TopCoder Statistics - Problem Statement

Problem Statement

Fox Ciel is playing a board game with her friend Squirrel Liss. The game is played on an infinite strip of paper. The strip of paper is divided into consecutive cells. Each cell has an integer coordinate. Formally, for each integer i, the left neighbor of cell i is cell (i-1) and the right neighbor of cell i is cell (i+1).

Each of the players has a single token called the fencer. At the beginning of the game, Ciel's fencer is in cell 0 and Liss's fencer is in cell d. Each of the fencers has two limits: its maximum move length and its hitting range. For Ciel's fencer the maximum move length is mov1 and the hitting range is rng1. Similarly, for Liss's fencer we have the parameters mov2 and rng2. Note that the parameters of Liss's fencer may differ from the ones of Ciel's fencer.

The players take alternating turns. Ciel goes first. In each turn the current player starts by moving her fencer. The distance between the original cell and the destination cell must be at most equal to the fencer's maximum move length. (It is also allowed to leave the fencer in the same cell.) Then, the current player checks whether the other fencer lies within the hitting range - that is, whether the current distance between the fencers is at most equal to the current fencer's hitting range. If that is the case, the game ends and the current player wins.

You are given the ints mov1, mov2, rng1, rng2, and d. Return "Ciel" (quotes for clarity) if Fox Ciel has a winning strategy, "Liss" if Squirrel Liss has a winning strategy, and "Draw" otherwise.

Definition

Class:: FoxAndFencing
Method:: WhoCanWin
Parameters:: int, int, int, int, int
Returns:: String
Method signature:: String WhoCanWin(int mov1, int mov2, int rng1, int rng2, int d)
(be sure your method is public)

Constraints

mov1 will be between 1 and 100,000,000, inclusive.
mov2 will be between 1 and 100,000,000, inclusive.
rng1 will be between 1 and 100,000,000, inclusive.
rng2 will be between 1 and 100,000,000, inclusive.
d will be between 1 and 100,000,000, inclusive.

Examples

1

58

1

58

2

Returns: "Ciel"

The attributes of Ciel's fencer are much smaller than the attributes of Liss's fencer. Luckily for Ciel, she can win the game in her first turn: she should move her fencer to cell 1 and from there she can hit the other fencer.
2

1

1

100

50

Returns: "Liss"

Ciel cannot score a hit in the first turn. After Ciel's turn, her fencer will be on one of the cells {-2,-1,0,1,2}. Regardless of its precise location, Liss can always move her fencer one cell to the left and then hit Ciel.
2

1

1

100

150

Returns: "Draw"

Clearly, Ciel has no chance of winning this game. However, this time the initial distance d is big enough for Ciel to escape.
100

