TopCoder Statistics - Problem Statement

Problem Statement

Punctuality is not exactly one of Dr. Wesley's strengths. His student John always shows up for class at the scheduled starting time, but he never knows when Dr. Wesley will arrive. This is a problem for John because he cannot stay in the same place doing nothing for a long period of time. Therefore, he has come up with the following method to reduce the amount of time he spends waiting by the classroom door.

John arrives at time 0.
John waits for Dr. Wesley to arrive.
If after waitTime seconds Dr. Wesley has not arrived yet, John goes to take a walk for walkTime seconds.
John therefore arrives back to the classroom exactly at time waitTime + walkTime.
If Dr. Wesley has not arrived yet, John waits another waitTime seconds and then proceeds to take a new walk. The process is repeated until John becomes aware that Dr. Wesley has arrived.

Overall, John stands in front of the class door from time 0 to time waitTime, inclusive, then from time walkTime + waitTime to time walkTime + 2*waitTime, inclusive, and so on. At all other time moments he walks outside.

This has solved John's patience issues, but it has caused a new problem. When John returns from a walk, if Dr. Wesley is already in the classroom, it will appear that John has arrived late to class. Dr. Wesley does not like that, and he will deny John access to the class if he arrives lateTime or more seconds after the time at which Dr. Wesley arrived.

There are multiple variables that affect Dr. Wesley's arrival time, but for the purpose of the problem, assume that the arrival time will be a real number chosen uniformly from bestArrival to worstArrival, inclusive. Return the probability that John will be denied access to Dr. Wesley's class.

Definition

Class:: LateProfessor
Method:: getProbability
Parameters:: int, int, int, int, int
Returns:: double
Method signature:: double getProbability(int waitTime, int walkTime, int lateTime, int bestArrival, int worstArrival)
(be sure your method is public)

Notes

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

Constraints

waitTime, walkTime, lateTime and worstArrival will each be between 1 and 10000000, inclusive.
bestArrival will be between 0 and worstArrival, inclusive.

Examples

20

30

10

0

50

Returns: 0.4

The professor will arrive at some random moment between 0 and 50 seconds, inclusive. During this interval, these are John's activities: He waits from time 0 to time 20, inclusive. He takes a walk between times 20 and 50, non-inclusive. He arrives back at time 50. John will only be too late if the professor arrives while he is away, and more than 10 seconds before he returns. This only happens if the professor arrives strictly between times 20 and 40. The probability that this will happen is (40-20)/(50-0) = 0.4.
20

30

10

30

100

Returns: 0.42857142857142855

If the professor arrives between 30 and 40 seconds or between 70 and 90 seconds, John will be late to the class.
20

40

50

0

300

Returns: 0.0

John's walking time is 40 seconds. Hence, even if the professor arrives while John is taking a walk, John will always be less than 50 seconds late.
10

100

50

59

60

Returns: 1.0
300

50

25

9000

10000

Returns: 0.075
20000

30000

10000

30000

30001

Returns: 1.0
100

200

10

3150

3170

Returns: 1.0
1000000

2000000

100000

0

100000

Returns: 0.0
101

230

10

654

17890

Returns: 0.6637270828498492
120000

180000

150000

600000

1400000

Returns: 0.1125
20

30

10

10

10

Returns: 0.0
20

30

10

90

90

Returns: 1.0

Dr. Wesley will always arrive at time 90 seconds. John will arrive at time 100 seconds after taking two different walks. Since the time difference is equal to 10 seconds, John will be too late.
1000

