Statistics

Problem Statement for "PermutationSubsequence"

Problem Statement

We say that a permutation P of size n (i.e., a permutation of values 0 to n-1) contains a permutation Q of values 0 to k-1 if k ≤ n and P has a subsequence P' of length k such that the relative sizes of elements in P' are the same as in Q. In other words, if we change the smallest value in P' to 0, the second smallest to 1, and so on, we should get the permutation Q. Note that P' may be any subsequence of P, it does not have to be a contiguous one.

Examples:

  • P = {2,1,3,0} contains Q = {0,1} because we can take P' = {2,3}. Another possibility is to take P' = {1,3}.
  • P = {2,1,3,0} contains Q = {1,2,0} because we can take P' = {2,3,0}.
  • P = {2,1,3,0} does not contain Q = {0,1,2} because P has no increasing subsequence of length 3.

Let f(P,k) be the number of distinct permutations of 0 to k-1 that are contained in P. For instance, for P1 = {0,2,1,3} we have f(P1,2) = 2 because both {0,1} and {1,0} are contained in P1. For P2 = {2,3,1,4,0} we have f(P2,4) = 4.

Obviously, if P is a permutation of size n then f(P,k) is at most equal to the binomial coefficient (n choose k). For a given permutation P of size n, let g(P) be the number of k such that 1 ≤ k ≤ n and f(P,k) = (n choose k).

You are given a partially filled permutation of 0 to n-1 in the int[] arr with n elements. The value -1 denotes a missing element. You would like to fill in the missing elements in a way that maximizes g(arr). If there are multiple optimal solutions, you want to find the lexicographically smallest one. Find and return the resulting permutation.

Definition

Class:
PermutationSubsequence
Method:
findBest
Parameters:
int[]
Returns:
int[]
Method signature:
int[] findBest(int[] arr)
(be sure your method is public)

Constraints

  • arr will have between 1 and 12 elements, inclusive.
  • Each element of arr will be -1 and |arr|-1, inclusive.
  • All nonnegative elements of arr will be distinct.

Examples

  1. {3,-1,-1,-1}

    Returns: {3, 0, 1, 2 }

    There are six permutations that match the given partially-filled array. The lexicographically smallest of them is P = {3,0,1,2}. For this permutation we have: f(P,1) = 1 because P contains the permutation {0} f(P,2) = 2 because P contains both {0,1} and {1,0} f(P,3) = 2 because P contains just the two permutations {0,1,2} and {2,0,1} f(P,4) = 1 because the only permutation of size 4 contained in P is P itself Thus, we see that f(P,1) <(4 choose 1), f(P,2) < (4 choose 2), f(P,3) < (4 choose 3), and only f(P,4) equals (4 choose 4). Hence, g(P) = 1. If we analyze the other five possibilities in the same way, we'll see that none of them has g() greater than 1. And as we are to return the lexicographically smallest among all optimal answers, the only correct return value is {3,0,1,2}.

  2. {-1, -1, 3, -1}

    Returns: {2, 0, 3, 1 }

    In this case g({2,0,3,1}) = 2. In particular, note that this permutation contains (4 choose 3) = 4 different permutations of size 3: the permutations {0,2,1}, {1,0,2}, {1,2,0}, and {2,0,1}.

  3. {7,2,5,3,4,0,6,1}

    Returns: {7, 2, 5, 3, 4, 0, 6, 1 }

    In this case, we have no choice of elements to fill in.

