Statistics

Problem Statement for "GameOfLifeDivTwo"

Problem Statement

Cat Taro and Rabbit Hanako invented a new variation of "Game Of Life".

N cells are arranged around a circle. The cells are numbered from 0 to N-1. For each i between 0 and N-2, inclusive, the i-th cell and the (i+1)-th cell are adjacent to each other. The (N-1)-th cell and the 0-th cell are adjacent to each other. Each cell has exactly two adjacent cells. Each cell has a state: "live" or "die".

Taro and Hanako can decide the states of the cells at time 0. For time t > 0, the states are determined as follows:
  • Consider three cells: the i-th cell and the two cells that are adjacent to the i-th cell.
  • If at least two of the three cells are "live" at time t-1, the state of the i-th cell at time t will be "live".
  • If at least two of the three cells are "die" at time t-1, the state of the i-th cell at time t will be "die".
You are given a String init. The number of cells in the game (N) is equal to the number of characters in init. The i-th character of init represents the state they assign to the i-th cell at time 0. '1' means "live" and '0' means "die". Return a string that describes the states at time T using the same encoding.

Definition

Class:
GameOfLifeDivTwo
Method:
theSimulation
Parameters:
String, int
Returns:
String
Method signature:
String theSimulation(String init, int T)
(be sure your method is public)

Constraints

  • init will contain between 3 and 50 characters, inclusive.
  • Each character in init will be '0' (zero) or '1' (one).
  • T will be between 0 and 1,000, inclusive.

Examples

  1. "01010"

    2

    Returns: "00000"

    At time 0, Taro and Hanako set the state to "01010". At time 1, the state becomes "00100". At time 2, the state becomes "00000".

  2. "010101"

    5

    Returns: "101010"

    The state alternates between "010101" and "101010" repeatedly.

  3. "111010"

    58

    Returns: "111111"

  4. "111111111"

    511

    Returns: "111111111"

    The state never changes.

  5. "110010000010111110010100001001"

    1000

    Returns: "110000000001111110000000000001"

  6. "11111111111111111111111111111111111111111111111111"

    1000

    Returns: "11111111111111111111111111111111111111111111111111"

  7. "00001111111111111111111111111111111110000000000000"

    1000

    Returns: "00001111111111111111111111111111111110000000000000"

  8. "11111111111111111111111111110000000001111111111111"

    1000

    Returns: "11111111111111111111111111110000000001111111111111"

  9. "11111111111111110000000000011100000000000001111111"

    1000

    Returns: "11111111111111110000000000011100000000000001111111"

  10. "00000000000001111111110000000000000000011111000000"

    1000

    Returns: "00000000000001111111110000000000000000011111000000"

  11. "11111111101110000000000000000001111111110000000001"

    1000

    Returns: "11111111111110000000000000000001111111110000000001"

  12. "11111111111111111111111111111111111100111100111011"

    1000

    Returns: "11111111111111111111111111111111111100111100111111"

  13. "11110111111111111100011110011111110000000011111111"

    1000

    Returns: "11111111111111111100011110011111110000000011111111"

  14. "00000000000000100000000111110001100000000000000110"

    1000

    Returns: "00000000000000000000000111110001100000000000000110"

  15. "00000011111000000000011100000011001111111100111100"

    1000

    Returns: "00000011111000000000011100000011001111111100111100"

  16. "01011100101001010001010110101010100101010110101010"

    1000

    Returns: "00111100000000000000011111111000000000111111110000"

  17. "01101010010110101010101011101011101010010101010101"

    1000

    Returns: "11111000001111111111111111111111111000000000011111"

  18. "10101010101010100001101011010101010101101011010101"

    1000

    Returns: "11111111000000000001111111111111111111111111111111"

  19. "01011011010101010110010101010101001010101010100101"

    1000

    Returns: "11111111111111111110000000000000000000000000000000"

  20. "01011010010101010101010101010101010110101101011010"

    1000

    Returns: "00111100000000000000001111111111111111111111111100"

  21. "01011010101010101010101011010101011010101010101001"

    1000

    Returns: "01111111111111111111111111111111111111111000000000"

  22. "01010010101101010101010101010101010101010110101010"

    1000

    Returns: "00000000111111111111111111111111111111111111110000"

  23. "10101010101010101010101010101010101100101010101010"

    1000

    Returns: "00000000000111111111111111111111111100000000000000"

  24. "01010101010101011010101010101010101010101010101010"