600

1

17000

17000

Returns: 0.0
20

30

10

89

89

Returns: 1.0
20

30

10

91

91

Returns: 0.0
17

20

14

58798

58818

Returns: 0.3
12

15

20

170324

170340

Returns: 0.0
15

2

19

503939

503951

Returns: 0.0
15

2

5

117525

117528

Returns: 0.0
3

9

18

325671

325685

Returns: 0.0
20

19

7

187871

187881

Returns: 0.0
4

2

6

743659

743670

Returns: 0.0
3

10

1

299006

299016

Returns: 0.6
13

16

2

676576

676595

Returns: 0.631578947368421
11

10

1

93882

93885

Returns: 1.0
8

16

15

70555

70575

Returns: 0.05
5

10

16

601464

601481

Returns: 0.0
6

13

14

945270

945273

Returns: 0.0
5

6

14

957655

957667

Returns: 0.0
20

14

10

671701

671708

Returns: 0.0
19

12

14

37945

37961

Returns: 0.0
10

15

10

69345

69352

Returns: 0.0
2

3

10

801989

802007

Returns: 0.0
5

20

10

867898

867912

Returns: 0.5
13

14

20

689760

689763

Returns: 0.0
910962

967045

672717

181666

181682

Returns: 0.0
344978

621265

104920

168820

168831

Returns: 0.0
413937

86547

53027

413339

413355

Returns: 0.0
703524

56660

492404

318459

318473

Returns: 0.0
62849

693858

997881

73175

73194

Returns: 0.0
417913

368356

150984

321483

321500

Returns: 0.0
988276

280415

234542

582818

582820

Returns: 0.0
227339

168075

318377

311781

311785

Returns: 0.0
331218

763736

991481

539781

539793

Returns: 0.0
715732

403199

315087

614978

614993

Returns: 0.0
622682

765931

57477

722602

722607

Returns: 1.0
972097

20375

392176

172850

172870

Returns: 0.0
482430

438809

594296

761418

761429

Returns: 0.0
372760

42199

516341

568770

568775

Returns: 0.0
707714

583669

347666

655457

655467

Returns: 0.0
114929

200856

606921

715107

715125

Returns: 0.0
732799

3498

803715

508483

508485

Returns: 0.0
935817

538186

937432

743545

743548

Returns: 0.0
964447

85032

89613

997120

997138

Returns: 0.0
574307

845669

533616

266685

266703

Returns: 0.0
733080

137870

836766

573505

573553

Returns: 0.0
91922

208382

639173

231037

231132

Returns: 0.0
18591

245097

740461

209819

209886

Returns: 0.0
693708

922954

719107

900626

900687

Returns: 0.0
964087

294685

751974

840395

840403

Returns: 0.0
179080

230443

798121

503974

503978

Returns: 0.0
834830

483139

164941

836257

836285

Returns: 1.0
507630

853721

815446

249489

249493

Returns: 0.0
716490

905890

901884

497641

497723

Returns: 0.0
195125

142330

890045

458282

458382

Returns: 0.0
721568

358367

247562

43653

43718

Returns: 0.0
41959

815785

940120

728357

728392

Returns: 0.0
60949

935161

482514

783452

783464

Returns: 0.0
127426

194183

837926

825484

825556

Returns: 0.0
461341

411083

395148

608064

608099

Returns: 0.0
946151

514386

488702

882784

882876

Returns: 0.0
296410

467233

959733

8599

8647

Returns: 0.0
395926

301514

831922

773360

773424

Returns: 0.0
47377

414723

874619

300577

300649

Returns: 0.0
113039

751870

991493

135592

135661

Returns: 0.0
293631

164582

894034

211029

211337

Returns: 0.0
192241

124624

346923

882214

882858

Returns: 0.0
298244

729830

893965

576101

576321

Returns: 0.0
785661

230173

351853

301832

302482

Returns: 0.0
189680

6651

906825

280749

280904

Returns: 0.0
44003

564255

639370

264983

265683

Returns: 0.0
384007

83640

535207

485501

485622

Returns: 0.0
587125

705034

841679

281279

282031

Returns: 0.0
388298

