Statistics

Problem Statement for "DigitalCounter"

Problem Statement

We have an N-digit digital counter that increments every second. The counter is cyclic: after it reaches 10^N - 1, it starts once again from zero.

Each digit is shown using the standard seven-segment display. The exact forms of all the digits are shown in the ASCII art below. 

    +   +---+   +---+   +   +   +---+
    |       |       |   |   |   |
    +   +---+   +---+   +---+   +---+
    |   |           |       |       |
    +   +---+   +---+       +   +---+

+---+   +---+   +---+   +---+   +---+
|           |   |   |   |   |   |   |
+---+       +   +---+   +---+   +   +
|   |       |   |   |       |   |   |
+---+       +   +---+       +   +---+

Each line segment that connects two adjacent '+' symbols represents a single lit segment. For example, '1' contains two lit segments, and '9' contains five lit segments.

You are given a String current that contains the current number shown by the counter.
The number of characters in current is equal to the number N of displayed digits.

Return the smallest positive number of seconds after which the counter will have the same total number of lit segments as it does now.

Definition

Class:
DigitalCounter
Method:
nextEvent
Parameters:
String
Returns:
long
Method signature:
long nextEvent(String current)
(be sure your method is public)

Notes

  • The digits 1, 2, ..., 9, and 0 have 2, 5, 5, 4, 5, 6, 3, 7, 5, and 6 lit segments, respectively.
  • The counter does always show leading zeroes. (See Examples #3 and #5.)
  • As the counter is cyclic, the answer always exists and for any valid input the answer fits into a long.

Constraints

  • current will contain between 1 and 15 characters, inclusive.
  • Each character in current will be a digit ('0'-'9').

Examples

  1. "1"

    Returns: 10

    No other digit has exactly two segments lit, thus the next time there will be two segments lit will be in 10 seconds.

  2. "3"

    Returns: 2

    In 2 seconds the display will show "5", and "5" and "3" both have exactly five lit segments.

  3. "9"

    Returns: 3

    In 3 seconds, the display will show "2".

  4. "99"

    Returns: 5

    The number "99" is shown using 5+5=10 lit segments. In 5 seconds, the display will show "04", with 6+4=10 lit segments again.

  5. "888888888888888"

    Returns: 1000000000000000

  6. "988888888888888"

    Returns: 20000000000000

  7. "654371"

    Returns: 43

  8. "999"

    Returns: 8

  9. "12542352325125"

    Returns: 4

  10. "124127777777"

    Returns: 134

  11. "124288888888"

    Returns: 100000000

  12. "12428888811111"

    Returns: 100003

  13. "111111111111111"

    Returns: 1000000000000000

  14. "322222222222222"

    Returns: 1

  15. "388888888888888"

    Returns: 200000000000000

  16. "788888888888888"

    Returns: 11120000000000

  17. "000000000000000"

    Returns: 6

  18. "000000000000001"

    Returns: 9

  19. "030133652081062"

    Returns: 1

  20. "056833948135792"

    Returns: 1

  21. "05713470"

    Returns: 6

  22. "057134701111111"

    Returns: 9000000

  23. "057134708888888"

    Returns: 60000000

  24. "065927413"

    Returns: 2

  25. "065927413111111"

    Returns: 1000006

  26. "065927413888888"

    Returns: 2000000

  27. "1072221"

    Returns: 10

  28. "107222111111111"

    Returns: 1000000000

  29. "107222188888888"

    Returns: 11200000

  30. "226403832336"

    Returns: 12

  31. "226403832336111"

    Returns: 1001

  32. "226403832336888"

    Returns: 1200

  33. "2330"

    Returns: 6

  34. "233011111111111"

    Returns: 90000000000

  35. "233088888888888"

    Returns: 600000000000

  36. "23897035"

    Returns: 4

  37. "238970351111111"

    Returns: 20000003

  38. "238970358888888"

    Returns: 2000000

  39. "247975864814"

    Returns: 27

  40. "247975864814111"

    Returns: 3006

  41. "247975864814888"

    Returns: 200

  42. "30516305653579"