100

100

100

100000000

Returns: "Draw"
100

1

100

1

100000000

Returns: "Ciel"
100

1

100

250

100000000

Returns: "Draw"
100

1

100

150

100000000

Returns: "Ciel"
100

50

100

1

100000000

Returns: "Ciel"
100

150

100

1

100000000

Returns: "Draw"
2569385

8205287

3508712

4698116

5015999

Returns: "Ciel"
3322451

9267903

3549829

8287879

8693771

Returns: "Liss"
957180

109481

128187

975766

707284

Returns: "Ciel"
4885

393

3358

5764

9144

Returns: "Ciel"
47828

84275537

46406583

78262476

70148557

Returns: "Liss"
819

411

800

845

583

Returns: "Ciel"
797

947

923

776

958

Returns: "Ciel"
295

822

470

283

864

Returns: "Liss"
275

592

305

494

405

Returns: "Ciel"
7

10

5

8

6

Returns: "Ciel"
5088

3173

18425

67832

43733

Returns: "Liss"
18263

96382

46436

62936

79951

Returns: "Liss"
5132039

4292513

1669585

9050987

6835888

Returns: "Liss"
933

508

9667

66929

47312

Returns: "Liss"
8162034

9177151

906682

4158573

9228270

Returns: "Draw"
387261

378065

53878

666420

628401

Returns: "Liss"
12085507

5039466

3054874

90944580

76972734

Returns: "Liss"
29493

15873

41926

1618

88588

Returns: "Ciel"
100

91

87

99

87

Returns: "Ciel"
1212548

4702178

5032818

1951676

7426047

Returns: "Draw"
4789835

98364290

38694042

62902990

74070072

Returns: "Liss"
8353478

5988082

8766831

4752979

4508890

Returns: "Ciel"
912047

549358

721854

8636719

5496524

Returns: "Liss"
503

723

137

449

790

Returns: "Liss"
209621

373252

657622

35017

874549

Returns: "Draw"
4997

1970

1975

467

9503

Returns: "Ciel"
6236883

8280717

941853

6140221

3546904

Returns: "Ciel"
133832

416965

386898

614094

938494

Returns: "Liss"
9

10

10

9

10

Returns: "Ciel"
4631

2319

6080

4649

2410

Returns: "Ciel"
1227613

8414187

3730912

5229840

5789543

Returns: "Liss"
3837

9341

4025

3794

9832

Returns: "Liss"
242388

563800

294388

700843

868166

Returns: "Liss"
83190499

50805774

20516560

12979495

73949245

Returns: "Ciel"
114149

877480

26353

296346

183703

Returns: "Liss"
101408

30370

90818

417939

277114

Returns: "Liss"
89459

26835

58654

25639

94536

Returns: "Ciel"
168776

26562

275478

733107

519391

Returns: "Liss"
6410867

210266

4670926

7637362

6089422

Returns: "Ciel"
91005

12669

29302

36046

9991

Returns: "Ciel"
844541

198979

778236

10579

191313

Returns: "Ciel"
420

834

500

825

555

Returns: "Ciel"
4407

8605

2511

3768

8510

Returns: "Liss"
5582428

16237668

64765445

66158021

96740237

Returns: "Liss"
3299752

9751005

281828

797004

9511734

Returns: "Liss"
281

413

51

162

702

Returns: "Draw"
970629

552652

2734390

1287708

3799484

Returns: "Ciel"
624

2437

2136

5177

6635

Returns: "Liss"
4286235

4524727

2014354

9267315

8600375

Returns: "Liss"
92562275

32806788

73274426

83395956

10325308

Returns: "Ciel"
9

9

7

8

10

Returns: "Ciel"
880953

913358

692305

914300

972764

Returns: "Ciel"
6620077

8487727

9564696

9612653

5197776

Returns: "Ciel"
412009

856519

177581

203996

502850

Returns: "Ciel"
2896

9489

7040

7775

6686

Returns: "Ciel"
56234149

25225858

18080362

23908892

66870275

Returns: "Ciel"
183838

422233

351628

915907

916278

Returns: "Liss"
84058

91823

70705

85211

86483

Returns: "Ciel"
86801837

47686016

43020073

78283375

85130624

Returns: "Ciel"
80279067

47496845

5812448

63816234

92135504

Returns: "Draw"
48207

40447

12418

91157

70612

Returns: "Liss"
4828

3528

28123

18755

85530

Returns: "Ciel"
10

10

9

10

9

Returns: "Ciel"
862

698

912

634

813

Returns: "Ciel"
179268

41505

633873

167086

210001

Returns: "Ciel"
366877

12942

198485

165615

743424

Returns: "Ciel"
930

280

687

731

471

Returns: "Ciel"