    1000

    Returns: "00000000111111111111111111111111100000000000000000"

  25. "01010101010101010101010101010101010101010101010101"

    1000

    Returns: "01010101010101010101010101010101010101010101010101"

  26. "1111101"

    7

    Returns: "1111111"

  27. "010101010101101010"

    6

    Returns: "000000111111111000"

  28. "111100111000"

    3

    Returns: "111100111000"

  29. "00011010"

    9

    Returns: "00011100"

  30. "01010011010011010101010101010101010"

    3

    Returns: "00000011100011111010101010101010000"

  31. "1010110110010110"

    8

    Returns: "1111111110001111"

  32. "0000001011010110101111101101001010111"

    2

    Returns: "0000000111111111111111111110000011111"

  33. "0010100010011"

    3

    Returns: "0000000000011"

  34. "11111111111111111000100111111110010101111111"

    2

    Returns: "11111111111111111000000111111110000111111111"

  35. "0011"

    9

    Returns: "0011"

  36. "001011010101010101010101010110100101010"

    5

    Returns: "000111111110101010101011111111000000000"

  37. "01101010101010101010101010101010101010"

    4

    Returns: "01111110101010101010101010101010100000"

  38. "0010000101011001000100100000100"

    5

    Returns: "0000000001111000000000000000000"

  39. "0001100001110"

    0

    Returns: "0001100001110"

  40. "101010101001011010101010101001010"

    2

    Returns: "101010100000111110101010100000010"

  41. "001101111101110010000001110110100"

    8

    Returns: "001111111111110000000001111111000"

  42. "101010101010101010101011010101010101010101010101"

    1

    Returns: "110101010101010101010111101010101010101010101011"

  43. "11101101"

    5

    Returns: "11111111"

  44. "000110101001010101001010110"

    8

    Returns: "000111100000000000000011110"

  45. "11110001011011100000101100000111111"

    9

    Returns: "11110000111111100000011100000111111"

  46. "10101010101010101010101010101010101010101010101010"

    0

    Returns: "10101010101010101010101010101010101010101010101010"

  47. "11111111111111111111111111111111111111111111111111"

    0

    Returns: "11111111111111111111111111111111111111111111111111"

  48. "0101010101010101010101010101010101010101010101010"

    1

    Returns: "0010101010101010101010101010101010101010101010100"

  49. "0101010101010101010101010101010101010101010101010"

    22

    Returns: "0000000000000000000000010100000000000000000000000"

  50. "0101010101010101010101010101010101010101010101010"

    23

    Returns: "0000000000000000000000001000000000000000000000000"

  51. "1010101010101010101010101010101010101010101010101"

    24

    Returns: "1111111111111111111111111111111111111111111111111"

  52. "1010101010101010101010101010101010101010101010101"

    25

    Returns: "1111111111111111111111111111111111111111111111111"

  53. "0101010101010101010101010101010101010101010101010"

    26

    Returns: "0000000000000000000000000000000000000000000000000"

  54. "111"

    1000

    Returns: "111"

  55. "111"

    0

    Returns: "111"

  56. "110"

    1000

    Returns: "111"

  57. "010"

    0

    Returns: "010"

  58. "00101110011"

    0

    Returns: "00101110011"

  59. "101000100001000001111000111000110010101001"

    1000

    Returns: "110000000000000001111000111000110000000001"

  60. "011100101010101010101111"

    9

    Returns: "111100000000011111111111"

  61. "1111"

    0

    Returns: "1111"

  62. "101"

    1

    Returns: "111"

  63. "01010111011111111000000101011010101010010101"

    1000

    Returns: "11111111111111111000000001111111100000000000"

  64. "111111111"

    100

    Returns: "111111111"

  65. "10101"

    1

    Returns: "11011"

  66. "10101010101010101010101010101010101010101010101010"

    1000

    Returns: "10101010101010101010101010101010101010101010101010"

  67. "1010"

    1

    Returns: "0101"

  68. "10010"

    1

    Returns: "00001"

  69. "0101"

    1

    Returns: "1010"

  70. "11010"

    1

    Returns: "11101"

  71. "011"

    1

    Returns: "111"

  72. "0101"

    100

    Returns: "0101"

  73. "10100"

    1

    Returns: "01000"

  74. "1110110101010101010"

    346

    Returns: "1111111111111111111"

  75. "0101010101"

    0

    Returns: "0101010101"

  76. "11111"

    0

    Returns: "11111"

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