  4. {-1, 1, -1, 5, -1, 0, -1, -1, 7, -1, 3, -1}

    Returns: {4, 1, 8, 5, 11, 0, 9, 2, 7, 10, 3, 6 }

  5. {-1}

    Returns: {0 }

  6. {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  7. {-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}

    Returns: {3, 0, 5, 2, 7, 4, 9, 6, 11, 8, 1, 10 }

  8. {-1, -1, -1, -1, -1, -1, -1, 11, -1, -1, -1, -1}

    Returns: {7, 2, 10, 5, 0, 8, 3, 11, 6, 1, 9, 4 }

  9. {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 0}

    Returns: {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 0 }

  10. {-1,-1,-1,-1,-1,-1}

    Returns: {0, 2, 4, 1, 3, 5 }

  11. {-1,-1,-1,-1,-1,-1}

    Returns: {0, 2, 4, 1, 3, 5 }

  12. {-1,-1,1,-1}

    Returns: {0, 2, 1, 3 }

  13. {-1,-1,1,-1}

    Returns: {0, 2, 1, 3 }

  14. {-1,-1,-1,-1}

    Returns: {1, 3, 0, 2 }

  15. {3,-1,4,7,-1,-1,2,1}

    Returns: {3, 0, 4, 7, 5, 6, 2, 1 }

  16. {-1,3,-1,-1}

    Returns: {1, 3, 0, 2 }

  17. {-1,-1,-1,-1,-1}

    Returns: {0, 2, 4, 1, 3 }

  18. {6,0,-1,-1,5,4,-1,1}

    Returns: {6, 0, 2, 3, 5, 4, 7, 1 }

  19. {-1,-1,-1,-1}

    Returns: {1, 3, 0, 2 }

  20. {-1,-1,-1,-1,2,-1,9,10,-1,-1,-1}

    Returns: {0, 1, 3, 4, 2, 5, 9, 10, 6, 7, 8 }

  21. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 3, 6, 1, 4, 9, 2, 7, 10, 5, 8 }

  22. {-1,-1,6,-1,-1,-1,-1,-1,-1,-1,-1,9}

    Returns: {0, 3, 6, 1, 4, 7, 10, 2, 8, 11, 5, 9 }

  23. {-1,-1,-1,0,-1}

    Returns: {1, 4, 2, 0, 3 }

  24. {-1,-1,2,-1,-1,8,-1,3,1,-1}

    Returns: {0, 4, 2, 7, 5, 8, 6, 3, 1, 9 }

  25. {-1,-1,-1,-1,-1,5,4,0,-1,-1}

    Returns: {1, 2, 3, 6, 7, 5, 4, 0, 8, 9 }

  26. {2,-1,0,4,3}

    Returns: {2, 1, 0, 4, 3 }

  27. {-1,-1,-1,7,-1,-1,-1,-1,-1,-1,4,-1}

    Returns: {0, 3, 10, 7, 1, 5, 8, 2, 6, 9, 4, 11 }

  28. {1,2,-1}

    Returns: {1, 2, 0 }

  29. {5,7,0,-1,2,-1,4,10,-1,11,-1,1}

    Returns: {5, 7, 0, 6, 2, 8, 4, 10, 3, 11, 9, 1 }

  30. {-1,-1,-1,-1,0,-1,-1,-1}

    Returns: {4, 1, 6, 3, 0, 5, 2, 7 }

  31. {2,-1,-1,-1,-1,1,3,-1,-1,6,-1,-1}

    Returns: {2, 0, 4, 7, 5, 1, 3, 8, 10, 6, 9, 11 }

  32. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  33. {7,9,1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {7, 9, 1, 3, 0, 2, 4, 6, 8, 5, 10 }

