Statistics

Problem Statement for "PyramidSequences"

Problem Statement

A pyramid sequence of height X > 1 is an infinite sequence of positive integers with period 2X-2. Its first 2X-2 terms are 1, 2, ..., X-1, X, X-1, ..., 2.

You are given ints N and M. Consider two pyramid sequences A and B, A of height N and B of height M. Return the number of distinct pairs of integers (x,y) such that for some i > 0 we have x=A[i] and y=B[i].

Definition

Class:
PyramidSequences
Method:
distinctPairs
Parameters:
int, int
Returns:
long
Method signature:
long distinctPairs(int N, int M)
(be sure your method is public)

Constraints

  • N will be between 2 and 1,000,000,000, inclusive.
  • M will be between 2 and 1,000,000,000, inclusive.

Examples

  1. 3

    4

    Returns: 6

    These are the first several terms of pyramid sequences of height 3 and 4: {1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1} {1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1} We can see the following pairs: (1, 1), (2, 2), (3, 3), (2, 4), (1, 3), (3, 1). No other pairs will appear later in the sequences.

  2. 3

    5

    Returns: 5

    The sequences begin with: {1, 2, 3, 2, 1, 2, 3, 2, 1} {1, 2, 3, 4, 5, 4, 3, 2, 1}

  3. 43

    76

    Returns: 895

  4. 2

    1000000000

    Returns: 1000000000

  5. 100000

    95555

    Returns: 4777750000

  6. 1000000000

    1000000000

    Returns: 1000000000

  7. 1000000000

    999999999

    Returns: 499999999500000000

  8. 438483157

    765337608

    Returns: 167793825263334228

  9. 688253904

    57365928

    Returns: 19741161951291456

  10. 110532835

    560034097

    Returns: 9457273853694310

  11. 999624130

    743084835

    Returns: 371402765851534275

  12. 494388873

    449911164

    Returns: 111215536660039086

  13. 556899004

    396135040

    Returns: 61279780234524040

  14. 995823432

    418011900

    Returns: 208133022437420400

  15. 177532453

    720048931

    Returns: 19529896923849004

  16. 726839826

    897052143

    Returns: 326006611765523559

  17. 7629670

    618515310

    Returns: 2359533852623850

  18. 861795970

    832466670

    Returns: 358708210682659950

  19. 834829201

    67355939

    Returns: 1629523005048529

  20. 709350356

    131572821

    Returns: 16799620867655516

  21. 433425880

    876727495

    Returns: 39876163902521440

  22. 570228485

    542319820

    Returns: 154623104672036350

  23. 140716365

    130579644

    Returns: 9187346423337030

  24. 165181264

    813247300

    Returns: 37314782379782160

  25. 933240150

    816127797

    Returns: 380821613845724775

  26. 437485610

    226499070

    Returns: 49545041901691350

  27. 577058130

    232349795

    Returns: 67039669104291675

  28. 278862508

    757286908

    Returns: 58660812784995972

  29. 34842194

    768489304

    Returns: 13387926708446488

  30. 725082608

    169706632

    Returns: 61525663662728128

  31. 526099750

    755810755

    Returns: 110453291316679736

  32. 305488380

    18281492

    Returns: 2792391687531480

  33. 241459754

    362348887

    Returns: 43746336558596899

  34. 6253746

    479431020

    Returns: 1499119911800460

  35. 228110100

    74451844

    Returns: 8491608790012200

  36. 76875564

    113992570

    Returns: 4381621555279740

  37. 896081580

    703221384

    Returns: 315071864432253360

  38. 138962876

    472092224

    Returns: 32801646592138112

  39. 683380145

    190583386

    Returns: 65120450979635485

  40. 571057504

    40578576

    Returns: 11586350163217152

  41. 885609226

    750115202

    Returns: 332154471727026826

  42. 377552871

    530779593

    Returns: 75149009588469006

  43. 460705125

    152740610

    Returns: 35184190911313125

  44. 997721556

    274778838

    Returns: 137076384902615964

  45. 704113577

    707166484

    Returns: 248962761291876634

  46. 175737134

    390362864

    Returns: 5953001091182758

  47. 230923259

    749055195

    Returns: 791640074967035

  48. 851567625

    965109975

    Returns: 308196153250875066

  49. 427460970

    213730485

    Returns: 45680720218335225

  50. 471421650

    432938250

    Returns: 102048232081556250

  51. 184314696

    645101436

    Returns: 21402301445437332

  52. 155956070

    62382428

    Returns: 4864459153968980

  53. 552228807

    321446619

    Returns: 66567030987498147

  54. 706290900

    141258180

    Returns: 49884683542281000

  55. 167371182

    781065516

    Returns: 65363929316179956

  56. 408220246

    816440492

    Returns: 166643769244300516

  57. 482047535

    96409507

    Returns: 17427736877661087

  58. 557520568

    487830497

    Returns: 135987767887581148

  59. 73042544

    730425440

    Returns: 26676066169959680

  60. 132668850

    66334425

    Returns: 4400255940080625

  61. 65055480

    628869640

    Returns: 20455708143813600

  62. 893385276

    372243865

    Returns: 166278594036165870

  63. 670321072

    335160536

    Returns: 112332584891807296

  64. 682490988

    909987984

    Returns: 310529299134144096

  65. 967293708

    322431236

    Returns: 155942852922731544

  66. 710718800

    177679700

    Returns: 63140151584180000

  67. 305776700

    580975730

    Returns: 88824420749745500

  68. 635903772

    272530188

    Returns: 86651487266534568

  69. 958991352

    599369595

    Returns: 287395129128371220

  70. 73911756

    381877406

    Returns: 5080541301290156

  71. 568410521

    81201503

    Returns: 17308420653628396

  72. 818179440

    545452960

    Returns: 223139198679571200

  73. 521717104

    586931742

    Returns: 153106164340957584

  74. 74911698

    674205282

    Returns: 25252931237594418

  75. 373344138

    871136322

    Returns: 162616819608790218

  76. 689346240

    258504840

    Returns: 89099669737900800

  77. 779727928

    334169112

    Returns: 130280494650679968

  78. 622742865

    415161910

    Returns: 129269558636136075

  79. 140388369

    233980615

    Returns: 12318058797253978

  80. 268042423

    536084846

    Returns: 71846740527710929

  81. 286977500

    631350500

    Returns: 90591694056875000

  82. 63025270

    882353780

    Returns: 27805292610010300

  83. 331424148

    552373580

    Returns: 91534971564604920

  84. 989674140

    913545360

    Returns: 452056109254495200

  85. 956688586

    956688586

    Returns: 956688586

  86. 191942492

    959712460

    Returns: 92104800587925160

  87. 425329764

    389885617

    Returns: 82914978732802194

  88. 100000

    20000000

    Returns: 1000000000000

  89. 320189654

    823344823

    Returns: 5763413704

  90. 631

    219

    Returns: 51715

  91. 999999999

    999999997

    Returns: 374999998250000002

  92. 5

    7

    Returns: 12

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