x1+x2+x3+x4=20的非负整数解的Matlab解法

也可以是用Java程序解．谢谢啦！！

第1个回答 2007-07-02

这个matlab程序如何？个人觉着不算太好，需要修改。

clc;clear;
k=0
for x1=1:20
for x2=1:20
for x3=1:20
for x4=1:20
if x1+x2+x3+x4==20
X=[x1,x2,x3,x4]
k=k+1;
end
end
end
end
end
k

结果：
X =

1 1 1 17

X =

1 1 2 16

X =

1 1 3 15

X =

1 1 4 14

X =

1 1 5 13

X =

1 1 6 12

X =

1 1 7 11

X =

1 1 8 10

X =

1 1 9 9

X =

1 1 10 8

X =

1 1 11 7

X =

1 1 12 6

X =

1 1 13 5

X =

1 1 14 4

X =

1 1 15 3

X =

1 1 16 2

X =

1 1 17 1

X =

1 2 1 16

X =

1 2 2 15

X =

1 2 3 14

X =

1 2 4 13

X =

1 2 5 12

X =

1 2 6 11

X =

1 2 7 10

X =

1 2 8 9

X =

1 2 9 8

X =

1 2 10 7

X =

1 2 11 6

X =

1 2 12 5

X =

1 2 13 4

X =

1 2 14 3

X =

1 2 15 2

X =

1 2 16 1

X =

1 3 1 15

X =

1 3 2 14

X =

1 3 3 13

X =

1 3 4 12

X =

1 3 5 11

X =

1 3 6 10

X =

1 3 7 9

X =

1 3 8 8

X =

1 3 9 7

X =

1 3 10 6

X =

1 3 11 5

X =

1 3 12 4

X =

1 3 13 3

X =

1 3 14 2

X =

1 3 15 1

X =

1 4 1 14

X =

1 4 2 13

X =

1 4 3 12

X =

1 4 4 11

X =

1 4 5 10

X =

1 4 6 9

X =

1 4 7 8

X =

1 4 8 7

X =

1 4 9 6

X =

1 4 10 5

X =

1 4 11 4

X =

1 4 12 3

X =

1 4 13 2

X =

1 4 14 1

X =

1 5 1 13

X =

1 5 2 12

X =

1 5 3 11

X =

1 5 4 10

X =

1 5 5 9

X =

1 5 6 8

X =

1 5 7 7

X =

1 5 8 6

X =

1 5 9 5

X =

1 5 10 4

X =

1 5 11 3

X =

1 5 12 2

X =

1 5 13 1

X =

1 6 1 12

X =

1 6 2 11

X =

1 6 3 10

X =

1 6 4 9

X =

1 6 5 8

X =

1 6 6 7

X =

1 6 7 6

X =

1 6 8 5

X =

1 6 9 4

X =

1 6 10 3

X =

1 6 11 2

X =

1 6 12 1

X =

1 7 1 11

X =

1 7 2 10

X =

1 7 3 9

X =

1 7 4 8

X =

1 7 5 7

X =

1 7 6 6

X =

1 7 7 5

X =

1 7 8 4

X =

1 7 9 3

X =

1 7 10 2

X =

1 7 11 1

X =

1 8 1 10

X =

1 8 2 9

X =

1 8 3 8

X =

1 8 4 7

X =

1 8 5 6

X =

1 8 6 5

X =

1 8 7 4

X =

1 8 8 3

X =

1 8 9 2

X =

1 8 10 1

X =

1 9 1 9

X =

1 9 2 8

X =

1 9 3 7

X =

1 9 4 6

X =

1 9 5 5

X =

1 9 6 4

X =

1 9 7 3

X =

1 9 8 2

X =

1 9 9 1

X =

1 10 1 8

X =

1 10 2 7

X =

1 10 3 6

X =

1 10 4 5

X =

1 10 5 4

X =

1 10 6 3

X =

1 10 7 2

X =

1 10 8 1

X =

1 11 1 7

X =

1 11 2 6

X =

1 11 3 5

X =

1 11 4 4

X =

1 11 5 3

X =

1 11 6 2

X =

1 11 7 1

X =

1 12 1 6

X =

1 12 2 5

X =

1 12 3 4

X =

1 12 4 3

X =

1 12 5 2

X =

1 12 6 1

X =

1 13 1 5

X =

1 13 2 4

X =

1 13 3 3

X =

1 13 4 2

X =

1 13 5 1

X =

1 14 1 4

X =

1 14 2 3

X =

1 14 3 2

X =

1 14 4 1

X =

1 15 1 3

X =

1 15 2 2

X =

1 15 3 1

X =

1 16 1 2

X =

1 16 2 1

X =

1 17 1 1

X =

2 1 1 16

X =

2 1 2 15

X =

2 1 3 14

X =

2 1 4 13

X =

2 1 5 12

X =

2 1 6 11

X =

2 1 7 10

X =

2 1 8 9

X =

2 1 9 8

X =

2 1 10 7

X =

2 1 11 6

X =

2 1 12 5

X =

2 1 13 4

X =

2 1 14 3

X =

2 1 15 2

X =

2 1 16 1

X =

2 2 1 15

X =

2 2 2 14

X =

2 2 3 13

X =

2 2 4 12

X =

2 2 5 11

X =

2 2 6 10

X =

2 2 7 9

X =

2 2 8 8

X =

2 2 9 7

X =

2 2 10 6

X =

2 2 11 5

X =

2 2 12 4

X =

2 2 13 3

X =

2 2 14 2

X =

2 2 15 1

X =

2 3 1 14

X =

2 3 2 13

X =

2 3 3 12

X =

2 3 4 11

X =

2 3 5 10

X =

2 3 6 9

X =

2 3 7 8

X =

2 3 8 7

X =

2 3 9 6

X =

2 3 10 5

X =

2 3 11 4

X =

2 3 12 3

X =

2 3 13 2

X =

2 3 14 1

X =

2 4 1 13

X =

2 4 2 12

X =

2 4 3 11

X =

2 4 4 10

X =

2 4 5 9

X =

2 4 6 8

X =

2 4 7 7

X =

2 4 8 6

X =

2 4 9 5

X =

2 4 10 4

X =

2 4 11 3

X =

2 4 12 2

X =

2 4 13 1

X =

2 5 1 12

X =

2 5 2 11

X =

2 5 3 10

X =

2 5 4 9

X =

2 5 5 8

X =

2 5 6 7

X =

2 5 7 6

X =

2 5 8 5

X =

2 5 9 4

X =

2 5 10 3

