TopCoder Statistics - Problem Statement

Problem Statement

Fox Ciel was very bored, so she invented a single player game. The rules of the game are:

You start with 0 points.

You make exactly nA+nB moves.

You have two types of moves available. These are called move A and move B.

Exactly nA times you will make move A. Exactly nB times you will make move B. The moves can be in any order.

The moves affect your score in the following ways:

Each time you make move A, you add scoreA to your score.
Each time you make move B, you multiply your score by scoreB.

You are given int nA, int nB, int paramA and int paramB. Calculate scoreA and scoreB as follows ("/" denotes exact division, without any rounding):

scoreA = paramA/1000.0
scoreB = paramB/1000.0

Return the maximum possible score after nA+nB moves.

Definition

Class:: FoxPlayingGame
Method:: theMax
Parameters:: int, int, int, int
Returns:: double
Method signature:: double theMax(int nA, int nB, int paramA, int paramB)
(be sure your method is public)

Notes

The returned value must have an absolute or relative error less than 1e-9.

Constraints

nA will be between 0 and 50, inclusive.
nB will be between 0 and 50, inclusive.
paramA will be between -10000 and 10000, inclusive.
paramB will be between -2000 and 2000, inclusive.

Examples

5

4

3000

2000

Returns: 240.0

scoreA = 3000/1000 = 3 scoreB = 2000/1000 = 2 The optimal order of operations is: (3 + 3 + 3 + 3 + 3) * 2 * 2 * 2 * 2 = 240
3

3

2000

100

Returns: 6.0

scoreA = 2000/1000 = 2 scoreB = 100/1000 = 0.1 Multiplying the score by scoreB decreases its absolute value, so it's better to do all multiplications before additions. Thus, the optimal order of operations is: 0 * 0.1 * 0.1 * 0.1 + 2 + 2 + 2 = 6
4

3

-2000

2000

Returns: -8.0

Multiplying the score by scoreB increases its absolute value, but given that scoreA is negative, the overall score will be negative as well, so it's better to do multiplications before additions again to keep the absolute value small.
5

5

2000

-2000

Returns: 160.0

Multiplication increases the absolute value of the score, but if you do all 5 multiplications after additions, you'll end up with negative score. Thus, the optimal order of operations is: (0 * (-2) + 2 + 2 + 2 + 2 + 2) * (-2) * (-2) * (-2) * (-2) = 160
50