3737

8075

7463

9946

4025

Returns: "Ciel"
7

10

4

9

5

Returns: "Ciel"
21

11

54

34

87

Returns: "Ciel"
4183

7994

5356

6805

5505

Returns: "Ciel"
5196111

6999976

2847383

2428843

8052255

Returns: "Draw"
28487649

38806932

30448895

6326062

63098333

Returns: "Draw"
2268

864

944

9525

7639

Returns: "Liss"
4686175

2897609

8565062

3507478

4427457

Returns: "Ciel"
7650835

3564508

9075974

5808399

1668465

Returns: "Ciel"
23

15

22

66

58

Returns: "Liss"
5841

5567

836

189

7791

Returns: "Draw"
32678223

19019413

84333699

73303616

56741424

Returns: "Ciel"
731933

455177

917619

442074

86855

Returns: "Ciel"
2492

579

4955

7311

9165

Returns: "Draw"
23

60

59

59

100

Returns: "Liss"
558

504

156

992

831

Returns: "Liss"
17585

98227

71487

16448

31586

Returns: "Ciel"
922384

8694304

2505056

816335

5485369

Returns: "Liss"
472

928

514

982

954

Returns: "Ciel"
10170

51735

3257

78026

5117

Returns: "Ciel"
191

241

617

824

951

Returns: "Liss"
75943

35098

8347

95616

93613

Returns: "Draw"
2878644

6240792

1774757

854388

7575104

Returns: "Draw"
8894

4073

6714

9640

8072

Returns: "Ciel"
60031756

44206409

685336

35145713

96497946

Returns: "Draw"
1883

7342

3555

2535

9455

Returns: "Liss"
11820121

64903717

21349412

71624984

89719575

Returns: "Liss"
8366806

8174420

6805316

8119340

8637244

Returns: "Ciel"
86465

30191

80623

97191

6288

Returns: "Ciel"
101594

777888

301037

241349

212950

Returns: "Ciel"
227012

94566

224694

40948

721077

Returns: "Ciel"
675997

574064

844652

61681

695256

Returns: "Ciel"
53789845

5096114

6726066

57234281

70718756

Returns: "Draw"
100

1

100

197

100000000

Returns: "Ciel"
100

1

100

198

100000000

Returns: "Draw"
100

99

100

1

100000000

Returns: "Ciel"
100

100

100

1

100000000

Returns: "Draw"
1000000

100000000

1000000

100000000

2000000

Returns: "Ciel"
1000000

100000000

1000000

100000000

2000001

Returns: "Liss"
100

69

85

46

89

Returns: "Ciel"
40

39

28

81

80

Returns: "Liss"
224

237

425

932

946

Returns: "Liss"
329

771

433

987

763

Returns: "Liss"
93

91

94

94

93

Returns: "Ciel"
38

84

27

20

91

Returns: "Liss"
83

18

12

24

96

Returns: "Ciel"
45

2

5

95

52

Returns: "Liss"
54

57

24

34

79

Returns: "Draw"
13

50

32

11

61

Returns: "Liss"
92

100

94

91

99

Returns: "Ciel"
97

99

99

96

99

Returns: "Ciel"
89

42

93

97

86

Returns: "Ciel"
49

96

63

68

74

Returns: "Ciel"
100

100

100

100

100

Returns: "Ciel"
58

45

41

49

100

Returns: "Draw"
3956

4788

4174

7300

8722

Returns: "Liss"
28

60

42

39

90

Returns: "Liss"
11

7

11

7

42

Returns: "Ciel"
14

37

13

6

53

Returns: "Liss"
19

20

16

60

67

Returns: "Liss"
82

58

98

63

89

Returns: "Ciel"
24

25

36

86

97

Returns: "Liss"
18

55

38

59

97

Returns: "Liss"
22

40

53

57

89

Returns: "Draw"
83

56

84

53

55

Returns: "Ciel"
100

100

100

100

100

Returns: "Ciel"
19

98

50

28

69

Returns: "Ciel"
55

34

42

54

98

Returns: "Draw"
64

17

26

61

91

Returns: "Draw"
54

54

41

97

97

Returns: "Liss"
68

25

24

40

94

Returns: "Ciel"
21

53

33

23

55

Returns: "Liss"
48

29

75

64

70

Returns: "Ciel"
34

45

12

37

65

Returns: "Liss"
76

75

60

96

95

Returns: "Ciel"
39

38

92

47

35

Returns: "Ciel"
29

17

26

93

82

Returns: "Draw"
54

85

59

85

71

Returns: "Ciel"
60

11

27

23

88

Returns: "Ciel"
34

44

55

82

49

Returns: "Ciel"
80

80

82

97

98

Returns: "Ciel"
14

14

39

18

79

Returns: "Draw"
39

26

87

69

56

Returns: "Ciel"
66

99

13

46

92

Returns: "Draw"
43

71

26

53

81

Returns: "Liss"
98

95

97

99

96

Returns: "Ciel"
61

59

95

39

52

Returns: "Ciel"
7

33

90

