TopCoder Statistics - Problem Statement

Problem Statement

There is an infinitely long straight road. Fox Ciel is going to plant trees of three kinds: apple trees, kiwi trees, and grape trees. There will be infinitely many trees of each kind. Trees of each kind will be placed along the entire road in regular intervals.

More precisely, you are given ints apple, kiwi, and grape with the following meaning: The distance between any two consecutive apple trees must be apple, the distance between any two consecutive kiwi trees must be kiwi, and the distance between any two consecutive grape trees must be grape.

Ciel can only plant the trees at integer coordinates, but she gets to choose those coordinates as long as the above conditions are satisfied. In other words, Ciel gets to choose three integers x, y, and z such that:

She plants apple trees at coordinates ..., x - 2 * apple, x - apple, x, x + apple, x + 2 * apple, ...
She plants kiwi trees at coordinates ..., y - 2 * kiwi, y - kiwi, y, y + kiwi, y + 2 * kiwi, ...
She plants grape trees at coordinates ..., z - 2 * grape, z - grape, z, z + grape, z + 2 * grape, ...

Ciel wants to maximize the distance between two closest trees (of any kind). Return this distance.

Definition

Class:: FruitTrees
Method:: maxDist
Parameters:: int, int, int
Returns:: int
Method signature:: int maxDist(int apple, int kiwi, int grape)
(be sure your method is public)

Constraints

apple will be between 1 and 2,000, inclusive.
kiwi will be between 1 and 2,000, inclusive.
grape will be between 1 and 2,000, inclusive.

Examples

1

5

8

Returns: 0

Apple trees will be planted at all integer coordinates, so at least two trees will be planted where a kiwi tree is planted.
3

3

6

Returns: 1

One of the optimal solutions is as follows: Plant apple trees at ..., -5, -2, 1, 4, ... Plant kiwi trees at ..., -4, -1, 2, 5, ... Plant grape trees at ..., -9, -3, 3, 9, ...
40

30

20

Returns: 5
899

1073

1147

Returns: 14
2000

2000

2000

Returns: 666
1977

1977

1977

Returns: 659
1255

1255

1255

Returns: 418
1416

708

1416

Returns: 354
747

1494

1494

Returns: 373
776

388

1164

Returns: 129
1275

1700

425

Returns: 141
825

1100

1925

Returns: 91
654

1308

1308

Returns: 327
324

1620

1296

Returns: 108
1890

315

1575

Returns: 105
310

1560

1670

Returns: 3
936

420

372

Returns: 4
760

970

390

Returns: 3
1300

160

350

Returns: 5
1395

360

495

Returns: 15
425

1139

1071

Returns: 5
979

363

1551

Returns: 5
1281

1155

1449

Returns: 7
330

435

90

Returns: 7
1740

40

780

Returns: 10
641

942

1251

Returns: 0
1781

1045

1153

Returns: 0
456

210

990

Returns: 3
1497

1716

1874

Returns: 0
573

1983

412

Returns: 0
1730

1005

839

Returns: 0
366

1257

1672

Returns: 0
1845

976

1593

Returns: 0
839

1800

995

Returns: 0
1614

920

1780

Returns: 1
444

1480

1110

Returns: 74
1221

1332

1628

Returns: 55
1425

1900

456

Returns: 28
720

330

1188

Returns: 15
1050

550

1540

Returns: 25
288

1824

1368

Returns: 36
645

900

860

Returns: 7
1323

504

196

Returns: 14
1596

437

1932

Returns: 9
980

1440

735

Returns: 7
1

1

2000

Returns: 0
1

2000

2000

Returns: 0
6

10

15

Returns: 1
10

20

30

Returns: 3
4

12

20

Returns: 1
19

21

12

Returns: 0
2000

150

50

Returns: 16
2

4

8

Returns: 1
18

20

4

Returns: 1
2

4

6

Returns: 0
2

4

4

Returns: 1
2000

2000

1000

Returns: 500
2000

1999

1997

Returns: 0
1997

2000

2000

Returns: 0
2000

1000

500

Returns: 250
1104

736

1840

Returns: 122
30

40

50

Returns: 3
2

2

4

Returns: 0
6

6

12

Returns: 2
10

2000

2000

Returns: 5
1000

1000

2000

Returns: 333
82

28

62

Returns: 0
10

20

20

Returns: 5
4

4

3

Returns: 0
1993

1997

1999

Returns: 0
10

4

2

Returns: 0
4

4

2

Returns: 1
200

200

201

Returns: 0
5

100

200

Returns: 2
20

40

80

Returns: 10
100

100

200

Returns: 33
4

8

12

Returns: 1
10

10

5

Returns: 2
100

200

300

Returns: 33
2

96

98

Returns: 0
200

300

500

Returns: 33
1995

1998

1992

Returns: 1
12

8

4

Returns: 1
4

8

8

Returns: 2
5

10

15

Returns: 1
2

6

6

Returns: 1
1974

1758

1385

Returns: 0
2

4

2000

Returns: 1
20

30

50

Returns: 3
1997

1999

2000

Returns: 0
70

80

90

Returns: 3
2000

2

2

Returns: 0
1976

1988

1968

Returns: 2
783

1241

1736

Returns: 0
6

8

10

Returns: 0
2

8

2

Returns: 0
25

100

400

Returns: 12
1682

1989

1955

Returns: 0
12

16

20

Returns: 1
14

28

56

Returns: 7
30

60

90

Returns: 10
47

47

188

Returns: 15
5

10

5

Returns: 1
10

100

100

Returns: 5
2

2000

2000

Returns: 1
77

88

99

Returns: 3
10

100

1000

Returns: 5
17

34

51

Returns: 5
97

970

388

Returns: 48
4

8

48

Returns: 2
12

1200

1800

Returns: 6
20

40

60

Returns: 6
1996

1998

2000

Returns: 1
1997

1998

1999

Returns: 0
1650

1500

352

Returns: 2
30

30

30

Returns: 10
50

150

2000

Returns: 16
8

4

2

Returns: 1
7

7

7

Returns: 2
6

4

4

Returns: 1
544

702

1940

Returns: 1
28

44

77

Returns: 2
221

247

323

Returns: 6
8

16

32

Returns: 4
99

77

63

Returns: 3
1997

1314

1879

Returns: 0
14

7

21

Returns: 2
10

50

50

Returns: 5

Statistics

Problem Statement for "FruitTrees"

Problem Statement

Definition

Constraints

Examples