X =

2 5 11 2

X =

2 5 12 1

X =

2 6 1 11

X =

2 6 2 10

X =

2 6 3 9

X =

2 6 4 8

X =

2 6 5 7

X =

2 6 6 6

X =

2 6 7 5

X =

2 6 8 4

X =

2 6 9 3

X =

2 6 10 2

X =

2 6 11 1

X =

2 7 1 10

X =

2 7 2 9

X =

2 7 3 8

X =

2 7 4 7

X =

2 7 5 6

X =

2 7 6 5

X =

2 7 7 4

X =

2 7 8 3

X =

2 7 9 2

X =

2 7 10 1

X =

2 8 1 9

X =

2 8 2 8

X =

2 8 3 7

X =

2 8 4 6

X =

2 8 5 5

X =

2 8 6 4

X =

2 8 7 3

X =

2 8 8 2

X =

2 8 9 1

X =

2 9 1 8

X =

2 9 2 7

X =

2 9 3 6

X =

2 9 4 5

X =

2 9 5 4

X =

2 9 6 3

X =

2 9 7 2

X =

2 9 8 1

X =

2 10 1 7

X =

2 10 2 6

X =

2 10 3 5

X =

2 10 4 4

X =

2 10 5 3

X =

2 10 6 2

X =

2 10 7 1

X =

2 11 1 6

X =

2 11 2 5

X =

2 11 3 4

X =

2 11 4 3

X =

2 11 5 2

X =

2 11 6 1

X =

2 12 1 5

X =

2 12 2 4

X =

2 12 3 3

X =

2 12 4 2

X =

2 12 5 1

X =

2 13 1 4

X =

2 13 2 3

X =

2 13 3 2

X =

2 13 4 1

X =

2 14 1 3

X =

2 14 2 2

X =

2 14 3 1

X =

2 15 1 2

X =

2 15 2 1

X =

2 16 1 1

X =

3 1 1 15

X =

3 1 2 14

X =

3 1 3 13

X =

3 1 4 12

X =

3 1 5 11

X =

3 1 6 10

X =

3 1 7 9

X =

3 1 8 8

X =

3 1 9 7

X =

3 1 10 6

X =

3 1 11 5

X =

3 1 12 4

X =

3 1 13 3

X =

3 1 14 2

X =

3 1 15 1

X =

3 2 1 14

X =

3 2 2 13

X =

3 2 3 12

X =

3 2 4 11

X =

3 2 5 10

X =

3 2 6 9

X =

3 2 7 8

X =

3 2 8 7

X =

3 2 9 6

X =

3 2 10 5

X =

3 2 11 4

X =

3 2 12 3

X =

3 2 13 2

X =

3 2 14 1

X =

3 3 1 13

X =

3 3 2 12

X =

3 3 3 11

X =

3 3 4 10

X =

3 3 5 9

X =

3 3 6 8

X =

3 3 7 7

X =

3 3 8 6

X =

3 3 9 5

X =

3 3 10 4

X =

3 3 11 3

X =

3 3 12 2

X =

3 3 13 1

X =

3 4 1 12

X =

3 4 2 11

X =

3 4 3 10

X =

3 4 4 9

X =

3 4 5 8

X =

3 4 6 7

X =

3 4 7 6

X =

3 4 8 5

X =

3 4 9 4

X =

3 4 10 3

X =

3 4 11 2

X =

3 4 12 1

X =

3 5 1 11

X =

3 5 2 10

X =

3 5 3 9

X =

3 5 4 8

X =

3 5 5 7

X =

3 5 6 6

X =

3 5 7 5

X =

3 5 8 4

X =

3 5 9 3

X =

3 5 10 2

X =

3 5 11 1

X =

3 6 1 10

X =

3 6 2 9

X =

3 6 3 8

X =

3 6 4 7

X =

3 6 5 6

X =

3 6 6 5

X =

3 6 7 4

X =

3 6 8 3

X =

3 6 9 2

X =

3 6 10 1

X =

3 7 1 9

X =

3 7 2 8

X =

3 7 3 7

X =

3 7 4 6

X =

3 7 5 5

X =

3 7 6 4

X =

3 7 7 3

X =

3 7 8 2

X =

3 7 9 1

X =

3 8 1 8

X =

3 8 2 7

X =

3 8 3 6

X =

3 8 4 5

X =

3 8 5 4

X =

3 8 6 3

X =

3 8 7 2

X =

3 8 8 1

X =

3 9 1 7

X =

3 9 2 6

X =

3 9 3 5

X =

3 9 4 4

X =

3 9 5 3

X =

3 9 6 2

X =

3 9 7 1

X =

3 10 1 6

X =

3 10 2 5

X =

3 10 3 4

X =

3 10 4 3

X =

3 10 5 2

X =

3 10 6 1

X =

3 11 1 5

X =

3 11 2 4

X =

3 11 3 3

X =

3 11 4 2

X =

3 11 5 1

X =

3 12 1 4

X =

3 12 2 3

X =

3 12 3 2

X =

3 12 4 1

X =

3 13 1 3

X =

3 13 2 2

X =

3 13 3 1

X =

3 14 1 2

X =

3 14 2 1

X =

3 15 1 1

X =

4 1 1 14

X =

4 1 2 13

X =

4 1 3 12

X =

4 1 4 11

X =

4 1 5 10

X =

4 1 6 9

X =

4 1 7 8

X =

4 1 8 7

X =

4 1 9 6

X =

4 1 10 5

X =

4 1 11 4

X =

4 1 12 3

X =

4 1 13 2

X =

4 1 14 1

X =

4 2 1 13

X =

4 2 2 12

X =

4 2 3 11

X =

4 2 4 10

X =

4 2 5 9

X =

4 2 6 8

X =

4 2 7 7

X =

4 2 8 6

X =

4 2 9 5

X =

4 2 10 4

X =

4 2 11 3

X =

4 2 12 2

X =

4 2 13 1

X =

4 3 1 12

X =

4 3 2 11

X =

4 3 3 10

X =

4 3 4 9

X =

4 3 5 8

X =

4 3 6 7

X =

4 3 7 6

X =

4 3 8 5

X =

4 3 9 4

X =

4 3 10 3

X =

4 3 11 2

X =

4 3 12 1

X =

4 4 1 11

X =

4 4 2 10

X =

4 4 3 9

X =

4 4 4 8

X =

4 4 5 7

X =

4 4 6 6

X =

4 4 7 5

X =

4 4 8 4

X =

4 4 9 3

X =

4 4 10 2

X =

4 4 11 1

X =

4 5 1 10

X =

