

95.

96.

97.

Y
敧
擌
䕏嚎
摿
呀
sted Artificial In
tel
Tru
lig
e
α COT A I
Y
e
nc
•{
A
ng
Y
Y
Y 䞌怦吼䋳撜兕
Ž{ O Ä
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
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éX‡"
Ì‡kµ
( z•{¶
¡•é–•{¶
Zy{"

98.

99.

100.

Y
擌
䕏嚎
摿
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Y
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Ž{ O Ä •{
– 1. ( z•{
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
• gŽ´gº•e!ÅÚ¦°§¦¯K©)†õU
z"
¹
gº•eµòE,…Œ
K '…Ú-:¶
¯K¦)
Ž{Ä:
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éX‡"
¯K§éÑ¯
ÅÚ¦°µòE,¯K²eZÚ°z?n§
^/n«Ä ( 09Ä öŠ £ãŽ{"
O•{
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5µ
ÎÜg‘S.¶
g( ˜ß¶
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¬
[z

101.

102.

103.

104.

105.

106.

107.

Y
擌
䕏嚎
摿
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Y
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
Ž{ O Ä •{
– 2. ¡•é–•{
Ì‡Ú½µ
3‰½ Ä– gþ£OaÚé–¶
¹
£Où é–Úa
ŠÂ¶
¯K¦)
£OaÚé–ƒm
'X¶
Ž{Ä:
¢yaÚé–"
8
O•{
˜‡«~
` 5µ
‘ g
Ä–z
éX‡"
µC5
õ 5
U«5
-^5

108.

109.

110.

111.

112.

113.

114.

115.

116.

117.

Y
擌
䕏嚎
摿
呀
Y
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
Ž{ O Ä
– 3. Zy{
•{
Ì‡Ú½µ
O{ü‡N¶
‰Dƒ{üá5ÚpÄ5K¶
{ü‡NpÄ¥&¢¯K)§¿‰Ñ·AŠ"

118.

Y
擌
䕏嚎
摿
呀
Y
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
Ž{ O Ä
– 3. Zy{
•{
Ì‡Ú½µ
O{ü‡N¶
‰Dƒ{üá5ÚpÄ5K¶
{ü‡NpÄ¥&¢¯K)§¿‰Ñ·AŠ"
¹
¯K¦)
Ž{Ä:
O•{
Zy5
{ü‡N•U¢y{ü ?Ö§
õ‡‡N%U ¤E, ?Ö"
˜‡«~
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` 5µ
éX‡"
¢y{ü¶
¥%z"
[4]

119.

120.

121.

122.

123.

124.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
˜‡¯K¦)
Ž{«~
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
¦ü‡
ê •Œú ê
¯K©Ûµü‡
êÆ .µa, b > 0
†b/c pŸ¶
ê§•Œú ê¶
ê§¦c§cU
Øa, b§…a/c
Ž{ Oµn)<ó¦)üê •Œú êL§§ÏL
/qÞ}Á0Œ±/ÁÑ0a, bk= ú ê§¿òù
ú ê/\¦0§ÒU
•Œú ê;
äN Oµ
^forÌ‚qÞŒU Ïê§¿^Cþ\¦¦Ñ Ïê¶
5¿ Ïê23/4§80ü‡êâ¥Ñyüg§¤±§ÿ
Á,Ïê´Ä¤‰êâ Ïêž§AT^Ì‚Šé Ø
´^‡Šé"

125.

126.

127.

128.

129.

130.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
•Œú ê¦) Ž{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 8 greatest common divisor
Input: int a, b
Output: c
1: c ← 1
2: for (i = 2; i <= a and i <= b; i + +) do
3:
while a mod i = 0 and b mod i = 0 do
4:
c←c∗i
5:
a ← a/i
6:
b ← b/i
7:
end while
8: end for
9: return c

131.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
•Œú ê¦) Ž{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 9 greatest common divisor
Input: int a, b
Output: c
1: c ← 1
2: for (i = 2; i <= a and i <= b; i + +) do
3:
while a mod i = 0 and b mod i = 0 do
4:
c←c∗i
5:
a ← a/i
6:
b ← b/i
7:
end while
8: end for
9: return c