71

69

Returns: "Ciel"
33

91

59

77

92

Returns: "Ciel"
1

99929110

2

37162

3

Returns: "Ciel"
1

97

99999999

491

99999999

Returns: "Ciel"
99999976

99996528

9

75210

99999985

Returns: "Ciel"
1

100000000

99999975

98144560

99999977

Returns: "Liss"
7

7

94878

100000000

100000000

Returns: "Liss"
1

1

99999105

99999999

100000000

Returns: "Draw"
2

1

2

1

99936302

Returns: "Ciel"
99999995

2

1

99999992

100000000

Returns: "Draw"
2

1

281

1

285943

Returns: "Ciel"
1

1

99999570

13999166

99999985

Returns: "Draw"
1

7

9

5

99999940

Returns: "Liss"
1

9

8

1

213

Returns: "Draw"
2

3

1

19886125

49833623

Returns: "Liss"
3

3

1173

98017837

99999994

Returns: "Draw"
3

2

6

5

100

Returns: "Draw"
8

7

16

16

1000000

Returns: "Draw"
5

4

3

2

100

Returns: "Draw"
5

4

1

1

100

Returns: "Draw"
11

10

100

100

100000000

Returns: "Draw"
10

1

100

108

200

Returns: "Draw"
11

10

2

1

100000

Returns: "Draw"
3

1

1

2

5

Returns: "Draw"
2

1

1

1

5

Returns: "Draw"
100

75

50

1

100000

Returns: "Draw"
1

100

1

100

100000000

Returns: "Liss"
2

1

2

2

10

Returns: "Draw"
1

2

1

1

1000

Returns: "Draw"
1

2

1000

1000

1005

Returns: "Draw"
13

10

100

100

100000000

Returns: "Draw"
10

5

5

5

100

Returns: "Draw"
10

5

5

5

100000

Returns: "Draw"
5

4

3

1

100

Returns: "Draw"
101

100

1

100

200

Returns: "Draw"
2

2

1

10

11

Returns: "Draw"
4

2

1

1

8

Returns: "Draw"
100

50

60

60

1185928

Returns: "Draw"
4

3

4

2

100

Returns: "Draw"
2

1

1

1

7

Returns: "Draw"
100

99

100

100

1000000

Returns: "Draw"
2

1

1

1

100

Returns: "Draw"
1

2

5

5

100

Returns: "Draw"
50

51

50

50

1000

Returns: "Draw"
2

1

1

1

1000

Returns: "Draw"
20

714

871

247

956

Returns: "Liss"
10

9

1

1

1000

Returns: "Draw"
10

9

100

100

100000

Returns: "Draw"
20

20

40

10

100

Returns: "Draw"
5

5

1000

10

50000

Returns: "Draw"
50

50

40

60

100

Returns: "Draw"
10

90

90

10

2000

Returns: "Draw"
9

7

16

16

1000000

Returns: "Draw"
10

4

5

5

100000

Returns: "Ciel"
2

1

1

1

10

Returns: "Draw"
1

1

1

10000

1000

Returns: "Liss"
5

5

1

10

10

Returns: "Liss"
40000001

40000000

1001

1000

100000000

Returns: "Draw"
10000

10

1

18000

10100

Returns: "Draw"
10

9

10

10

10000

Returns: "Draw"
1

1

1

50

50

Returns: "Liss"
10

9

10

10

1000

Returns: "Draw"
100

50

100

100

100000000

Returns: "Draw"
1

1

2

5

3

Returns: "Ciel"
100

50

100

100

10000

Returns: "Draw"
99

101

101

99

10100000

Returns: "Draw"
3

2

4

4

10000

Returns: "Draw"
14

3

1

10

100000

Returns: "Draw"
50

49

49

49

100000

Returns: "Draw"
4

3

4

2

20

Returns: "Draw"
50

11

10

1

1000

Returns: "Ciel"
10

9

5

2

10000000

Returns: "Draw"
3

2

4

2

8

Returns: "Ciel"
5

5

100

200

2001000

Returns: "Draw"
5

4

4

1

100

Returns: "Draw"
5

4

7

5

50

Returns: "Draw"
40000005

40000000

1005

1000

100000000

Returns: "Draw"
7

4

5

7

1000000

Returns: "Draw"
200

100

100

100

10100000

Returns: "Draw"
2

100

2

1

10

Returns: "Liss"
1

100

2

1

100

Returns: "Liss"
10

9

5

2

1000000

Returns: "Draw"
5

10

95

91

10000000

Returns: "Draw"
6

1

1

5

1000000

Returns: "Draw"
2

1

9

10

999

Returns: "Draw"
11

10

5

2

100

Returns: "Draw"
10

9

1

21

20

Returns: "Liss"
4

1

4

6

15

Returns: "Draw"
10

5

10

10

100

Returns: "Draw"
3

3

3

10

1000000

Returns: "Draw"
4

2

1

1

100

Returns: "Draw"
100

99

100

99

1000

Returns: "Draw"
100

50

100

99

100000000

Returns: "Ciel"
10

9

10

10

100

Returns: "Draw"
1

1

9

11

11

Returns: "Liss"

Statistics

Problem Statement for "FoxAndFencing"

Problem Statement

Definition

Constraints

Examples