50

10000

2000

Returns: 5.62949953421312E17
41

34

9876

-1234

Returns: 515323.9982341775
31

16

-1234

-1569

Returns: 32886.75382013723
31

17

-7717

-1322

Returns: 27526.115739436027
23

34

-9422

-180

Returns: 39.00708
23

35

-3581

-599

Returns: 49.335437
41

19

414

-509

Returns: 16.974
41

20

5511

-918

Returns: 225.951
0

0

10000

2000

Returns: 0.0
0

0

8481

-512

Returns: 0.0
0

1

-414

-1851

Returns: 0.0
0

1

4144

2000

Returns: 0.0
1

0

1885

424

Returns: 1.885
1

0

-5153

31

Returns: -5.153
1

1

-4142

-321

Returns: 1.329582
1

1

-951

-243

Returns: 0.231093
1

1

2534

-1001

Returns: 2.534
1

2

4515

-1002

Returns: 4.533078059999999
50

1

5293

1403

Returns: 371.30395000000004
45

1

-5918

-1

Returns: 0.26631
25

9

0

1592

Returns: 0.0
39

50

-1

-2

Returns: 7.8E-5
40

45

-1

1

Returns: -4.0000000000000037E-137
31

49

1000

1000

Returns: 31.0
22

23

-1000

-1000

Returns: 22.0
37

41

-1001

1001

Returns: -37.037
43

12

999

-1001

Returns: 43.47532863383772
41

23

-104

-1000

Returns: 4.264
40

9

-4796

-146

Returns: 28.00864
26

26

-8930

1839

Returns: -232.18
14

34

2898

-912

Returns: 40.572
18

14

-8184

-412

Returns: 60.69254399999999
25

7

-2350

-564

Returns: 33.135
47

44

9508

-171

Returns: 446.876
4

41

-5461

1574

Returns: -21.844
29

5

-4769

-1401

Returns: 746.476253539108
38

43

-6852

482

Returns: -6.118198950390014E-12
23

49

8654

-861

Returns: 199.042
47

34

4635

271

Returns: 217.845
7

11

7987

-1398

Returns: 1594.2390346449097
26

34

3143

-187

Returns: 81.71799999999999
17

20

-6315

522

Returns: -2.4223245811644934E-4
45

41

3155

702

Returns: 141.975
18

27

5835

-1325

Returns: 158097.93614918503
47

26

1529

1709

Returns: 8.08721472123053E7
38

8

-4286

-1678

Returns: 6100.697043704332
45

15

-3938

1389

Returns: -177.21
34

50

1662

-4

Returns: 56.507999999999996
27

13

-7130

1387

Returns: -192.51
14

27

-3023

-872

Returns: 36.904784
49

12

-9628

-687

Returns: 324.107364
6

13

-5577

1913

Returns: -33.462
13

42

6461

-1089

Returns: 3015.8799017856522
14

31

-602

-1575

Returns: 1.1000738188400714E7
39

22

8645

-1529

Returns: 3844096.5203036075
38

0

493

-1024

Returns: 18.733999999999998
12

12

-7128

1651

Returns: -85.536
3

13

-8205

-707

Returns: 17.402805
50

50

-10000

-2000

Returns: 2.81474976710656E17
50

49

-10000

-2000

Returns: 2.81474976710656E17
50

50

-10000

2000

Returns: -500.0
50

50

10000

-2000

Returns: 5.62949953421312E17
50

49

10000

-2000

Returns: 1.40737488355328E17
50

50

1

1001

Returns: 0.052562241621737275
50

50

1

-1001

Returns: 0.052562241621737275
50

50

-10000

0

Returns: -0.0
50

0

-9188

0

Returns: -459.40000000000003
48

0

-1004

0

Returns: -48.192
50

50

1160

116

Returns: 57.99999999999999
5

7

-3000

-2000

Returns: 1920.0
2

4

-1000

-500

Returns: 1.0
5

5

-5000

-500

Returns: 12.5
9

9

-1500

-1

Returns: 0.0135
49

49

-1000