    Returns: 18

  43. "305163056535791"

    Returns: 126

  44. "305163056535798"

    Returns: 3

  45. "3312230888772"

    Returns: 1

  46. "331223088877211"

    Returns: 100

  47. "331223088877288"

    Returns: 100

  48. "39023125"

    Returns: 4

  49. "390231251111111"

    Returns: 20000003

  50. "390231258888888"

    Returns: 2000000

  51. "4"

    Returns: 10

  52. "41002008254663"

    Returns: 2

  53. "410020082546631"

    Returns: 16

  54. "410020082546638"

    Returns: 20

  55. "411111111111111"

    Returns: 300000000000006

  56. "421905125"

    Returns: 4

  57. "421905125111111"

    Returns: 2000003

  58. "421905125888888"

    Returns: 200000

  59. "44974872362"

    Returns: 1

  60. "449748723621111"

    Returns: 10000

  61. "449748723628888"

    Returns: 10000

  62. "488888888888888"

    Returns: 20000000000000

  63. "50144227913925"

    Returns: 4

  64. "501442279139251"

    Returns: 23

  65. "501442279139258"

    Returns: 2

  66. "52846"

    Returns: 6

  67. "528461111111111"

    Returns: 10000000001

  68. "528468888888888"

    Returns: 12000000000

  69. "61731363885861"

    Returns: 11

  70. "617313638858611"

    Returns: 101

  71. "617313638858618"

    Returns: 6

  72. "62238363597"

    Returns: 15

  73. "622383635971111"

    Returns: 140001

  74. "622383635978888"

    Returns: 1112

  75. "62731107981"

    Returns: 13

  76. "627311079811111"

    Returns: 100003

  77. "627311079818888"

    Returns: 1120

  78. "65151"

    Returns: 23

  79. "651511111111111"

    Returns: 200000000003

  80. "651518888888888"

    Returns: 1120000000

  81. "65922"

    Returns: 1

  82. "659221111111111"

    Returns: 10000000000

  83. "659228888888888"

    Returns: 10000000000

  84. "6829110500"

    Returns: 6

  85. "682911050011111"

    Returns: 90000

  86. "682911050088888"

    Returns: 600000

  87. "7"

    Returns: 10

  88. "711111111111111"

    Returns: 400000000000006

  89. "779825967"

    Returns: 3

  90. "779825967111111"

    Returns: 3000000

  91. "779825967888888"

    Returns: 111200

  92. "788888888888888"

    Returns: 11120000000000

  93. "8120409870"

    Returns: 6

  94. "812040987011111"

    Returns: 90000

  95. "812040987088888"

    Returns: 600000

  96. "87338"

    Returns: 20

  97. "873381111111111"

    Returns: 10000000003

  98. "873388888888888"

    Returns: 200000000000

  99. "9115006"

    Returns: 22

  100. "911500611111111"

    Returns: 100000001

  101. "911500688888888"

    Returns: 120000000

  102. "235232555255555"

    Returns: 4

  103. "235232999999999"

    Returns: 113

  104. "007"

    Returns: 11

    Note that the input can have leading zeroes.

  105. "111117111111111"

    Returns: 54000000000

  106. "88888888888888"

    Returns: 100000000000000

  107. "002438414123697"

    Returns: 5

  108. "117177111111111"

    Returns: 234000000000

  109. "188888888888888"

    Returns: 11200000000000

  110. "887888888888888"

    Returns: 111200000000

  111. "889888888888888"

    Returns: 9000000000000

  112. "99991234567876"

    Returns: 5

  113. "12384523068978"

    Returns: 9

  114. "123456789123456"

    Returns: 6

  115. "998888888888"

    Returns: 1200000000

  116. "7687612160"

    Returns: 6

  117. "899999999999999"

    Returns: 112

  118. "111111111111"

    Returns: 1000000000000

  119. "123456789101129"

    Returns: 3

  120. "000100000000007"

    Returns: 11

  121. "654371111111111"

    Returns: 40000000003

  122. "688888888888888"

    Returns: 120000000000000

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