  34. {-1,-1,-1,-1,-1,-1,0,-1,-1,-1,-1,-1}

    Returns: {1, 4, 7, 2, 5, 9, 0, 6, 10, 3, 8, 11 }

  35. {0,2,8,7,-1,10,3,6,-1,-1,-1}

    Returns: {0, 2, 8, 7, 1, 10, 3, 6, 4, 5, 9 }

  36. {10,8,-1,-1,-1,5,-1,4,11,-1,1,-1}

    Returns: {10, 8, 0, 2, 7, 5, 9, 4, 11, 3, 1, 6 }

  37. {1,-1,6,4,-1,0,5,-1,7,-1,-1}

    Returns: {1, 3, 6, 4, 2, 0, 5, 9, 7, 10, 8 }

  38. {-1,-1,-1,-1,-1,-1}

    Returns: {0, 2, 4, 1, 3, 5 }

  39. {-1,-1,-1,-1,-1,-1,1,-1,7,5,-1,-1}

    Returns: {0, 2, 4, 6, 3, 8, 1, 10, 7, 5, 9, 11 }

  40. {-1,6,-1,3,1,-1,4,9,0,5}

    Returns: {2, 6, 8, 3, 1, 7, 4, 9, 0, 5 }

  41. {-1,8,-1,-1,-1,-1,-1,9,4,-1,-1}

    Returns: {0, 8, 2, 5, 10, 3, 6, 9, 4, 1, 7 }

  42. {-1,6,-1,-1,3,4,-1}

    Returns: {0, 6, 1, 2, 3, 4, 5 }

  43. {6,9,0,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {6, 9, 0, 3, 7, 1, 4, 8, 11, 2, 5, 10 }

  44. {3,2,8,7,-1,1,6,4,-1,9,0}

    Returns: {3, 2, 8, 7, 5, 1, 6, 4, 10, 9, 0 }

  45. {-1,-1,-1,-1,-1,-1,-1,-1,-1,3,-1}

    Returns: {0, 4, 7, 1, 5, 8, 2, 10, 6, 3, 9 }

  46. {-1,9,-1,7,10,11,-1,-1,2,3,-1,5}

    Returns: {0, 9, 1, 7, 10, 11, 4, 6, 2, 3, 8, 5 }

  47. {0,5,-1,-1,9,-1,2,-1,8,-1,4}

    Returns: {0, 5, 1, 3, 9, 7, 2, 6, 8, 10, 4 }

  48. {7,9,-1,-1,-1,-1,-1,11,-1,-1,6,-1}

    Returns: {7, 9, 0, 2, 4, 1, 3, 11, 5, 8, 6, 10 }

  49. {7,9,1,-1,2,-1,6,-1,-1,-1}

    Returns: {7, 9, 1, 4, 2, 0, 6, 3, 5, 8 }

  50. {-1,-1,-1,-1,-1,-1,-1,-1,5}

    Returns: {0, 6, 3, 8, 1, 4, 7, 2, 5 }

  51. {2,-1,-1,3,-1,0}

    Returns: {2, 4, 1, 3, 5, 0 }

  52. {11,-1,-1,-1,4,3,9,10,2,-1,7,1}

    Returns: {11, 0, 5, 6, 4, 3, 9, 10, 2, 8, 7, 1 }

  53. {-1,3,7,-1,-1,1,6,-1,-1}

    Returns: {0, 3, 7, 2, 4, 1, 6, 8, 5 }

  54. {3,4,1,0,-1,5}

    Returns: {3, 4, 1, 0, 2, 5 }

  55. {-1,-1,-1,9,-1,1,-1,-1,-1,6}

    Returns: {4, 7, 2, 9, 5, 1, 8, 3, 0, 6 }

  56. {-1,-1,7,-1,3,-1,-1,-1,-1,-1}

    Returns: {1, 4, 7, 0, 3, 6, 9, 2, 5, 8 }

  57. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,4}

    Returns: {0, 1, 2, 5, 6, 7, 8, 9, 10, 11, 3, 4 }

  58. {-1,-1,-1,-1,-1,4,-1,-1,-1,-1,-1,8}

    Returns: {0, 3, 6, 1, 9, 4, 7, 10, 2, 5, 11, 8 }

  59. {-1,-1,-1,-1,-1,-1,-1,3,-1,-1,-1}

    Returns: {0, 4, 7, 1, 10, 5, 8, 3, 6, 9, 2 }

  60. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 3, 6, 1, 4, 9, 2, 7, 10, 5, 8 }

  61. {10,-1,-1,3,-1,-1,-1,-1,0,-1,-1,-1}

    Returns: {10, 1, 6, 3, 8, 5, 2, 7, 0, 9, 4, 11 }

  62. {-1,8,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 8, 2, 5, 9, 1, 4, 7, 10, 3, 6, 11 }