132.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
•Œú ê¦) Ž{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 10 greatest common divisor
Input: int a, b
Output: c
1: c ← 1
2: for (i = 2; i <= a and i <= b; i + +) do
3:
while a mod i = 0 and b mod i = 0 do
4:
c←c∗i
5:
a ← a/i
6:
b ← b/i
7:
end while
8: end for
9: return c

133.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
•Œú ê¦) Ž{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 11 greatest common divisor
Input: int a, b
Output: c
1: c ← 1
2: for (i = 2; i <= a and i <= b; i + +) do
3:
while a mod i = 0 and b mod i = 0 do
4:
c←c∗i
5:
a ← a/i
6:
b ← b/i
7:
end while
8: end for
9: return c

134.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
•Œú ê¦) Ž{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 12 greatest common divisor
Input: int a, b
Output: c
1: c ← 1
2: for (i = 2; i <= a and i <= b; i + +) do
3:
while a mod i = 0 and b mod i = 0 do
4:
c←c∗i
5:
a ← a/i
6:
b ← b/i
7:
end while
8: end for
9: return c

135.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
•Œú ê¦) Ž{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 13 greatest common divisor
Input: int a, b
Output: c
1: c ← 1
2: for (i = 2; i <= a and i <= b; i + +) do
3:
while a mod i = 0 and b mod i = 0 do
4:
c←c∗i
5:
a ← a/i
6:
b ← b/i
7:
end while
8: end for
9: return c

136.

Y
擌
䕏嚎
摿
呀
Y
Euclid•Œú
ê½n
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
½nµØ”˜„5§b a > b > 0,
Kkgcd(a, b) = gcd(b, a mod b)"
y²µ
∵ a > b > 0, ∴ a = kb + r, ùpk, r
ê§Kr =
a mod b"
b d´a, b ˜‡ú ê§Kkd|a, d|b§ r = a − kb§
kd|r§Ïdd´(b, a mod b) ú ê"
Ó /§b d´(b, a mod b) ú ê§Kd|b, d|r§d
ua = kb + r§Ïdd•´(a, b) ú ê"
Ïd(a, b)Ú((b, a mod b) ú ê´˜
§Ù•Œú
ê•7,ƒ § y"

137.

Y
擌
䕏嚎
摿
呀
Y
EuclidŽ{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
Algorithm 14 Euclid algorithm for greatest common divisor
(Î=ƒØ{)
Input: int a, b
Output: a
1: while b ! = 0 do
2:
r←b
3:
b ← a%b
4:
a←r
5: end while
6: return a

138.

Y
擌
䕏嚎
摿
呀
Y
EuclidŽ{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
Algorithm 15 Euclid algorithm for greatest common divisor
(Î=ƒØ{)
Input: int a, b
Output: a
1: while b ! = 0 do
2:
r←b
3:
b ← a%b
4:
a←r
5: end while
6: return a

139.

Y
擌
䕏嚎
摿
呀
Y
EuclidŽ{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
Algorithm 16 Euclid algorithm for greatest common divisor
(Î=ƒØ{)
Input: int a, b
Output: a
1: while b ! = 0 do
2:
r←b
3:
b ← a%b
4:
a←r
5: end while
6: return a

140.

Y
擌
䕏嚎
摿
呀
Y
EuclidŽ{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
Algorithm 17 Euclid algorithm for greatest common divisor
(Î=ƒØ{)
Input: int a, b
Output: a
1: while b ! = 0 do
2:
r←b
3:
b ← a%b
4:
a←r
5: end while
6: return a

