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Problem Statement for "CraneSort"

Problem Statement

We are loading a container ship with a single crane. The containers are on the dock, adjacent to each other in a line. Each container is owned by one of our 4 customers. We need to rearrange them so that the containers are still in a line with no gaps located somewhere on the dock, with each customer's containers adjacent to each other.

We move a container by using our crane to pick up a single container and place it somewhere on the dock (but not on top of another container). The problem is to minimize the number of moves.

The String containers shows the original order of the containers, with each container appearing as 'A','B','C', or 'D' according to which of our customers is the owner. Return the minimum number of moves required.

Definition

Class:
CraneSort
Method:
moves
Parameters:
String
Returns:
int
Method signature:
int moves(String containers)
(be sure your method is public)

Constraints

  • containers will contain between 1 and 50 characters, inclusive.
  • containers will contain only the characters 'A','B','C', or 'D'.

Examples

  1. "CBBADDD"

    Returns: 0

    The containers are already arranged so that each customer's containers are adjacent.

  2. "ABCAA"

    Returns: 1

    We can move the leftmost container to the right end of the line.

  3. "CCCCBAAABA"

    Returns: 3

    We can move the first B to a temporary location somewhere on the dock. Then move the rightmost A to the spot where that B used to be. Finally move the B from its temporary location to the right end of the line, resulting in CCCCAAAABB. (There are other ways to do it in 3 moves.)

  4. "ABCDABCDABCDABCDABCDABCDABCDABCDABCDABCDABCDABCDAB"

    Returns: 37

  5. "ABCDABCDABCCCCCCCCCCCCCDABCDABCDABCDABCDABCDABCDAB"

    Returns: 27

  6. "ABCDA"

    Returns: 1

  7. "AAAAABAAAABA"

    Returns: 3

  8. "ABCDCD"

    Returns: 3

  9. "ABA"

    Returns: 1

  10. "D"

    Returns: 0

  11. "DA"

    Returns: 0

  12. "DAC"

    Returns: 0

  13. "ABDABADB"

    Returns: 4

  14. "ADCBCDAD"

    Returns: 4

  15. "ABCDCDCBA"

    Returns: 6

  16. "DBBACDAADD"

    Returns: 4

  17. "BABABDCBBB"

    Returns: 4

  18. "BCCABCCCCAAACBABADBCADABDCCDCDCBCBADDCCCDCBDDBBBAB"

    Returns: 29

  19. "DADDCCCDCADABBDAAACDDAACDDCCDCDACCDBCDBADDDCCCDCDB"

    Returns: 30

  20. "DBDBCCACABCAABBABBACCDCABACCADCCBADCDCAACDBBBBCCBD"

    Returns: 30

  21. "DDDCDBAACBACDBAAAAABCADBDBCCDADBBAADADCCBABAADBDCB"

    Returns: 31

  22. "DCCCABBADADACDACBADBCABDDBDBCBDBDBCDCBDBBCCDABBCDD"

    Returns: 31

  23. "DBACDCDACBDCAADCCDBADDDDDAABBBBCDDCBBBABDADBDDDDDD"

    Returns: 29

  24. "AACABCDAAADDDDDBCDCACDCBABDDCAABADAACBCBACBCBBCACC"

    Returns: 30

  25. "CCCCBCCCACDDDDCAADACDCBCDAABDACABABCCBACCDCCBDDACC"

    Returns: 29

  26. "BABBACABAAAABAABBABBBABABBABBABBABCBCAABAAAAACAAAC"

    Returns: 25

  27. "AABBAAACBBBBBBBBACCAABAABAAABBAABBCAAAABBBABBBBBCB"

    Returns: 26

  28. "AACDADCDABAAAAABDCDDADADABDDADBDCCCDBAACAADCBACDBC"

    Returns: 27

  29. "DCCABBBDDDCCBAADACABAACAABBDADACCCBABCABDDABDABDAD"

    Returns: 28

  30. "DACDACBACB"

    Returns: 7

  31. "DDCBBBADCACADCBBDBACDAACBDCDBAABCBABDDAACBBCDDADBC"

    Returns: 34

  32. "ACCCCCCBDDACCCDBBCAABABAAABAABDBDDBDDDDDABDDDBADAD"

    Returns: 23

  33. "BDDAAABBCDDDCBBBDCDCCCBCBCCBDCCCDCCCCCBBCBADBBBBDC"