-500

Returns: 24.5
1

2

-3000

-2000

Returns: 6.0
4

5

-1

-1

Returns: 4.0E-6
50

50

-1000

-500

Returns: 25.0
1

3

-5000

-500

Returns: 2.5
2

50

-10000

-999

Returns: 19.98
37

8

-5173

-564

Returns: 107.950164
1

4

-100

-3

Returns: 3.0000000000000003E-4
50

50

-1

-1

Returns: 5.0E-5
10

10

-10000

-500

Returns: 50.0
20

21

-2000

-900

Returns: 36.0
2

4

-100

-100

Returns: 0.020000000000000004
8

10

-2000

-500

Returns: 8.0
5

5

-100

-100

Returns: 0.05
25

25

500

-2000

Returns: 2.097152E8
37

49

-5843

-483

Returns: 104.420253
2

3

-5000

-2000

Returns: 80.0
50

48

-1000

-50

Returns: 2.5
50

50

1000

1000

Returns: 50.0
4

4

-2000

-500

Returns: 4.0
40

40

-100

-300

Returns: 1.2
1

1

-1000

-1000

Returns: 1.0
3

3

-2000

-100

Returns: 0.6000000000000001
3

3

-2000

100

Returns: -0.006000000000000002
5

5

-1000

200

Returns: -0.0016000000000000003
5

5

-10000

-100

Returns: 5.0
1

0

-1000

0

Returns: -1.0
10

10

-1000

-100

Returns: 1.0
2

2

-10000

1999

Returns: -20.0
5

5

-10000

-500

Returns: 25.0
40

0

-1000

0

Returns: -40.0
5

5

-1000

-2000

Returns: 160.0
2

2

2

0

Returns: 0.0040
3

3

-1000

-750

Returns: 2.25
4

5

-1000

-100

Returns: 0.4
1

2

6107

0

Returns: 6.107
50

50

-1000

-1

Returns: 0.05
5

4

-2000

-500

Returns: 5.0
5

5

-1000

-100

Returns: 0.5
49

49

-3000

-675

Returns: 99.22500000000001
1

10

-1000

-100

Returns: 0.1
5

10

-300

-100

Returns: 0.15000000000000002
5

5

-2000

-50

Returns: 0.5
10

3

-1000

500

Returns: -1.25
10

1

-1000

-2000

Returns: 20.0
50

10

-10000

500

Returns: -0.48828125
2

3

-2000

-100

Returns: 0.4
1

0

2000

500

Returns: 2.0
10

10

-600

-1500

Returns: 230.66015625
50

50

-9999

567

Returns: -2.3882485204200707E-10
1

0

-10

0

Returns: -0.01
50

3

-1000

-500

Returns: 25.0
2

5

-2000

-500

Returns: 2.0
1

50

-10000

-1

Returns: 0.01
10

10

2000

-800

Returns: 20.0
1

10

-2

-999

Returns: 0.001998
10

0

-1

-200

Returns: -0.01
3

0

-2000

-100

Returns: -6.0
4

4

-5000

-500

Returns: 10.0
2

50

-2000

2000

Returns: -4.0
5

0

-1000

-2000

Returns: -5.0
10

6

-2000

-500

Returns: 10.0
50

0

-5000

-1000

Returns: -250.0
49

49

-9999

1000

Returns: -489.951
3

10

-3000

-500

Returns: 4.5
10

3

-1

-1

Returns: 1.0E-5
50

50

-1500

-500

Returns: 37.5
10

5

-10000

-900

Returns: 90.0
50

50

9432

-1868

Returns: 1.747500831749391E16
1

5

-1000

-1

Returns: 0.0010
3

3

100

-100

Returns: 0.30000000000000004
1

10

-2000

-200

Returns: 0.4
11

40

-100

-3

Returns: 0.0033000000000000004
10

0

-1000

0

Returns: -10.0
6

6

-2000

-2000

Returns: 384.0
1

2

-1000

-500

Returns: 0.5
1

0

-2000

-5

Returns: -2.0
4

5

-2000

-500

Returns: 4.0
10

10

-500

-500

Returns: 2.5
5

5

10000

2000

Returns: 1600.0
3

20

-2000

100

Returns: -6.000000000000007E-20
1

1

-1

0

Returns: -0.0
1

10

-100

-500

Returns: 0.05
5

5

-2000

-1

Returns: 0.01
1

0

2000

100