  63. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  64. {-1,-1,10,8,-1,9,-1,6,-1,-1,1}

    Returns: {0, 2, 10, 8, 5, 9, 3, 6, 4, 7, 1 }

  65. {5,-1,-1,-1,4,3,-1,6,10,8,0,1}

    Returns: {5, 2, 7, 9, 4, 3, 11, 6, 10, 8, 0, 1 }

  66. {11,-1,-1,10,2,-1,-1,1,-1,-1,6,-1}

    Returns: {11, 0, 5, 10, 2, 7, 4, 1, 8, 3, 6, 9 }

  67. {-1,7,-1,-1,-1,-1,4,9,-1,-1,10,-1}

    Returns: {0, 7, 2, 5, 8, 11, 4, 9, 1, 6, 10, 3 }

  68. {-1,-1,-1,-1,10,-1,7,-1,-1,1,-1,-1}

    Returns: {0, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 11 }

  69. {-1,-1,-1,-1,-1,-1,-1,3,-1,8,10,-1}

    Returns: {0, 2, 4, 1, 5, 7, 9, 3, 11, 8, 10, 6 }

  70. {-1,-1,-1,4,3,-1,11,-1,-1,-1,-1,-1}

    Returns: {0, 1, 2, 4, 3, 5, 11, 6, 7, 8, 9, 10 }

  71. {3,-1,-1,10,-1,1,-1,8,5,9,-1}

    Returns: {3, 0, 2, 10, 4, 1, 6, 8, 5, 9, 7 }

  72. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  73. {10,-1,-1,-1,4,11,-1,7,-1,9,-1,2}

    Returns: {10, 5, 0, 8, 4, 11, 1, 7, 3, 9, 6, 2 }

  74. {0,9,2,-1,-1,-1,3,-1,1,-1}

    Returns: {0, 9, 2, 4, 6, 8, 3, 5, 1, 7 }

  75. {-1,-1,8,1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 3, 8, 1, 4, 7, 10, 5, 2, 9, 6, 11 }

  76. {-1,-1,-1,2,-1,-1,-1,-1,5}

    Returns: {0, 3, 6, 2, 4, 7, 1, 8, 5 }

  77. {0,-1,-1,-1,-1,-1}

    Returns: {0, 2, 4, 1, 3, 5 }

  78. {-1,5,-1,8,1,0,6,4,9,3}

    Returns: {2, 5, 7, 8, 1, 0, 6, 4, 9, 3 }

  79. {3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {3, 0, 5, 2, 7, 10, 4, 8, 1, 6, 9 }

