Statistics

Problem Statement for "Similars"

Problem Statement

Given two positive integers x and y, their similarity S(x, y) is defined as follows: To compute S(x, y) we count all d between 0 and 9, inclusive, such that both x and y contain the digit d when written in base 10 (without any leading zeros). For example, S(1123, 220181) = 2 since both numbers contain the digit 1 and both contain the digit 2.

You are given two ints L and R that define a range. Find two distinct integers in this range that have the largest similarity. Formally, return the maximum of S(a, b) over all a, b such that L <= a < b <= R.

Definition

Class:
Similars
Method:
maxsim
Parameters:
int, int
Returns:
int
Method signature:
int maxsim(int L, int R)
(be sure your method is public)

Constraints

  • R will be between 2 and 100,000, inclusive.
  • L will be between 1 and R - 1, inclusive.

Examples

  1. 1

    10

    Returns: 1

    We have S(1, 10) = 1 since both numbers contain the digit 1. All other pairs of numbers within this range have similarity 0.

  2. 1

    99

    Returns: 2

    There are many pairs with similarity 2, for example pairs (23,32) and (38,83).

  3. 99

    100

    Returns: 0

    Here we have only one pair (99, 100) and its similarity is 0.

  4. 1000

    1010

    Returns: 2

  5. 444

    454

    Returns: 2

  6. 130

    200

    Returns: 3

  7. 999

    1010

    Returns: 2

  8. 1

    100000

    Returns: 5

  9. 99861

    100000

    Returns: 4

  10. 123

    98765

    Returns: 5

  11. 12

    1021

    Returns: 3

  12. 4535

    4600

    Returns: 4

  13. 32521

    33006

    Returns: 5

  14. 64988

    64999

    Returns: 4

  15. 72321

    72322

    Returns: 3

  16. 4352

    12521

    Returns: 5

  17. 12305

    12311

    Returns: 4

  18. 12300

    12310

    Returns: 4

  19. 10000

    10101

    Returns: 4

  20. 99500

    100000

    Returns: 4

  21. 117

    138

    Returns: 3

  22. 11189

    11191

    Returns: 2

  23. 1117

    11117

    Returns: 5

  24. 33333

    43333

    Returns: 5

  25. 55555

    55999

    Returns: 4

  26. 55555

    55599

    Returns: 3

  27. 8761

    18761

    Returns: 5

  28. 5188

    15454

    Returns: 5

  29. 16875

    35118

    Returns: 5

  30. 414

    581

    Returns: 3

  31. 1449

    4757

    Returns: 4

  32. 1497

    3720

    Returns: 4

  33. 15349

    76740

    Returns: 5

  34. 2890

    4512

    Returns: 4

  35. 1114

    1802

    Returns: 4

  36. 34

    210

    Returns: 3

  37. 288

    773

    Returns: 3

  38. 23068

    29929

    Returns: 5

  39. 3

    6

    Returns: 0

  40. 1495

    2710

    Returns: 4

  41. 810

    5916

    Returns: 4

  42. 5541

    34851

    Returns: 5

  43. 17074

    26817

    Returns: 5

  44. 2428

    4948

    Returns: 4

  45. 756

    15513

    Returns: 5

  46. 8322

    14129

    Returns: 5

  47. 28637

    32616

    Returns: 5

  48. 1491

    88575

    Returns: 5

  49. 9

    445

    Returns: 3

  50. 4

    6

    Returns: 0

  51. 159

    186

    Returns: 3

  52. 62259

    65309

    Returns: 5

  53. 2

    5

    Returns: 0

  54. 3137

    4391

    Returns: 4

  55. 2007

    22258

    Returns: 5

  56. 44343

    87716

    Returns: 5

  57. 982

    37122

    Returns: 5

  58. 531

    1030

    Returns: 3

  59. 19379