Returns: 2.0
1

1

-500

-500

Returns: 0.25
4

3

-2000

-200

Returns: 1.6
10

12

-500

-700

Returns: 3.5
10

10

-2000

-100

Returns: 2.0
5

0

-1000

-200

Returns: -5.0
1

3

-500

-500

Returns: 0.25
5

2

-1000

1

Returns: -4.9999999999999996E-6
5

5

-2000

-500

Returns: 5.0
10

10

-2345

-2000

Returns: 12006.400000000001
5

5

-3000

-2000

Returns: 480.0
0

0

0

0

Returns: 0.0
2

3

-2000

-2000

Returns: 32.0
1

3

-1000

-100

Returns: 0.1
50

50

-1000

1

Returns: -5.000000000000005E-149
10

9

-2000

-100

Returns: 2.0
2

3

1000

-2000

Returns: 8.0
46

3

1696

-969

Returns: 78.01599999999999
1

9

-1000

-200

Returns: 0.2
1

2

-1000

-1000

Returns: 1.0
5

3

-2000

-200

Returns: 2.0
10

10

1000

-10

Returns: 10.0
10

10

-100

-100

Returns: 0.1
2

2

-1000

-2000

Returns: 4.0
1

0

2000

2000

Returns: 2.0
1

5

-7966

-373

Returns: 2.971318
1

3

-5000

-2000

Returns: 40.0
5

4

-2000

-100

Returns: 1.0
3

3

-100

-100

Returns: 0.030000000000000006
3

5

-2000

-200

Returns: 1.2000000000000002
50

2

-5000

-1500

Returns: 375.0
1

0

-1

0

Returns: -0.0010
10

6

-1500

1500

Returns: -15.0
1

10

-1000

-500

Returns: 0.5
29

16

-4552

-1079

Returns: 412.9732500259706
50

50

-1000

-200

Returns: 10.0
3

4

-2000

-500

Returns: 3.0
3

2

-3706

0

Returns: -0.0
1

1

-1000

-2000

Returns: 2.0
4

5

-3000

-800

Returns: 9.600000000000001
6

5

-2000

-500

Returns: 6.0
2

5

-2000

-2000

Returns: 128.0
1

3

1000

-500

Returns: 1.0
13

13

-2000

-100

Returns: 2.6
10

5

-5000

-500

Returns: 25.0
1

3

500

-500

Returns: 0.5
5

5

-3000

-200

Returns: 3.0
1

1

-1000

0

Returns: -0.0
5

5

2000

2000

Returns: 320.0
50

0

-10000

0

Returns: -500.0
2

11

-2000

-100

Returns: 0.4
2

4

-5000

-200

Returns: 2.0
10

10

2000

-600

Returns: 20.0
5

5

-2000

0

Returns: -0.0
1

3

-10000

-999

Returns: 9.99
49

49

-10000

1

Returns: -4.9000000000000054E-145
2

4

-3000

-200

Returns: 1.2000000000000002
2

2

-1000

10

Returns: -2.0E-4
3

0

-2000

-500

Returns: -6.0
2

3

-5000

-100

Returns: 1.0
40

20

-2000

400

Returns: -8.79609302220801E-7
50

0

-10000

-1

Returns: -500.0
2

1

-1000

-1000

Returns: 2.0
50

0

-5000

-500

Returns: -250.0
10

10

10

0

Returns: 0.1
5

5

-2000

-1999

Returns: 319.2007996001001
5

4

-3000

-100

Returns: 1.5
1

1

-1000

100

Returns: -0.1
1

2

-5000

0

Returns: -0.0
1

0

-1000

-1000

Returns: -1.0
10

0

10000

2000

Returns: 100.0
5

5

-5000

-100

Returns: 2.5
50

50

-2000

-100

Returns: 10.0
50

50

-3000

-100

Returns: 15.0
5

6

-2000

-100

Returns: 1.0
49

49

-10000

1192

Returns: -490.0
10

11

-1000

-10

Returns: 0.1
5

4

-1000

-200

Returns: 1.0
1

2

-2000

-2000

Returns: 4.0
1

0

1000

2000

Returns: 1.0
50

50

-10000

-1

Returns: 0.5
50

50

-300

-70

Returns: 1.05
4

0

-2000

-2000

Returns: -8.0
10

20

-2000

-10

Returns: 0.2
3

0

-1000

-750

Returns: -3.0
5

0

-2000

-200

Returns: -10.0
2

0

-2000

