Statistics

Problem Statement for "PerfectPowers"

Problem Statement

A number is called a perfect power if it can be written in the form m^k, where m and k are positive integers, and k > 1.
Given two positive integers A and B, find the two perfect powers between A and B, inclusive, that are closest to each other, and return the absolute difference between them. If less than two perfect powers exist in the interval, return -1 instead.

Definition

Class:
PerfectPowers
Method:
nearestCouple
Parameters:
long, long
Returns:
long
Method signature:
long nearestCouple(long A, long B)
(be sure your method is public)

Notes

  • 1 is a perfect power.

Constraints

  • A will be between 1 and 10^18, inclusive.
  • B will be between A+1 and 10^18, inclusive.

Examples

  1. 1

    4

    Returns: 3

    1 and 4 are the first pair of perfect powers.

  2. 8

    9

    Returns: 1

    8 and 9 are the closest pair of perfect powers.

  3. 10

    15

    Returns: -1

    No pair of perfect powers is present in the interval.

  4. 10

    24

    Returns: -1

  5. 9

    16

    Returns: 7

  6. 16

    25

    Returns: 9

  7. 17

    25

    Returns: -1

  8. 16

    24

    Returns: -1

  9. 36

    49

    Returns: 13

  10. 36

    48

    Returns: -1

  11. 37

    49

    Returns: -1

  12. 25

    27

    Returns: 2

  13. 26

    27

    Returns: -1

  14. 25

    26

    Returns: -1

  15. 27

    32

    Returns: 5

  16. 28

    32

    Returns: -1

  17. 27

    31

    Returns: -1

  18. 1

    1000000000000000000

    Returns: 1

    This is the largest possible range, and 8 and 9 are the closest pair of perfect powers.

