Statistics

Problem Statement

A number is written on a traditional digital display. If the display looks identical when flipped horizontally (i.e., around a vertical axis), the number is called a "mirror number". On a digital display, the digits 0, 1 and 8 are symmetrical, and the digits 2 and 5 are mirror images of each other. No other digits make sense when flipped horizontally. For example, 0, 101 and 1521 are all mirror numbers, while 1221 and 1010 are not (see images below). Given two Strings A and B, both representing integers with no extra leading zeroes, return the number of mirror numbers between A and B, inclusive.

Mirror numbers (both remain unchanged after mirroring):
    

Not mirror numbers (1221 mirrors to 1551, and 1010 mirrors to 0101):
    

Definition

Class:

MirrorNumber

Method:

count

Parameters:

String, String

Returns:

int

Method signature:

int count(String A, String B)

(be sure your method is public)

Constraints

• A will represent an integer between 0 and 10^18, inclusive.
• B will represent an integer between A and 10^18, inclusive.
• Both A and B will have no extra leading zeros.

Examples

1. "0"

   "10"

   Returns: 3

   There is only 0, 1 and 8 here.

2. "0"

   "100"

   Returns: 7

   Few more: 11, 25, 52, 88.

3. "143"

   "23543"

   Returns: 54

4. "1234"

   "23452354235234"

   Returns: 87478

5. "0"

   "1000000000000000000"

   Returns: 3124999

6. "1"

   "1000000000"

   Returns: 2498

7. "102"

   "10000000000001234"

   Returns: 624992

8. "0"

   "200000004"

   Returns: 1374

9. "3456"

   "365426457654646453"

   Returns: 2343720

10. "3453426345"

    "3453453455"

    Returns: 0

11. "64575675"

    "6786897866"

    Returns: 3500

12. "0"

    "0"

    Returns: 1

13. "0"

    "1"

    Returns: 2

14. "354758"

    "456472905830476354"

    Returns: 2343600

15. "88"

    "100"

    Returns: 1

16. "84902"

    "3464576867980563"

    Returns: 468656

17. "9999999"

    "10000001"

    Returns: 1

18. "9999999999999"

    "10000000000001"

    Returns: 1

19. "999"

    "100000001"

    Returns: 981

20. "4762198"

    "23456456456345"

    Returns: 87150

21. "22"

    "333333333"

    Returns: 1745

22. "200004"

    "200000004"

    Returns: 1250

23. "0"

    "20000004"

    Returns: 624

24. "0"

    "20000000000005"

    Returns: 78125

25. "200000000000000004"

    "200000000000000005"

    Returns: 1

26. "1"

    "825522225255552258"

    Returns: 2948437

27. "0"

    "985218125012580150"

    Returns: 3124999

28. "12345"

    "98765432198765432"

    Returns: 1562452

29. "502"

    "299999995212555555"

    Returns: 2343736

30. "2"

    "1000000000000000000"

    Returns: 3124997

31. "135"

    "88828888888888828"

    Returns: 1558740

32. "183410081237571912"

    "988018741012831234"

    Returns: 1203125

33. "2123521082"

    "2172858103"

    Returns: 35

34. "51555122212"

    "1555555522222220"

    Returns: 361688

35. "1328500121615471"

    "810120434455345681"

    Returns: 2457575

36. "11"

    "700000000000000000"

    Returns: 2734371

37. "0"

    "100000000000000"

    Returns: 124999

38. "13132134124"

    "2343414212431313"

    Returns: 431375

39. "0"

    "888888888888888888"

    Returns: 3124999

40. "582"

    "525252528252525"

    Returns: 244125

41. "10000000000"

    "100000000000"

    Returns: 7500

42. "456"

    "609005240670030000"

    Returns: 2734361

43. "0"

    "4"

    Returns: 2

44. "7"

    "85270391700472531"

    Returns: 1494997

45. "12321"

    "1000000000000000000"

    Returns: 3124952

46. "1435"

    "28825025883"

    Returns: 8691

47. "458943"

    "321412341441344334"

    Returns: 2343600

48. "1"

    "53674575473745745"

    Returns: 1234373

49. "251"

    "285"

    Returns: 1

50. "999999999999999999"

    "999999999999999999"

    Returns: 0

51. "12"

    "12545674000005678"

    Returns: 752495

52. "0"

    "3"

    Returns: 2

53. "888888888888888888"

    "1000000000000000000"

    Returns: 1

54. "1"

    "999999999999999999"

    Returns: 3124998

55. "1"

    "1000000000000000000"

    Returns: 3124998

56. "151"

    "171"

    Returns: 0

57. "111111111111111111"

    "999999999999999999"

    Returns: 1464844

58. "0"

    "109"

    Returns: 8

59. "707"

    "10770"

    Returns: 25

60. "0"

    "53"

    Returns: 6

61. "23135165316"

    "999999999999999999"

    Returns: 3117000

62. "1521"

    "85555555822222228"

    Returns: 1503884

63. "58"

    "100"

    Returns: 1

64. "867254749"

    "1013063236"

    Returns: 115

65. "123"

    "1000000000000000000"

    Returns: 3124990

66. "52355"

    "463412312312312347"

    Returns: 2343672

67. "888888888"

    "11111111111111111"

    Returns: 681096

68. "3"

    "76"

    Returns: 4

69. "0"

    "9"

    Returns: 3

70. "81"

    "81"

    Returns: 0

71. "8"

    "25008888188880025"

    Returns: 1001871

72. "73"

    "104"

    Returns: 2

73. "1251"

    "1251"

    Returns: 1

74. "0"

    "23"

    Returns: 4

75. "12312312"

    "125000821085212"

    Returns: 148824

76. "222555"

    "222555"

    Returns: 1

77. "0"

    "99999999999999999"

    Returns: 1562499

78. "0"

    "1000000"

    Returns: 199