-100

Returns: -4.0
5

0

2000

2000

Returns: 10.0
3

18

-2548

-230

Returns: 1.7581200000000001
50

50

900

2000

Returns: 5.066549580791808E16
5

5

-3000

-100

Returns: 1.5
1

0

1

0

Returns: 0.0010
5

0

-1000

0

Returns: -5.0
1

1

-1000

-500

Returns: 0.5
1

0

-1000

-500

Returns: -1.0
1

1

-2000

2000

Returns: -2.0
3

0

-1000

-2000

Returns: -3.0
1

1

-100

0

Returns: -0.0
10

10

-2000

-2000

Returns: 10240.0
5

5

5000

2000

Returns: 800.0
10

0

-1200

0

Returns: -12.0
2

0

-2000

-500

Returns: -4.0
1

10

-2000

-500

Returns: 1.0
10

0

-1100

-100

Returns: -11.0
3

1

-2000

-500

Returns: 3.0
2

2

-500

-2000

Returns: 2.0
3

3

-1

1

Returns: -3.0E-12
50

50

-5000

-2000

Returns: 1.40737488355328E17
5

5

-100

900

Returns: -0.29524500000000004
1

1

10000

2000

Returns: 20.0
5

5

-2000

-300

Returns: 3.0
4

5

-5000

-500

Returns: 10.0
5

4

-6000

-2000

Returns: 240.0
49

49

-9998

-1997

Returns: 2.56232604543883936E17
2

2

-3000

-2000

Returns: 12.0
1

1

-1000

500

Returns: -0.5
5

5

-2000

-100

Returns: 1.0
41

17

-666

-500

Returns: 13.653
50

50

2000

100

Returns: 100.0
4

3

-2

-2

Returns: 1.6E-5
10

1

-1000

500

Returns: -5.0
4

4

-3000

-2000

Returns: 96.0
50

50

8000

0

Returns: 400.0
50

50

3000

-200

Returns: 150.0
10

49

-1000

-900

Returns: 9.0
1

0

7

0

Returns: 0.0070
2

3

-2000

-500

Returns: 2.0
10

19

-1

-1

Returns: 1.0E-5
50

50

-10000

-10

Returns: 5.0
10

0

-10000

0

Returns: -100.0
4

0

-5000

-500

Returns: -20.0
10

0

10000

1

Returns: 100.0
1

0

-2000

-300

Returns: -2.0
10

10

-1345

-5

Returns: 0.06725
1

10

-2000

-5

Returns: 0.01
1

5

2000

2000

Returns: 64.0
1

2

-10000

-2000

Returns: 20.0
10

1

-10

0

Returns: -0.0
5

4

3000

1000

Returns: 15.0
50

50

-1000

-100

Returns: 5.0
5

5

500

500

Returns: 2.5
3

0

-1000

0

Returns: -3.0
4

3

2000

-2000

Returns: 32.0
1

0

-500

-500

Returns: -0.5
1

1

-100

-100

Returns: 0.010000000000000002
40

37

-9874

589

Returns: -1.2325910823419878E-6
50

50

-1000

-999

Returns: 49.95
4

2

-5000

-1700

Returns: 34.0
50

50

-4000

-500

Returns: 100.0
4

0

-2000

2000

Returns: -8.0
5

3

-5000

-500

Returns: 12.5
10

3

-1000

99

Returns: -0.009702990000000002
1

0

-300

0

Returns: -0.3
1

0

-1000

-1

Returns: -1.0
1

5

-2000

-500

Returns: 1.0
2

2

-1000

2000

Returns: -2.0
10

10

-10

0

Returns: -0.0
50

49

-5000

-500

Returns: 125.0
1

2

900

2000

Returns: 3.6
5

0

-2000

-500

Returns: -10.0
10

0

-1000

-100

Returns: -10.0
50

50

-900

900

Returns: -0.23191988432940538
5

5

-1000

-500

Returns: 2.5
49

49

-999

-999

Returns: 48.902049
10

10

-2000

500

Returns: -0.01953125
50

50

1111

1111

Returns: 10724.745875895354
10

9

-2000

-2000

Returns: 10240.0
10

10

-1000

-10

Returns: 0.1
0

10

2000

2000

Returns: 0.0

Statistics

Problem Statement for "FoxPlayingGame"

Problem Statement

Definition

Notes

Constraints

Examples