  19. 1000000

    1000000000000

    Returns: 15

  20. 1000000000000

    1000000000000000000

    Returns: 207

  21. 999999998000000001

    1000000000000000000

    Returns: 1999999999

  22. 999999998000000002

    1000000000000000000

    Returns: -1

  23. 999999993000000002

    1000000000000000000

    Returns: 1999999995

  24. 1000

    1000000

    Returns: 7

  25. 161334

    56717268054716399

    Returns: 15

  26. 436

    23958404177868

    Returns: 7

  27. 84599

    9441492765358

    Returns: 8

  28. 6840615042794867

    1000000000000000000

    Returns: 207

  29. 89028511238167

    6629727766507817

    Returns: 297

  30. 9196195400165

    55937585912850

    Returns: 427

  31. 32596826223

    80054627775

    Returns: 431

  32. 281550369145

    295257537268

    Returns: 5868

  33. 83993338427067219

    84822848977681802

    Returns: 328682

  34. 4

    8

    Returns: 4

  35. 38

    63

    Returns: -1

  36. 8

    96

    Returns: 1

  37. 568

    2249

    Returns: 10

  38. 93

    60114

    Returns: 3

  39. 8

    13637

    Returns: 1

  40. 55461

    62742

    Returns: 217

  41. 25

    4352

    Returns: 2

  42. 26

    5750

    Returns: 3

  43. 5

    8

    Returns: -1

  44. 6

    9

    Returns: 1

  45. 1

    5

    Returns: 3

  46. 2

    6

    Returns: -1

  47. 1

    3

    Returns: -1

  48. 2

    8

    Returns: 4

  49. 9

    1834

    Returns: 2

  50. 24

    27

    Returns: 2

  51. 45

    129

    Returns: 3

  52. 1

    7

    Returns: 3

  53. 34

    48

    Returns: -1

  54. 125

    510

    Returns: 3

  55. 25

    698498

    Returns: 2

  56. 3

    8

    Returns: 4

  57. 676

    2107

    Returns: 23

  58. 7

    8

    Returns: -1

  59. 7

    9

    Returns: 1

  60. 33948

    277859

    Returns: 8

  61. 9

    14

    Returns: -1

  62. 8

    1000000

    Returns: 1

  63. 9

    90

    Returns: 2

  64. 50

    107

    Returns: 17

  65. 20

    443520

    Returns: 2

  66. 26

    84

    Returns: 4

  67. 25

    77

    Returns: 2

  68. 26

    530717

    Returns: 3

  69. 25

    2813

    Returns: 2

  70. 45592

    839361

    Returns: 8

  71. 9

    191122

    Returns: 2

  72. 44

    65

    Returns: 15

  73. 692

    819928

    Returns: 7

  74. 8087

    28572

    Returns: 39

  75. 9951

    1000000

    Returns: 7

  76. 4

    7435

    Returns: 1

  77. 827

    861

    Returns: -1

  78. 76

    1000000

    Returns: 3

  79. 4

    519198

    Returns: 1

  80. 29

    150067

    Returns: 3

  81. 3136

    27486

    Returns: 11

  82. 40897

    1000000

    Returns: 8

  83. 452933

    1000000

    Returns: 74

  84. 94

    6379

    Returns: 3

  85. 949

    27171

    Returns: 10

  86. 61387

    141424

    Returns: 8

  87. 9433

    44605

    Returns: 7

  88. 8214

    151296

    Returns: 7

  89. 26

    918431

    Returns: 3

  90. 4368

    1000000

    Returns: 7

  91. 63861276

    522033078334618613

    Returns: 17

  92. 2419282

    44834075129262

    Returns: 17

  93. 29792348612659523

    44690969710344224

    Returns: 3051

  94. 64

    266

    Returns: 3

  95. 579472211452

    21086971031117958

    Returns: 297

  96. 527903

    13475520

    Returns: 15

  97. 2

    533882184367704685

    Returns: 1

  98. 9544

    33140324341489854

    Returns: 7

  99. 184907834900625

    7335920245350370

    Returns: 297

  100. 925997623

    69796927920134

    Returns: 17

  101. 1238

    25720811031125

    Returns: 7

  102. 7133236474

    38925111759140213

    Returns: 17

  103. 2

    88

    Returns: 1

  104. 62738525

    3969836812

    Returns: 19

  105. 42121971839158

    1000000000000000000

    Returns: 207

  106. 224

    73231

    Returns: 7

  107. 347681013

    601394109920173

    Returns: 17

  108. 9164

    16372102913983585

    Returns: 7

  109. 7

    9011678008

    Returns: 1

  110. 7082486047

    995746526339929755

    Returns: 17

  111. 80000

    90000

    Returns: 80

  112. 9

    1000000000000000000

    Returns: 2

  113. 999999998000000001

    1000000000000000000

    Returns: 1999999999

  114. 999999998000000002

    1000000000000000000

    Returns: -1

  115. 999999990000000000

    1000000000000000000

    Returns: 1999999991

  116. 100

    150

    Returns: 3

  117. 999999999999999999

    1000000000000000000

    Returns: -1

  118. 999999998000000001

    999999999999999999

    Returns: -1

  119. 999999998000000002

    999999999999999999

    Returns: -1

  120. 999999990000000000

    999999991000000000

    Returns: -1

  121. 999999990000000000

    999999994000000000

    Returns: 1999999991

  122. 1024

    2048

    Returns: 23

  123. 64

    128

    Returns: 3

  124. 1000

    1023

    Returns: -1

  125. 1000

    1024

    Returns: 24

  126. 900000000000000000

    1000000000000000000

    Returns: 38682

  127. 900

    1000

    Returns: 39

  128. 961

    1000

    Returns: 39

  129. 900

    960

    Returns: -1

  130. 900

    961

    Returns: 61

  131. 901

    999

    Returns: -1

  132. 962

    1023

    Returns: -1

  133. 999999996000000004

    1000000000000000000

    Returns: 1999999997

  134. 999999996000000004

    999999999999999999

    Returns: 1999999997

  135. 999999996000000005

    999999999999999999

    Returns: -1

  136. 962

    1023

    Returns: -1

  137. 961

    1024

    Returns: 24

  138. 999

    1000

    Returns: -1

  139. 1000000

    1002001

    Returns: 2001

  140. 2

    8

    Returns: 4

  141. 999999996000000005

    1000000000000000000

    Returns: 1999999999

  142. 2

    7

    Returns: -1

  143. 9

    15

    Returns: -1

  144. 5

    8

    Returns: -1

  145. 32

    64

    Returns: 4

  146. 121

    144

    Returns: 3

  147. 121

    127

    Returns: 4

  148. 125

    128

    Returns: 3

  149. 122

    127

    Returns: -1

  150. 125

    512

    Returns: 3

  151. 2086563001503744

    2086563092861569

    Returns: 91357825

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