Statistics

Problem Statement for "SelfCatalogue"

Problem Statement

A self-catalogue is a sentence that truthfully and comprehensively describes its own composition. In this problem, we are concerned with sentences that count numerals occurring in themselves, such as the following.

This sentence contains 1 occurrence of 0, 2 occurrences of 1, 3 occurrences of 2, and 2 occurrences of 3.

The above is a self-catalogue because it gives an accurate count for each numeral occurring in itself. The following sentence, although accurate in the counts that it gives, is not a self-catalogue because it does not give a count for the numeral 3.

This sentence contains 3 occurrences of 1, 1 occurrence of 8, and 1 occurrence of 9.

A self-catalogue must not give more than one count for the same numeral. Thus, the following is not a self-catalogue.

This sentence contains 4 occurrences of 4, and 4 occurrences of 4.

Given a int[] specifying a count for each of the numerals 0 through 9, try to find a self-catalogue that agrees with these counts. A count of 0 means that the numeral does not appear in the sentence at all, and a specified count of -1 means that any count (including 0) is acceptable. If there is no sentence meeting this specification, return an empty int[]. Otherwise, return a int[] of the same size as the input and containing the same non-negative counts, but with each -1 replaced by an accurate count. If several self-catalogues are possible, choose the one that yields the smallest value in element 0 of the result. If a tie remains, select for the smallest value in element 1; if there is still a tie, select for the smallest value in element 2; and so forth.

Definition

Class:
SelfCatalogue
Method:
construct
Parameters:
int[]
Returns:
int[]
Method signature:
int[] construct(int[] counts)
(be sure your method is public)

Notes

  • Leading zeros are not permitted for any number appearing in a self-catalogue.

Constraints

  • counts contains exactly 10 elements.
  • Each element of counts is between -1 and 100, inclusive.

Examples

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

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

    The first sentence from the problem statement satisfies the input specification that there be exactly one occurrence of the numeral 0: This sentence contains 1 occurrence of 0, 2 occurrences of 1, 3 occurrences of 2, and 2 occurrences of 3.

  2. {100, -1, -1, -1, -1, -1, -1, -1, -1, -1}

    Returns: { }

    It is impossible to make a self-catalogue with 100 zeros.

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

    Returns: {1, 7, 3, 2, 1, 1, 1, 2, 1, 1 }

    This sentence contains 1 occurrence of 0, 7 occurrences of 1, 3 occurrences of 2, 2 occurrences of 3, 1 occurrence of 4, 1 occurrence of 5, 1 occurrence of 6, 2 occurrences of 7, 1 occurrence of 8, and 1 occurrence of 9.

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

    Returns: {1, 11, 0, 1, 1, 1, 1, 1, 1, 1 }

    Note that 11 contains two occurrences of 1.

  5. {-1, 11, -1, -1, -1, -1, -1, -1, -1, -1}

    Returns: {0, 11, 1, 1, 1, 1, 1, 1, 1, 1 }

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

    Returns: { }

  7. {-1, -1, 2, -1, -1, -1, -1, -1, -1, -1}

    Returns: {0, 0, 2, 0, 0, 0, 0, 0, 0, 0 }

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

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

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

    Returns: { }

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

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

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

    Returns: { }

  12. {-1, -1, -1, -1, 4, -1, -1, -1, -1, -1}

    Returns: { }

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

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    The following self-catalogue illustrates this degenerate case: This is a sentence.

  14. {0,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  15. {1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

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

  16. {-1,0,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  17. {-1,2,-1,-1,-1,-1,-1,-1,-1,-1}

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

  18. {-1,3,-1,-1,-1,-1,-1,-1,-1,-1}

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

  19. {-1,4,-1,-1,-1,-1,-1,-1,-1,-1}

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

  20. {-1,5,-1,-1,-1,-1,-1,-1,-1,-1}

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

  21. {-1,6,-1,-1,-1,-1,-1,-1,-1,-1}

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

  22. {-1,7,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {1, 7, 3, 2, 1, 1, 1, 2, 1, 1 }

  23. {-1,11,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 11, 1, 1, 1, 1, 1, 1, 1, 1 }

  24. {-1,-1,0,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  25. {-1,-1,1,-1,-1,-1,-1,-1,-1,-1}

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

  26. {-1,-1,2,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 0, 2, 0, 0, 0, 0, 0, 0, 0 }

  27. {-1,-1,3,-1,-1,-1,-1,-1,-1,-1}

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

  28. {-1,-1,-1,0,-1,-1,-1,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  29. {-1,-1,-1,1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 11, 1, 1, 1, 1, 1, 1, 1, 1 }

  30. {-1,-1,-1,2,-1,-1,-1,-1,-1,-1}

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

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

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

  32. {-1,-1,-1,-1,0,-1,-1,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  33. {-1,-1,-1,-1,1,-1,-1,-1,-1,-1}

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

  34. {-1,-1,-1,-1,2,-1,-1,-1,-1,-1}

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

  35. {-1,-1,-1,-1,-1,0,-1,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  36. {-1,-1,-1,-1,-1,1,-1,-1,-1,-1}

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

  37. {-1,-1,-1,-1,-1,2,-1,-1,-1,-1}

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

  38. {-1,-1,-1,-1,-1,5,-1,-1,-1,-1}

    Returns: { }

  39. {-1,-1,-1,-1,-1,-1,0,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  40. {-1,-1,-1,-1,-1,-1,1,-1,-1,-1}

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

  41. {-1,-1,-1,-1,-1,-1,2,-1,-1,-1}

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

  42. {-1,-1,-1,-1,-1,-1,-1,0,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  43. {-1,-1,-1,-1,-1,-1,-1,1,-1,-1}

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

  44. {-1,-1,-1,-1,-1,-1,-1,2,-1,-1}

    Returns: {1, 7, 3, 2, 1, 1, 1, 2, 1, 1 }

  45. {-1,-1,-1,-1,-1,-1,-1,-1,0,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  46. {-1,-1,-1,-1,-1,-1,-1,-1,1,-1}

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

  47. {-1,-1,-1,-1,-1,-1,-1,-1,-1,0}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  48. {-1,-1,-1,-1,-1,-1,-1,-1,-1,1}

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

  49. {0,-1,-1,-1,-1,-1,-1,-1,-1,-1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  50. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  51. {1, 11, 0, 1, 1, 1, 1, 1, 1, 1}

    Returns: {1, 11, 0, 1, 1, 1, 1, 1, 1, 1 }

  52. {0, -1, -1, 1, -1, -1, -1, -1, -1, -1}

    Returns: {0, 11, 1, 1, 1, 1, 1, 1, 1, 1 }

  53. {-1, -1, -1, -1, -1, -1, -1, 2, -1, -1 }

    Returns: {1, 7, 3, 2, 1, 1, 1, 2, 1, 1 }

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