  80. {-1,8,-1,7,9,-1,-1,1,-1,-1}

    Returns: {0, 8, 2, 7, 9, 3, 5, 1, 4, 6 }

  81. {-1,9,10,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 11 }

  82. {-1,-1,-1,2,-1,-1,1,-1,9,-1}

    Returns: {0, 4, 7, 2, 5, 8, 1, 6, 9, 3 }

  83. {-1,-1,-1,-1,-1,-1,-1,5}

    Returns: {0, 3, 6, 1, 4, 7, 2, 5 }

  84. {-1,-1,-1,-1,-1,-1,7,-1,-1,-1,-1,-1}

    Returns: {0, 3, 6, 1, 4, 10, 7, 2, 9, 5, 11, 8 }

  85. {-1,9,7,8,-1,2,0,5,-1,11,6,3}

    Returns: {1, 9, 7, 8, 4, 2, 0, 5, 10, 11, 6, 3 }

  86. {-1,7,-1,-1,3,-1,10,-1,-1,-1,-1,-1}

    Returns: {1, 7, 11, 0, 3, 6, 10, 4, 8, 2, 5, 9 }

  87. {-1,2,-1,-1,-1,-1,-1,-1,0,-1,-1,-1}

    Returns: {5, 2, 7, 4, 1, 9, 6, 11, 0, 8, 3, 10 }

  88. {-1,1,-1,7,-1,-1,-1,-1,10,5,6,0}

    Returns: {2, 1, 3, 7, 4, 8, 9, 11, 10, 5, 6, 0 }

  89. {-1,4,-1,-1,8,2,7,3,0}

    Returns: {6, 4, 1, 5, 8, 2, 7, 3, 0 }

  90. {-1,-1,0,3,1,9,-1,6,2,8}

    Returns: {5, 7, 0, 3, 1, 9, 4, 6, 2, 8 }

  91. {-1,-1,-1,6,8,3,-1,1,-1,-1,10}

    Returns: {0, 2, 4, 6, 8, 3, 5, 1, 9, 7, 10 }

  92. {-1,-1,2,5,10,-1,0,4,6,9,-1,-1}

    Returns: {1, 7, 2, 5, 10, 3, 0, 4, 6, 9, 11, 8 }

  93. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  94. {-1,2,-1,-1,-1,11,-1,-1,9,-1,-1,6}

    Returns: {7, 2, 10, 4, 8, 11, 1, 5, 9, 0, 3, 6 }

  95. {10,-1,7,-1,-1,-1,-1,-1,-1,4,3,0}

    Returns: {10, 1, 7, 2, 5, 6, 8, 9, 11, 4, 3, 0 }

  96. {9,-1,6,0,3,7,-1,8,-1,1}

    Returns: {9, 2, 6, 0, 3, 7, 4, 8, 5, 1 }

  97. {6,7,1,9,0,8,2,5,4,3}

    Returns: {6, 7, 1, 9, 0, 8, 2, 5, 4, 3 }

  98. {4,-1,5,-1,-1,-1,-1,-1,7,-1,-1,-1}

    Returns: {4, 0, 5, 1, 3, 6, 2, 9, 7, 10, 8, 11 }

  99. {-1,-1,-1,-1,-1,-1,6,-1,-1,-1,-1}

    Returns: {0, 3, 7, 1, 4, 9, 6, 2, 8, 5, 10 }

  100. {-1,-1,-1,-1,-1,7,-1,8,4,3}

    Returns: {0, 1, 2, 5, 6, 7, 9, 8, 4, 3 }

  101. {0,1,-1,-1,-1,-1,8,-1,7,9,5,-1}

    Returns: {0, 1, 2, 3, 4, 6, 8, 10, 7, 9, 5, 11 }

  102. {7,11,6,-1,-1,-1,-1,-1,-1,-1,0,-1}

    Returns: {7, 11, 6, 1, 3, 5, 2, 4, 8, 10, 0, 9 }

  103. {5,-1,2,-1,1,-1,8,4,-1,-1,7}

    Returns: {5, 0, 2, 6, 1, 10, 8, 4, 9, 3, 7 }

  104. {-1,-1,-1,-1,-1,-1,-1,8,-1,-1}

    Returns: {0, 4, 7, 1, 9, 6, 3, 8, 5, 2 }

  105. {-1,-1,9,-1,11,-1,1,4,-1,-1,7,-1}

    Returns: {5, 2, 9, 6, 11, 8, 1, 4, 10, 0, 7, 3 }

  106. {-1,-1,1,6,-1,2,-1,-1,9,5}

    Returns: {0, 3, 1, 6, 8, 2, 4, 7, 9, 5 }

  107. {11,3,-1,-1,-1,10,6,-1,9,1,0,2}

    Returns: {11, 3, 4, 5, 7, 10, 6, 8, 9, 1, 0, 2 }

  108. {-1,-1,-1,-1,-1,-1,-1,7,-1,-1,-1,-1}

    Returns: {0, 3, 6, 1, 4, 9, 2, 7, 10, 5, 8, 11 }

  109. {-1,-1,2,-1,10,5,-1,1,-1,-1,-1}

    Returns: {4, 9, 2, 7, 10, 5, 8, 1, 6, 3, 0 }

  110. {-1,-1,4,-1,2,-1,7,-1,3,6,-1}

    Returns: {0, 8, 4, 9, 2, 5, 7, 1, 3, 6, 10 }

  111. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  112. {10,-1,-1,-1,7,8,6,0,-1,-1,11,5}

