一个无聊男人的疯狂《数据结构与算法分析-C++描述》学习笔记 用C++/lua/python/bash的四重实现（3） 最大子序列和问题

一个无聊男人的疯狂《数据结构与算法分析-C++描述》学习笔记 用C++/lua/python/bash的四重实现（3）
最大子序列和问题

write by 九天雁翎(JTianLing) --
blog.csdn.net/vagrxie



<<Data Structures and Algorithm Analysis in C++>>

--《数据结构与算法分析c++描述》 Mark Allen Weiss著 人民邮电大学出版 中文版第39-43面，图2-5，2-6,2-7,2-8最大子序列和问题的解

总算有点技术含量了，呵呵，虽然说重复实现一下代码不难（不就是相当于翻译嘛），但是算法4为什么是正确的需要好好理解一下。

以下为实现部分:

CPP:

1
//

2 //
Maximum contiguous subsequence sum algorithm 1 - 4, worst to best

3 //
From <<Data Structures and Algorithm Analysis in C++>> by Mark
Allen Weiss

4 //

5 //

6 #include
<stdio.h>

7 #include
<stdlib.h>

8 #include
<vector>

9 using namespace std;

10

11

12

13 int maxSubSum1(
const vector<int> &a)

14 {

15 int maxSum = 0;

16

17 for(int i=0; i<(int)a.size();
++i)

18 for(int j=i;
j<(int)a.size(); ++j)

19 {

20 int thisSum = 0;

21

22 for(int k=i;
k<=j; ++k)

23 thisSum
+= a[k];

24

25 if(thisSum > maxSum)

26 maxSum
= thisSum;

27 }

28 return maxSum;

29 }

30

31 int maxSubSum2(
const vector<int> &a)

32 {

33 int maxSum = 0;

34

35 for(int i=0; i<(int)a.size();
++i)

36 {

37 int thisSum = 0;

38 for(int j=i;
j<(int)a.size(); ++j)

39 {

40 thisSum
+= a[j];

41

42 if( thisSum > maxSum)

43 maxSum
= thisSum;

44 }

45 }

46 return maxSum;

47 }

48

49 int max3(int a, int b,
int c)

50 {

51 return ((a < b)?((b < c)?c:b):((a
< c)?c:a));

52 }

53

54

55 int maxSumRec(
const vector<int> &a, int left,
int right)

56 {

57 if(left == right)

58 if( a[left] > 0)

59 return a[left];

60 else

61 return 0;

62

63 int center = (left + right) / 2;

64 int maxLeftSum = maxSumRec(a, left,
center);

65 int maxRightSum = maxSumRec(a, center + 1, right);

66

67 int maxLeftBorderSum = 0;

68 int leftBorderSum = 0;

69

70 for(int i=center;
i >=left; --i)

71 {

72 leftBorderSum
+= a[i];

73 if(leftBorderSum > maxLeftBorderSum)

74 maxLeftBorderSum
= leftBorderSum;

75 }

76

77 int maxRightBorderSum = 0,rightBorderSum = 0;

78 for(int j
= center + 1; j <= right; ++j)

79 {

80 rightBorderSum
+= a[j];

81 if(rightBorderSum > maxRightBorderSum)

82 maxRightBorderSum
= rightBorderSum;

83 }

84

85

86 return max3(maxLeftSum, maxRightSum,
maxLeftBorderSum + maxRightBorderSum);

87 }

88

89 int maxSubSum3(const vector<int> &a)

90 {

91 return maxSumRec(a, 0, a.size() - 1);

92 }

93

94 int maxSubSum4(
const vector<int> &a)

95 {

96 int maxSum = 0,
thisSum = 0;

97

98 for( int j
= 0; j< (int)a.size();
++j)

99 {

100 thisSum
+= a[j];

101

102 if(thisSum > maxSum)

103 maxSum
= thisSum;

104 else if(thisSum
< 0)

105 thisSum

= 0;

106 }

107

108 return maxSum;

109 }

110

111

112

113 int main(int argc, char*
argv[])

114 {

115 // for easy

116 int a[] = { -2,
11, -4, 13, -5, -2};

117 vector<int> lvec(a, a + sizeof(a)/sizeof(int));

118

119 printf("maxSubSum1(lvec)):%d/n",maxSubSum1(lvec));

120 printf("maxSubSum2(lvec)):%d/n",maxSubSum2(lvec));

121 printf("maxSubSum3(lvec)):%d/n",maxSubSum3(lvec));

122 printf("maxSubSum4(lvec)):%d/n",maxSubSum4(lvec));

123

124

125 exit(0);

126 }

127

LUA:

1
#!/usr/bin/env
lua

2

3

4 function maxSubSum1(a)

5 assert(type(a) == "table", "Argument
a must be a number array.")

6

7 local maxSum = 0

8

9 for i=1,#a
do

10 for j=i,#a do

11 local thisSum = 0

12 for k=i,j do

13 thisSum
= thisSum + a[k]

14 end

15

16 if thisSum > maxSum then

17 maxSum
= thisSum

18 end

19 end

20 end

21

22 return maxSum

23 end

24

25 function maxSubSum2(a)

26 assert(type(a) == "table", "Argument
a must be a number array.")

27

28 local maxSum = 0

29

30 for i=1,#a
do

31 local thisSum = 0

32

33 for j=i,#a do

34 thisSum
= thisSum + a[j]

35

36 if(thisSum > maxSum) then

37 maxSum
= thisSum

38 end

39 end

40 end

41 return maxSum

42 end

43

44 function max3(n1,
n2, n3)

45 return (n1 > n2 and ((n1 > n3) and n1 or n3)
or ((n2 > n3) and n2 or n3))

46 end

47

48 -- require
math

49

50 function maxSumRec(a,
left, right)

51 assert(type(a) == "table", "Argument
a must be a number array.")