609302

9270

279815

280597

Returns: 0.0
441439

228015

769159

639966

640466

Returns: 0.0
675529

766094

687011

479740

480172

Returns: 0.0
636371

607725

668688

547580

547975

Returns: 0.0
784145

18479

824961

592576

593481

Returns: 0.0
205089

913436

315750

957908

958622

Returns: 0.0
937214

463860

309838

944247

944700

Returns: 1.0
552376

859261

834039

797536

797851

Returns: 0.0
645185

755104

300319

684108

684872

Returns: 1.0
425522

385073

485786

333633

334105

Returns: 0.0
460155

751065

784221

478819

479383

Returns: 0.0
942189

448778

201805

13244

13430

Returns: 0.0
38246

892286

396684

46629

66217

Returns: 1.0
412175

387007

62775

537294

577403

Returns: 1.0
865379

225279

21259

191505

200935

Returns: 0.0
752871

241358

762498

15019

51716

Returns: 0.0
851775

59511

20895

626055

689315

Returns: 0.0
187943

307088

578093

19912

105242

Returns: 0.0
429247

768

420025

738845

808770

Returns: 0.0
397417

589366

138587

885436

984029

Returns: 0.0
300064

729117

579025

226555

273756

Returns: 0.0
171266

958428

570961

603112

664105

Returns: 0.0
435940

757549

114932

35541

111482

Returns: 0.0
828978

537765

183384

0

9656

Returns: 0.0
545876

128464

586907

721974

796111

Returns: 0.0
498697

866191

783344

483712

502961

Returns: 0.2215180009351135
461038

172096

876212

630999

660670

Returns: 0.0
322872

26383

39995

662940

669976

Returns: 0.0
70837

596307

287895

892074

913046

Returns: 1.0
460336

885515

640917

0

50255

Returns: 0.0
153596

629825

85134

747461

814959

Returns: 0.0
435529

391868

233066

285055

314994

Returns: 0.0
84952

347328

986386

587196

622791

Returns: 0.0
154261

904502

459190

0

157874

Returns: 0.02288533894118094
808087

370289

760902

0

169637

Returns: 0.0
886325

477955

51428

0

248141

Returns: 0.0
399072

836239

599720

703835

835334

Returns: 0.0
339362

715983

71119

0

75214

Returns: 0.0
325895

384307

922392

563997

879550

Returns: 0.0
89094

974488

167178

192551

577369

Returns: 1.0
38738

275554

17060

496225

986371

Returns: 0.772320900303175
349662

341661

522736

143680

897197

Returns: 0.0
212735

199959

100154

0

170085

Returns: 0.0
620153

991681

249412

675433

900189

Returns: 1.0
141560

743485

770359

0

128268

Returns: 0.0
703661

145018

694831

0

315682

Returns: 0.0
693639

6037

73075

296089

369345

Returns: 0.0
598824

943184

417063

149355

494799

Returns: 0.0
763397

499182

776361

269819

593077

Returns: 0.0
546791

48816

250928

234670

594691

Returns: 0.0
215583

52181

34254

594230

903386

Returns: 0.057986906286793725
112125

938216

814808

968667

971379

Returns: 0.0
433138

597856

95631

863582

863582

Returns: 1.0
515869

635459

872940

714553

714553

Returns: 0.0
777057

60805

927343

173861

173861

Returns: 0.0
85891

78712

94135

377558

377558

Returns: 0.0
419271

756497

417360

468006

468006

Returns: 1.0
745246

786193

136604

338654

338654

Returns: 0.0
374485

38820

836045

265709

265709

Returns: 0.0
988750

537521

547725

189297

189297

Returns: 0.0
236722

572622

322507

258471

258471

Returns: 1.0
181684

713538

871000

972796

972796

Returns: 0.0
201765

166450

691252

567147

567147

Returns: 0.0
686727

473793

98035

555978

555978

Returns: 0.0
699587

60537

428454

654065

654065

Returns: 0.0
466093

432213