    Returns: {10, 1, 2, 3, 7, 8, 6, 0, 4, 9, 11, 5 }

  113. {10,0,-1,-1,-1,4,-1,9,-1,8,-1}

    Returns: {10, 0, 2, 5, 1, 4, 7, 9, 3, 8, 6 }

  114. {-1,-1,3,5,-1,-1,-1,-1,-1,7,-1,-1}

    Returns: {0, 6, 3, 5, 1, 4, 2, 8, 10, 7, 9, 11 }

  115. {11,4,-1,-1,-1,-1,8,-1,-1,-1,10,-1}

    Returns: {11, 4, 0, 9, 2, 5, 8, 1, 6, 3, 10, 7 }

  116. {-1,-1,-1,-1,-1,-1,-1,1,-1,9}

    Returns: {0, 3, 8, 5, 2, 7, 4, 1, 6, 9 }

  117. {-1,-1,-1,-1,-1,-1,-1,7,10,9,-1,-1}

    Returns: {0, 1, 2, 3, 4, 5, 6, 7, 10, 9, 8, 11 }

  118. {-1,11,-1,-1,-1,-1,-1,-1,-1,-1,9,4}

    Returns: {0, 11, 2, 7, 10, 1, 5, 8, 3, 6, 9, 4 }

  119. {5,3,2,-1,-1,6,-1,-1,-1,-1,-1,-1}

    Returns: {5, 3, 2, 0, 1, 6, 4, 7, 8, 9, 10, 11 }

  120. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,7}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  121. {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7 }

  122. {-1,10,4,0,-1,6,5,2,3,-1,1}

    Returns: {7, 10, 4, 0, 8, 6, 5, 2, 3, 9, 1 }

  123. {-1,-1,5,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 8, 5, 1, 7, 3, 10, 6, 2, 9, 4, 11 }

  124. {-1,-1,1,-1,11,-1,-1,-1,-1,-1,4,-1}

    Returns: {3, 6, 1, 8, 11, 0, 5, 2, 10, 7, 4, 9 }

  125. {-1,-1,-1,-1,-1,-1,-1,10,-1,8,-1,-1}

    Returns: {0, 3, 6, 1, 9, 4, 7, 10, 2, 8, 5, 11 }

  126. {-1,6,-1,7,2,10,9,3,-1,0,-1,-1}

    Returns: {1, 6, 4, 7, 2, 10, 9, 3, 5, 0, 8, 11 }

  127. {9,-1,-1,-1,-1,-1,11,-1,-1,7,-1,-1}

    Returns: {9, 0, 3, 6, 1, 8, 11, 5, 2, 7, 4, 10 }

  128. {-1,-1,-1,-1,3,-1,6,-1,-1,-1,5}

    Returns: {1, 4, 10, 7, 3, 9, 6, 0, 8, 2, 5 }

  129. {-1,5,-1,-1,-1,-1,-1,10,-1,-1,4,-1}

    Returns: {0, 5, 2, 8, 11, 3, 6, 10, 1, 7, 4, 9 }

  130. {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 0}

    Returns: {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 0 }

  131. {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0}

    Returns: {1, 3, 5, 7, 4, 6, 9, 11, 8, 10, 2, 0 }

  132. {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0}

    Returns: {1, 4, 7, 2, 5, 10, 3, 8, 11, 6, 9, 0 }

  133. {-1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1}

    Returns: {7, 2, 10, 5, 0, 8, 3, 11, 6, 1, 9, 4 }

  134. {-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1}

    Returns: {7, 2, 10, 5, 0, 8, 3, 11, 6, 1, 9, 4 }

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