4 5 2 9

X =

4 5 3 8

X =

4 5 4 7

X =

4 5 5 6

X =

4 5 6 5

X =

4 5 7 4

X =

4 5 8 3

X =

4 5 9 2

X =

4 5 10 1

X =

4 6 1 9

X =

4 6 2 8

X =

4 6 3 7

X =

4 6 4 6

X =

4 6 5 5

X =

4 6 6 4

X =

4 6 7 3

X =

4 6 8 2

X =

4 6 9 1

X =

4 7 1 8

X =

4 7 2 7

X =

4 7 3 6

X =

4 7 4 5

X =

4 7 5 4

X =

4 7 6 3

X =

4 7 7 2

X =

4 7 8 1

X =

4 8 1 7

X =

4 8 2 6

X =

4 8 3 5

X =

4 8 4 4

X =

4 8 5 3

X =

4 8 6 2

X =

4 8 7 1

X =

4 9 1 6

X =

4 9 2 5

X =

4 9 3 4

X =

4 9 4 3

X =

4 9 5 2

X =

4 9 6 1

X =

4 10 1 5

X =

4 10 2 4

X =

4 10 3 3

X =

4 10 4 2

X =

4 10 5 1

X =

4 11 1 4

X =

4 11 2 3

X =

4 11 3 2

X =

4 11 4 1

X =

4 12 1 3

X =

4 12 2 2

X =

4 12 3 1

X =

4 13 1 2

X =

4 13 2 1

X =

4 14 1 1

X =

5 1 1 13

X =

5 1 2 12

X =

5 1 3 11

X =

5 1 4 10

X =

5 1 5 9

X =

5 1 6 8

X =

5 1 7 7

X =

5 1 8 6

X =

5 1 9 5

X =

5 1 10 4

X =

5 1 11 3

X =

5 1 12 2

X =

5 1 13 1

X =

5 2 1 12

X =

5 2 2 11

X =

5 2 3 10

X =

5 2 4 9

X =

5 2 5 本回答被网友采纳

第2个回答 2019-04-22

这个matlab程序如何?个人觉着不算太好，需要修改。
clc;clear;
k=0
for
x1=1:20
for
x2=1:20
for
x3=1:20
for
x4=1:20
if
x1+x2+x3+x4==20
X=[x1,x2,x3,x4]
k=k+1;
end
end
end
end
end
k
结果:
X
=
1
1
1
17
X
=
1
1
2
16
X
=
1
1
3
15
X
=
1
1
4
14
X
=
1
1
5
13
X
=
1
1
6
12
X
=
1
1
7
11
X
=
1
1
8
10
X
=
1
1
9
9
X
=
1
1
10
8
X
=
1
1
11
7
X
=
1
1
12
6
X
=
1
1
13
5
X
=
1
1
14
4
X
=
1
1
15
3
X
=
1
1
16
2
X
=
1
1
17
1
X
=
1
2
1
16
X
=
1
2
2
15
X
=
1
2
3
14
X
=
1
2
4
13
X
=
1
2
5
12
X
=
1
2
6
11
X
=
1
2
7
10
X
=
1
2
8
9
X
=
1
2
9
8
X
=
1
2
10
7
X
=
1
2
11
6
X
=
1
2
12
5
X
=
1
2
13
4
X
=
1
2
14
3
X
=
1
2
15
2
X
=
1
2
16
1
X
=
1
3
1
15
X
=
1
3
2
14
X
=
1
3
3
13
X
=
1
3
4
12
X
=
1
3
5
11
X
=
1
3
6
10
X
=
1
3
7
9
X
=
1
3
8
8
X
=
1
3
9
7
X
=
1
3
10
6
X
=
1
3
11
5
X
=
1
3
12
4
X
=
1
3
13
3
X
=
1
3
14
2
X
=
1
3
15
1
X
=
1
4
1
14
X
=
1
4
2
13
X
=
1
4
3
12
X
=
1
4
4
11
X
=
1
4
5
10
X
=
1
4
6
9
X
=
1
4
7
8
X
=
1
4
8
7
X
=
1
4
9
6
X
=
1
4
10
5
X
=
1
4
11
4
X
=
1
4
12
3
X
=
1
4
13
2
X
=
1
4
14
1
X
=
1
5
1
13
X
=
1
5
2
12
X
=
1
5
3
11
X
=
1
5
4
10
X
=
1
5
5
9
X
=
1
5
6
8
X
=
1
5
7
7
X
=
1
5
8
6
X
=
1
5
9
5
X
=
1
5
10
4
X
=
1
5
11
3
X
=
1
5
12
2
X
=
1
5
13
1
X
=
1
6
1
12
X
=
1
6
2
11
X
=
1
6
3
10
X
=
1
6
4
9
X
=
1
6
5
8
X
=
1
6
6
7
X
=
1
6
7
6
X
=
1
6
8
5
X
=
1
6
9
4
X
=
1
6
10
3
X
=
1
6
11
2
X
=
1
6
12
1
X
=
1
7
1
11
X
=
1
7
2
10
X
=
1
7
3
9
X
=
1
7
4
8
X
=
1
7
5
7
X
=
1
7
6
6
X
=
1
7
7
5
X
=
1
7
8
4
X
=
1
7
9
3
X
=
1
7
10
2
X
=
1
7
11
1
X
=
1
8
1
10
X
=
1
8
2
9
X
=
1
8
3
8
X
=
1
8
4
7
X
=
1
8
5
6
X
=
1
8
6
5
X
=
1
8
7
4
X
=
1
8
8
3
X
=
1
8
9
2
X
=
1
8
10
1
X
=
1
9
1
9
X
=
1
9
2
8
X
=
1
9
3
7
X
=
1
9
4
6
X
=
1
9
5
5
X
=
1
9
6
4
X
=
1
9
7
3
X
=
1
9
8
2
X
=
1
9
9
1
X
=
1
10
1
8
X
=
1
10
2
7
X
=
1
10
3
6
X
=
1
10
4
5
X
=
1
10
5
4
X
=
1
10
6
3
X
=
1
10
7
2
X
=
1
10
8
1
X
=
1
11
1
7
X
=
1
11
2
6
X
=
1
11
3
5
X
=
1
11
4
4
X
=
1
11
5
3
X
=
1
11
6
2
X
=
1
11
7
1
X
=
1
12
1
6
X
=
1
12
2
5
X
=
1
12
3
4
X
=
1
12
4
3
X
=
1
12
5
2
X
=
1
12
6
1
X
=
1
13
1
5
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1
13
2
4
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=
1
13
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3
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=
1
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1
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1
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1
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1
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1