990464

933579

933579

Returns: 0.0
462670

228357

316069

248071

248071

Returns: 0.0
894851

21978

195563

688243

688243

Returns: 0.0
567982

367463

472046

645786

645786

Returns: 0.0
707730

48923

664291

726338

726338

Returns: 0.0
151787

414682

779622

591905

591905

Returns: 0.0
737086

520842

86354

923024

923024

Returns: 1.0
110654

439198

134130

373018

614023

Returns: 0.17719134457791333
45888

998669

122059

0

731646

Returns: 0.9372811441598806
811728

414034

65679

0

621099

Returns: 0.0
257845

753255

533795

585673

836339

Returns: 0.0
374864

712562

236878

0

235452

Returns: 0.0
994619

742416

31640

18827

906346

Returns: 0.0
318440

652442

963888

0

189859

Returns: 0.0
834151

8925

606595

0

329619

Returns: 0.0
211581

809384

812504

97495

941581

Returns: 0.0
920224

723627

876236

0

127724

Returns: 0.0
963459

994011

439268

0

876634

Returns: 0.0
966141

193767

5184

117251

172190

Returns: 0.0
135902

487762

127598

0

171943

Returns: 0.20961016150701103
949464

319653

571155

0

470385

Returns: 0.0
367268

795160

146465

9293

138178

Returns: 0.0
131487

882340

295484

0

221321

Returns: 0.40589912389696414
737681

650467

795714

228433

483794

Returns: 0.0
490875

560982

877390

237293

912607

Returns: 0.0
234224

759883

848915

0

568750

Returns: 0.0
113496

837665

204172

136538

688593

Returns: 1.0
504781

544634

19030

285466

997440

Returns: 0.6919620660305011
30325

53751

863797

318428

380591

Returns: 0.0
204601

271926

210630

0

327480

Returns: 0.18717478930010992
38900

487712

491573

1723

153323

Returns: 0.0
706212

118341

442071

0

573249

Returns: 0.0
951687

427004

499350

828983

957745

Returns: 0.0
298601

977218

124565

192164

463100

Returns: 0.6071507662326158
605165

739451

554037

520065

771981

Returns: 0.6621889836294638
730370

645015

734172

0

474528

Returns: 0.0
70371

840430

516031

0

211006

Returns: 0.6664976351383373
185315

716503

164908

316564

338752

Returns: 1.0
127317

980491

278983

242785

601405

Returns: 1.0
254526

668497

355235

70458

458224

Returns: 0.5253116570302708
525130

796222

745530

391397

957121

Returns: 0.08960553202621774
510100

964361

884630

461246

953506

Returns: 0.16196928452443832
41908

414411

349624

0

219293

Returns: 0.29543578682402083
972900

954724

698264

701045

978888

Returns: 0.02155173965152982
265015

839117

460082

0

621369

Returns: 0.5734981951143362
745249

791292

61559

0

23397

Returns: 0.0
100

42

15

110

131

Returns: 0.8095238095238095
1

1

1

3

3

Returns: 0.0
17

47

3

178532

323244

Returns: 0.6875172756924097
2

3

2

1

10000000

Returns: 0.200000020000002
1

1

1

0

10000000

Returns: 0.0
1

1

1

1

1

Returns: 0.0
2

2

2

1

1

Returns: 0.0
10

10

1

100

100

Returns: 0.0
10

10

10

10

10

Returns: 0.0
1

1

1

1

10000000

Returns: 0.0
1

1

10000000

1

10000000

Returns: 0.0
2

15

1

99

10000

Returns: 0.8233511766488234
23322

212322

12232

1000000

10000000

Returns: 0.8498831111111111
3

3

1

10

10

Returns: 1.0
10

10

2

5

25

Returns: 0.4
10

10

10

5

5

Returns: 0.0
1

2

1

0

10000000

Returns: 0.3333333
20

20

10

35

35

Returns: 0.0
3

150

5

35

35

Returns: 1.0
34

43

7

4567

10000000

Returns: 0.4675331223769896
25

25

1

25

75

Returns: 0.48
2

2

2

3

3

Returns: 0.0
1000000

100000

1

1

10000000