    88799

    Returns: 5

  60. 5498

    15622

    Returns: 5

  61. 598

    663

    Returns: 3

  62. 1

    10

    Returns: 1

  63. 2366

    2867

    Returns: 4

  64. 948

    3332

    Returns: 4

  65. 13152

    56837

    Returns: 5

  66. 1866

    5805

    Returns: 4

  67. 81598

    86963

    Returns: 5

  68. 5211

    6220

    Returns: 4

  69. 50498

    88442

    Returns: 5

  70. 26605

    36316

    Returns: 5

  71. 3390

    4949

    Returns: 4

  72. 2816

    4001

    Returns: 4

  73. 41390

    53834

    Returns: 5

  74. 122

    195

    Returns: 3

  75. 91

    182

    Returns: 3

  76. 5843

    60490

    Returns: 5

  77. 53455

    94634

    Returns: 5

  78. 3457

    4529

    Returns: 4

  79. 111

    257

    Returns: 3

  80. 16929

    24273

    Returns: 5

  81. 937

    1665

    Returns: 4

  82. 290

    303

    Returns: 2

  83. 3614

    5478

    Returns: 4

  84. 38

    40

    Returns: 1

  85. 1453

    5715

    Returns: 4

  86. 123

    298

    Returns: 3

  87. 214

    2983

    Returns: 4

  88. 1

    10000

    Returns: 4

  89. 1

    9

    Returns: 0

  90. 9

    99

    Returns: 2

  91. 2

    100000

    Returns: 5

  92. 99999

    100000

    Returns: 0

  93. 1231

    1239

    Returns: 3

  94. 1234

    1242

    Returns: 3

  95. 98

    101

    Returns: 2

  96. 1

    10005

    Returns: 4

  97. 100

    101

    Returns: 2

  98. 99

    101

    Returns: 2

  99. 12

    13

    Returns: 1

  100. 19

    21

    Returns: 1

  101. 10000

    100000

    Returns: 5

  102. 122

    123

    Returns: 2

  103. 1

    99999

    Returns: 5

  104. 12

    100000

    Returns: 5

  105. 11

    22

    Returns: 2

  106. 25433

    25467

    Returns: 5

  107. 123

    124

    Returns: 2

  108. 11234

    11235

    Returns: 3

  109. 91

    109

    Returns: 2

  110. 75

    76

    Returns: 1

  111. 109

    110

    Returns: 2

  112. 1

    1033

    Returns: 4

  113. 121

    122

    Returns: 2

  114. 10

    11

    Returns: 1

  115. 12345

    12353

    Returns: 4

  116. 13

    31

    Returns: 2

  117. 14

    15

    Returns: 1

  118. 989

    999

    Returns: 2

  119. 98

    100

    Returns: 1

  120. 9000

    9001

    Returns: 2

  121. 1

    10242

    Returns: 4

  122. 58027

    100000

    Returns: 5

  123. 13

    21

    Returns: 1

  124. 21

    121

    Returns: 3

  125. 2345

    2350

    Returns: 3

  126. 1

    10001

    Returns: 4

  127. 122

    133

    Returns: 3

  128. 1024

    1025

    Returns: 3

  129. 1234

    1237

    Returns: 3

  130. 102

    105

    Returns: 2

  131. 129

    130

    Returns: 1

  132. 18

    19

    Returns: 1

  133. 4543

    4553

    Returns: 3

  134. 6997

    7097

    Returns: 4

  135. 998

    1013

    Returns: 3

  136. 100

    120

    Returns: 3

  137. 12552

    13897

    Returns: 5

  138. 89

    121

    Returns: 3

  139. 100

    456

    Returns: 3

  140. 2

    11

    Returns: 1

  141. 9910

    10011

    Returns: 3

  142. 78

    79

    Returns: 1

  143. 7535

    91956

    Returns: 5

  144. 1

    1002

    Returns: 3

  145. 97

    98

    Returns: 1

  146. 999

    1001

    Returns: 2

  147. 1

    10010

    Returns: 4


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