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1
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1
15
1
3
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1
15
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1
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1
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=
2
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1
9
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2
1
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2
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14
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15
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2
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2
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2
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2
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2
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2
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2
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2
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2
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2
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2
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2
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1
X
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2
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1
11
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2
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2
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2
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3
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2
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2
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2
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2
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2
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2
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2
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4
X
=
2
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3
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2
11
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2
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1
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2
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2
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2
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4
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2
12
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2
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4
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2
13
2
3
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2
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2
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X
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2
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1
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2
15
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=
2
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1
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3
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3
1
4
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6
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3
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3
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12
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3
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3
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3
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3
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9
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3
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3
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4
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6
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3
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3
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3
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3
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1
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3
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3
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2
2
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3
13
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1
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3
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2
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3
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14
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2
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4
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1
4
11
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1
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2
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4
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3
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=
4
10
4
2
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1
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1
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1
3
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4
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2
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4
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1
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1
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1
1
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1
2
12
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5
1
3
11
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1
4
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10
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2
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3
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5
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9
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2
5

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如何用matlab求方程的所有整数解答：方法一、利用三循环语句和判断语句，求解其所有整数解 方法二、整数线性规划分支定界法，求解其所有整数解下面按第一种方法求解，其过程为 m=50;n=50;l=50;disp('满足条件：2x+3y+4z=100的解')for i=1:m for j=1:n for k=1:l x=i;y=j;z=k;xyz=100-(2*x+3*y+4*z);if ...

有人知道怎么解整数最优化吗?我要用数学软件(matlab, maple等)解一个...答：比如y(x1,x2,x3)=x1^2+x2^2+x3^2+x1*x3+x3*x1+100,x1,x2,x3areallintegersx1+x2+x3<=20最好给一个例子... 比如y(x1,x2,x3)=x1^2+x2^2+x3^2+x1*x3+x3*x1+100, x1,x2,x3 are all integersx1+x2+x3 <=20最好给一个例子展开 ...

20本书放在5个书架上,每个书架至少能够放20本书。答：【答案】：有520种。$设xi(i=1，2，…，5)为放在第i个书架上的书的数目，则x1+x2+x3+x4+x5=20 xi≥0 i=1，2，…，5其非负整数解个数为

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