Statistics

Problem Statement for "TandemRepeats"

Problem Statement

An important problem in DNA analysis is finding tandem repeats. A tandem repeat occurs when a base sequence of nucleotides appears twice in a row. (In this problem, a base sequence is simply a contiguous substring and a nucleotide is simply a letter.) For example, in the DNA sequence "GATCATCA", the base sequence "ATC" appears twice in a row. In contrast, "ATCGATC" is not a tandem repeat of the base sequence "ATC" because of the 'G' in between the two copies.

Real DNA often contains errors in which one nucleotide is substituted for another. A k-approximate tandem repeat occurs when a base sequence of nucleotides appears twice in a row, allowing the second copy of the base sequence to differ from the first copy in at most k nucleotides. For example, in the DNA sequence "GATCATGA", the base sequence "ATC" is immediately repeated with a single error as "ATG". Thus, "ATCATG" is a 1-approximate tandem repeat. Note that both copies of the base sequence must be the same length.

Given a DNA sequence dna (represented as a String) and a limit k on the number of errors, find the length of the longest sequence that appears in dna as the base sequence of a k-approximate tandem repeat. Note that a k-approximate tandem repeat contains at most k errors, but it is allowed to contain fewer errors.

Definition

Class:
TandemRepeats
Method:
maxLength
Parameters:
String, int
Returns:
int
Method signature:
int maxLength(String dna, int k)
(be sure your method is public)

Constraints

  • dna contains between 2 and 50 characters, inclusive.
  • Every character in dna is a 'G', 'A', 'T', or 'C'.
  • k is between 0 and 5, inclusive.

Examples

  1. "GATCATCA"

    0

    Returns: 3

    A tandem repeat with a base sequence of length 3 is "ATCATC", with base sequence "ATC".

  2. "GATCATGA"

    1

    Returns: 3

    A 1-approximate tandem repeat is "ATCATG". The base sequence "ATC" is repeated with a single error.

  3. "GATCATGA"

    0

    Returns: 0

    This example has no tandem repeats.

  4. "AGAGAAAGAA"

    3

    Returns: 5

  5. "ATTAGCATTGCACACCTTGAGGACTTAGACAAACCTAGTACACAGGTGTA"

    5

    Returns: 11

  6. "AATAGGACCCATTTTAGGGGGACCCCCC"

    5

    Returns: 6

  7. "TT"

    0

    Returns: 1

  8. "TG"

    0

    Returns: 0

  9. "GC"

    1

    Returns: 1

  10. "GC"

    5

    Returns: 1

  11. "CTGCTTCCAACTTCTAAAGCCCAATGCGCTTTTATTCACCCCCAAGAACT"

    5

    Returns: 8

  12. "GCTGGCAGCAAACGAGGGTTGGAATCAGATCGGCGACTTTCGTGACAACG"

    2

    Returns: 5

  13. "CAGCTCCTTGTAGCGTGCGGCTTTCCCGTCGACAGACAGCCATGACGATT"

    4

    Returns: 7

  14. "CCTCGTGATCGCATTTCGGTCCGTTGCATAGGCGCGGCTGGTTAGTAGGG"

    0

    Returns: 3

  15. "CATGTGCATGGATTAGTGGCTGGTGAGAAAAGACCGCGAGCACATCCAGT"

    5

    Returns: 11

  16. "ATCCACAAAACTCTCTGCTTCTCAGACCCCTGCCTTGTGGTTAGATGTTC"

    4

    Returns: 8

  17. "TCCCATATAATAATGGCCGGGCCTCGTCCCTAATCGAACGAGACAGTCAG"

    0

    Returns: 3

  18. "AGATGCGTAGTAACGTGCGTACTACCTGACTACACGCCCTGATGCGTTTA"

    1

    Returns: 4

  19. "TGCCTGATTGCCACCACATGGCTAGCACTTCGGTCACGGGGCTACCTCAG"