141.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
Stein•Œú ê n
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
gcd(a, a) = a¶
gcd(ka, kb) = k · gcd(a, b)§•Ò´•Œú ê$ŽÚ ¦
$ŽŒ± †§AÏ § k = 2ž§`²ü‡óê •Œú
ê7,U 2 Ø"
k þã5ÆÒŒ±‰ÑSteinŽ{Xeµ
˜a1 = a, b1 = bÚc1 = 1¶
XJai Úbi Ñ´óê, Kai+1 = an /2, bn+1 = bn /2, cn+1 =
2cn (5¿§¦2•‡r ê†£˜ =Œ§Ø2•‡r êm
£˜ =Œ)¶
XJai ´óê§bi Ø´óê§Kai+1 = ai /2, bi+1 = bi ,
ci+1 = ci (w,¤á§Ï•2Ø´Ûê
ê)¶
XJbi ´óê§ai Ø´óê§Kbi+1 = bi /2, ai+1 = ai ,
ci+1 = ci (w,¤á§Ï•2Ø´Ûê
ê)¶
XJai Úbi ÑØ´óê§Kai+1 = |ai −bi |, bi+1 = min(ai , bi ),
ci+1 = ci "
XJa = 0§b´•Œú ê§Ž{(å¶
XJb = 0§a´•Œú ê§Ž{(å¶

142.

143.

144.

145.

146.

147.

148.

149.

150.

151.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
SteinŽ{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 18 Stein algorithm for greatest common divisor
1: int gcd(int a, int b) {
2: if a == 0 then
3:
return b;
4: end if
5: if b == 0 then
6:
return a;
7: end if
8: if a%2 == 0 && b%2 == 0 then
9:
return 2gcd(a >> 1, b >> 1);
10: else if a%2 == 0 then
11:
return gcd(a >> 1, b);
12: else if b%2 == 0 then
13:
return gcd(a, b >> 1);
14: else
15:
return gcd(abs(a − b), min(a, b));
16: end if }

152.

Y
擌
䕏嚎
摿
呀
Y
ognitive C
ous C
om
om
pu
on
ti
ut
Ž{ O†©
Û
101ù Ž{
Vã
4öÅ
8
¹
¯K¦)
Ž{Ä:
O•{
˜‡«~
‘ g
éX‡"
SteinŽ{
A
ng
Y 䞌怦吼䋳撜兕
sted Artificial In
tel
Tru
lig
e
敧
Y
α COT A I
Y
e
nc
Algorithm 19 Stein algorithm for greatest common divisor
1: int gcd(int a, int b) {
2: if a == 0 then
3:
return b;
4: end if
5: if b == 0 then
6:
return a;
7: end if
8: if a%2 == 0 && b%2 == 0 then
9:
return 2gcd(a >> 1, b >> 1);
10: else if a%2 == 0 then
11:
return gcd(a >> 1, b);
12: else if b%2 == 0 then
13:
return gcd(a, b >> 1);
14: else
15:
return gcd(abs(a − b), min(a, b));
16: end if }

153.

Y
擌
䕏嚎
摿
呀
Y
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Algorithm 20 Stein algorithm for greatest common divisor
1: int gcd(int a, int b) {
2: if a == 0 then
3:
return b;
4: end if
5: if b == 0 then
6:
return a;
7: end if
8: if a%2 == 0 && b%2 == 0 then
9:
return 2gcd(a >> 1, b >> 1);
10: else if a%2 == 0 then
11:
return gcd(a >> 1, b);
12: else if b%2 == 0 then
13:
return gcd(a, b >> 1);
14: else
15:
return gcd(abs(a − b), min(a, b));
16: end if }

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Algorithm 21 Stein algorithm for greatest common divisor
1: int gcd(int a, int b) {
2: if a == 0 then
3:
return b;
4: end if
5: if b == 0 then
6:
return a;
7: end if
8: if a%2 == 0 && b%2 == 0 then
9:
return 2gcd(a >> 1, b >> 1);
10: else if a%2 == 0 then
11:
return gcd(a >> 1, b);
12: else if b%2 == 0 then
13:
return gcd(a, b >> 1);
14: else
15:
return gcd(abs(a − b), min(a, b));
16: end if }

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OŽÅŽ{.
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“Ê.
<aå ƒ•))5g²LÆ yâ.
MOOC, 2017.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford
Stein.
Introduction to Algorithms.
MIT Press, MA, 2009.07.
Joao Fabiano.
Emergence’s Devil Haunts the Moral Enhancer’s Kingdom Come.
Practical Ethics, 2013.

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Email: liu.hongbo@foxmail.com
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