Returns: 0.0899991089999109
20

40

100

100

100

Returns: 0.0
2

2

1

0

10000000

Returns: 0.25
20

20

10

71

71

Returns: 0.0
50

50

30

75

75

Returns: 0.0
20

20

20

25

25

Returns: 0.0
5

5

1

10

10

Returns: 0.0
1

2

1

1

10000000

Returns: 0.3333333333333333
5000

5000

1000

9500

9500

Returns: 0.0
2

4

2

3

3

Returns: 1.0
13

55

10

0

567

Returns: 0.6525573192239859
1

2

1

20

20

Returns: 1.0
1

1

10000000

10

10000000

Returns: 0.0
20

30

11

90

90

Returns: 0.0
20

30

10

23

74

Returns: 0.4117647058823529
2

2

1

4

4

Returns: 0.0
20

30

1000000

1000

1000

Returns: 0.0
10

10

1000000

50

90

Returns: 0.0
10

10

1

3

3

Returns: 0.0
40

10

10

40

40

Returns: 0.0
10

10

5

119

119

Returns: 0.0
121

222

101

65

17890

Returns: 0.3529873772791024
20

10

10

20

20

Returns: 0.0
1

1

100

0

10000000

Returns: 0.0
10000000

10000000

10000000

10000000

10000000

Returns: 0.0
30

20

2

49

49

Returns: 0.0
3

3

2

5

5

Returns: 0.0
4

4

3

6

6

Returns: 0.0
10

10

5

17

17

Returns: 0.0
10

10

1

5

7

Returns: 0.0
1

5

6

2

2

Returns: 0.0
1

1

1

100

102

Returns: 0.0
1

5

4

3

3

Returns: 0.0
20

30

9

99

99

Returns: 0.0
100

100

300

150

150

Returns: 0.0
2

5

2

6

6

Returns: 0.0
20

20

10

10

10

Returns: 0.0
30

5

100

65

65

Returns: 0.0
20

30

1

120

120

Returns: 0.0
10

10

1

0

10

Returns: 0.0
9999990

2

1

0

10000000

Returns: 1.0E-7
20

30

1

21

25

Returns: 1.0
1

100

50

70

70

Returns: 0.0
20

30

5

25

25

Returns: 1.0
2

2

1

1

10000000

Returns: 0.2500000250000025
100

42

15

110

130

Returns: 0.85
20

30

10

45

45

Returns: 0.0
10

10

5

19

19

Returns: 0.0
20

30

10

25

25

Returns: 1.0
1

10

1

10

10

Returns: 1.0
20

30

50

50

50

Returns: 0.0
1

2

1

2

2

Returns: 1.0
4

9

1

3

3

Returns: 0.0
1

3

1

1

2

Returns: 1.0
2

2

1

3

3

Returns: 1.0
1

2

1

0

29

Returns: 0.3448275862068966
86

42

24

30

30

Returns: 0.0
1

3

1

1

3

Returns: 1.0
1

29

1

100

100

Returns: 1.0
2000

7000

6000

400

5000

Returns: 0.21739130434782608
5

5

1

11

11

Returns: 0.0
1337

31337

239

21

9999999

Returns: 0.951642693613926
4

4

1

7

8

Returns: 0.0
3

3

1

4

4

Returns: 1.0
20

30

5

50

50

Returns: 0.0
2

4

2

1

1

Returns: 0.0
10

10

1

12

15

Returns: 1.0
1

2

1

10

10000000

Returns: 0.3333333333333333
9000000

9000000

100

9000200

10000000

Returns: 1.0
100

100

1

1

1

Returns: 0.0
10

10

5

15

15

Returns: 1.0
1

2

1

1

5

Returns: 0.5
100

100

50

175

175

Returns: 0.0
99

200

100

101

101

Returns: 1.0
5

6

5

10

10

Returns: 0.0
10

10

1

5

19

Returns: 0.6428571428571429
8

2

1

11

11

Returns: 0.0
5

5

1

6

6

Returns: 1.0
2

3

1

1

1

Returns: 0.0
20

20

1000

30

30

Returns: 0.0
100

100

99

150

150

Returns: 0.0
2000000

3000000

1000000

9999999

9999999

Returns: 0.0
10

30

1

30

30

Returns: 1.0
1

10

1

2

3

Returns: 1.0
2

1

1000000

0

10000000

Returns: 0.0
3

600

1

0

10

Returns: 0.7
10

2

1

2

2

Returns: 0.0
1000

566

125

1700

852129

Returns: 0.2815790618617192
1000

600

100

17502

17502

Returns: 0.0
2

4

3

4

4

Returns: 0.0
20

30

10

21

21

Returns: 1.0
20

30

20

25

25

Returns: 1.0
20

100

2

128

8997

Returns: 0.817566805727816

Statistics

Problem Statement for "LateProfessor"

Problem Statement

Definition

Notes

Constraints

Examples