    0

    Returns: 3

  20. "TGCGGACAACATACTCTGCAGCGTGTATCATTGAAGGACTAGACTCCGAC"

    3

    Returns: 7

  21. "GTTAGCGTGTCATGGGCATCCCTTAGTTAGCGTGTCATGGGCATCCCTTA"

    0

    Returns: 25

  22. "GTTAGCGTGTCATGGGCATCCCTTAGTTTGCGTGTCATGGGCATCCCTTA"

    2

    Returns: 25

  23. "ATCAT"

    1

    Returns: 1

  24. "ATCGGTACCGTCGAGCGTCTTCATAGTTAGCGTGGT"

    0

    Returns: 1

  25. "GCCCTACCTCTCCGAAGGGCCAACTTCTCAGTCGTTG"

    2

    Returns: 6

  26. "TATCCATCGAATAATCGCGGACTAACTTCGACAACGAC"

    5

    Returns: 11

  27. "GACATTTCACACGGATTCGTCCAGCTCCCACCCCTGCAA"

    1

    Returns: 4

  28. "TGCAATACCGCTAACCATCGTTAGATGACTAACAGGACTA"

    4

    Returns: 10

  29. "CGAGAAAATGAGATTCGTTTACTGCTCAGGAACTCGTTTTA"

    1

    Returns: 3

  30. "CGGAGTTGATAAGTGTTGGGTAGGCGCCGGGCTCGTCAGTGG"

    0

    Returns: 2

  31. "TGGGCCGAGTTGCATTTGTGAAAAGTGGGAACTGAGCCGACTT"

    5

    Returns: 9

  32. "GTCCACACTTGAAACTAGGGACCCATGCTGGGGCTGGTAGGAAG"

    0

    Returns: 2

  33. "ATGACGTGCTGTTTTTACTGAATCGCAAGTAGCCTCGGCGTCCAC"

    1

    Returns: 3

  34. "CTGACAGTTCACGGCCGATTAGTATTGGCGCACGATATCGCATCCC"

    5

    Returns: 10

  35. "GGATGACATGGAAGAGGGATTTTCTACGTTCTACCAACTTTTATATT"

    3

    Returns: 7

  36. "CGGCGAGTACAACTTAAATGGCTCTACGTTCCATTAGTCGCGCCAGAT"

    0

    Returns: 2

  37. "GGTGCTAGGTCCCATATGAGAGGGCGAACAGGTCTGTACTGATGCCTAG"

    1

    Returns: 3

  38. "TGCTGTGTACTGACGTTGGAGAACACCCGACGAAATCCAGCGCTGGGCCT"

    2

    Returns: 5

  39. "ATTAGCATTGCACACCTTGAGGACTTAGACAAACCTAGTACACAGGTGTA"

    5

    Returns: 11

  40. "AA"

    0

    Returns: 1

  41. "AAAAAA"

    1

    Returns: 3

  42. "CC"

    1

    Returns: 1

  43. "GATCAGATCGACAGGGGACGATACAGATTAGACGAGATTAAACCGGATTA"

    4

    Returns: 10

  44. "AA"

    5

    Returns: 1

  45. "GCA"

    5

    Returns: 1

  46. "AG"

    1

    Returns: 1

  47. "AGAGAAAGAA"

    3

    Returns: 5

  48. "AT"

    1

    Returns: 1

  49. "AA"

    1

    Returns: 1

  50. "AAA"

    5

    Returns: 1

  51. "GATCATCA"

    0

    Returns: 3

  52. "GG"

    1

    Returns: 1

  53. "AGTCTAGCC"

    0

    Returns: 1

  54. "AA"

    2

    Returns: 1

  55. "AGTCCTGGTCTACTA"

    0

    Returns: 3

  56. "GATC"

    4

    Returns: 2

  57. "GATCC"

    0

    Returns: 1

  58. "GATC"

    1

    Returns: 1

  59. "GG"

    0

    Returns: 1

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