52 assert(type(left) == "number" and type(right) == "number",

53 "Argument left&right must be number
arrays.")

54

55 if left == right then

56 if a[left] > 0 then

57 return a[left]

58 else

59 return 0

60 end

61 end

62

63 local center = math.floor((left
+ right) / 2)

64 local maxLeftSum = maxSumRec(a, left,
center)

65 local maxRightSum = maxSumRec(a, center+1, right)

66

67 local maxLeftBorderSum = 0

68 local leftBorderSum = 0

69 for i=center,left,-1 do

70 leftBorderSum
= leftBorderSum + a[i]

71 if leftBorderSum > maxLeftBorderSum then

72 maxLeftBorderSum
= leftBorderSum

73 end

74 i
= i - 1

75 end

76

77 local maxRightBorderSum = 0

78 local rightBorderSum = 0

79 for j=center+1,right
do

80 rightBorderSum
= rightBorderSum + a[j]

81 if rightBorderSum > maxRightBorderSum then

82 maxRightBorderSum
= rightBorderSum

83 end

84 end

85

86 return max3(maxLeftSum, maxRightSum,
maxLeftBorderSum + maxRightBorderSum)

87 end

88

89 function maxSubSum3(a)

90 assert(type(a) == "table", "Argument
a must be a number array.")

91

92 return maxSumRec(a, 1, 6)

93

94 end

95

96 function maxSubSum4(a)

97 assert(type(a) == "table", "Argument
a must be a number array.")

98

99 local maxSum = 0

100 local thisSum = 0

101

102 for i=1,#a
do

103 thisSum
= thisSum + a[i]

104

105 if thisSum > maxSum then

106 maxSum
= thisSum

107 elseif thisSum < 0 then

108 thisSum
= 0

109 end

110

111 end

112

113 return maxSum

114

115 end

116

117 -- Test Code

118

119 t = {-2, 11, -4, 13, -5, -2 }

120

121 print("maxSubSum1(t):" .. maxSubSum1(t))

122 print("maxSubSum2(t):" .. maxSubSum2(t))

123 print("maxSubSum3(t):" .. maxSubSum3(t))

124 print("maxSubSum4(t):" .. maxSubSum4(t))

125

126

127

PYTHON:

1
#!/usr/bin/env
python

2

3 # How Short
and Clean it is I shocked as a CPP Programmer

4 def maxSubSum1(a):

5 maxSum = 0

6

7 for i in a:

8 for j in a[i:]:

9 thisSum
= 0

10

11 for k in a[i:j]:

12 thisSum
+= k

13

14 if thisSum > maxSum:

15 maxSum
= thisSum

16

17 return maxSum

18

19 def maxSubSum2(a):

20 maxSum = 0

21

22 for i in a:

23 thisSum
= 0

24 for j in a[i:]:

25 thisSum
+= j

26

27 if thisSum > maxSum:

28 maxSum
= thisSum

29

30 return maxSum

31

32

33 def max3(n1,
n2, n3):

34 return ((n1 if n1
> n3 else n3) if n1 > n2 else (n2
if n2 > n3 else n3))

35

36 def maxSumRec(a,
left, right):

37 if left == right:

38 if a[left] > 0:

39 return a[left]

40 else:

41 return 0

42

43 center = (left +
right)//2

44 maxLeftSum =
maxSumRec(a, left, center)

45 maxRightSum =
maxSumRec(a, center+1, right)

46

47 maxLeftBorderSum
= 0

48 leftBorderSum = 0

49 for i in a[center:left:-1]:

50 leftBorderSum
+= i

51 if leftBorderSum > maxLeftBorderSum:

52 maxLeftBorderSum
= leftBorderSum

53

54 maxRightBorderSum
= 0

55 rightBorderSum =
0

56 for i in a[center+1:right]:

57 rightBorderSum
+= i

58 if rightBorderSum > maxRightBorderSum:

59 maxRightBorderSum
= rightBorderSum

60

61 return max3(maxLeftSum,
maxRightBorderSum, maxLeftBorderSum + maxRightBorderSum)

62

63 def maxSubSum3(a):

64 return maxSumRec(a, 0,
len(a)-1 )

65

66 def maxSubSum4(a):

67 maxSum = 0

68 thisSum = 0

69

70 for i in a:

71 thisSum
+= i

72

73 if thisSum > maxSum:

74 maxSum
= thisSum

75 elif thisSum < 0:

76 thisSum
= 0

77

78 return maxSum

79

80 def test():

81 t = (-2, 11, -4,
13, -5, -2)

82

83 print "maxSubSum1:%d" %
maxSubSum1(t)

84 print "maxSubSum2:%d" %
maxSubSum2(t)

85 print "maxSubSum3:%d" %
maxSubSum3(t)

86 print "maxSubSum4:%d" %
maxSubSum4(t)

87

88 if __name__ == '__main__':

89 test()

BASH:

1 #!/usr/bin/env bash

2 绕了我吧。。。。。特别是算法二。。复杂的递归用bash来写就是自虐。Bash似乎本来就不是用来描述算法用的，呵呵，以后没有什么事一般就不把bash搬出来了。







write by 九天雁翎(JTianLing) -- blog.csdn.net/vagrxie