    Returns: 22

  34. "BCBBBBADCABABCCDACACCADAAAADAADBAAAAAAADBDDDADCBBD"

    Returns: 20

  35. "DDDDDDCADDDBBDCBCCCCABCCDABDCCDBBBBABBBAAAAAACCAAA"

    Returns: 18

  36. "DAAAADDAADAAAAAADAAABADAADAACAAADAAAAAAADADAAAACAA"

    Returns: 16

  37. "CACCACCCCCACCCCCCCCCCCCCCCCCCCDCCCCCCACCCCCAACCCAC"

    Returns: 10

  38. "ABBAABABDBBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBDBBBBBBBB"

    Returns: 7

  39. "AAAAAAAAAAAAAAAAACAAAAAAAAAAAAAAAAAAAAAAABCAAADAAA"

    Returns: 6

  40. "DBAADDBADBCDBC"

    Returns: 6

  41. "DDCADDAADADADAAAACCAADCABAADCAAAADADDDBC"

    Returns: 21

  42. "CDCABCABCDD"

    Returns: 6

  43. "DCCDBCCDDDCCABCBDDCCDCCDCDDDDDCCDDBDABDBCCD"

    Returns: 22

  44. "CDDABBBBBBBABDBABDABDBDBDDBADDBDDDDBBDAAAAABDBD"

    Returns: 21

  45. "CBBCACBBAAACAABBCCBACBBADBCDBCABAABCB"

    Returns: 23

  46. "AACCACCCCACABDCBAAAAAACACACAABADAAACCCA"

    Returns: 17

  47. "DABCDBDDBACCCACDACAAADADADBABBCA"

    Returns: 16

  48. "CCCDCCCCCCCCCCCCBCCCB"

    Returns: 4

  49. "CAAACCCAACACCCCDCCCCCCACCCA"

    Returns: 8

  50. "ACACBABAAACBBAA"

    Returns: 7

  51. "DCDBBCBAABBDBB"

    Returns: 6

  52. "CCCDCDAAADD"

    Returns: 4

  53. "CBBB"

    Returns: 0

  54. "ACAABDBDBBCBBDAB"

    Returns: 8

  55. "ABAABABBABADBBCCAAABBABABAACBDAABABDACDB"

    Returns: 21

  56. "ABBBABBCCCABBCBABCCDBBBCBBCCBCBBDBBBCBAACBCBCCCB"

    Returns: 27

  57. "DBBCBCABBCACCDDDD"

    Returns: 7

  58. "DDCBDDBCADDBDDDDDDDDDCDADD"

    Returns: 9

  59. "BBCBCAADCBCBBCCBBDADABCCBBBDBBBBBDCBBBDBDABBBCBA"

    Returns: 24

  60. "CCCCDBCCAABDCCADAAAABBACABBCBADACDACA"

    Returns: 20

  61. "DDDCCDDADCCDDCDCDBDADDAADCDDDDDDADAADDDD"

    Returns: 19

  62. "DDBBBABDBBABABBADADBDBBBABDBAABDDDADBBBDB"

    Returns: 22

  63. "CBBBAADACCDDBDCDAD"

    Returns: 8

  64. "CBABCABACBAAABDBCBCABC"

    Returns: 12

  65. "CAAADABDDACADADCACA"

    Returns: 10

  66. "B"

    Returns: 0

  67. "ADDACDAADADCCADDCDDDACDCCBDADDDAA"

    Returns: 17

  68. "ACBBBDCBBAAAACBAABADBBA"

    Returns: 11

  69. "BDCBBDDAD"

    Returns: 4

  70. "CAACDDCBCAADCDDAADADDDADBDBADBCBC"

    Returns: 18

  71. "DCCBCDCCA"

    Returns: 5

  72. "BAABCBACADACAACAAAAABAADABC"

    Returns: 12

  73. "DCCDB"

    Returns: 2

  74. "CACADCBBCAADBACCAABDBCCAACCBBDACCCCDD"

    Returns: 22

  75. "BBBCDDDADBACBDDCABBCDADDDBDADBDDADDBDDD"

    Returns: 21

  76. "BCAACAAABAAACCACBCCCABACBCCB"

    Returns: 12

  77. "DAABDDDDDADDADBAADDBDDABDDABDDBDBBDDDAD"

    Returns: 19

  78. "BBCBBCBBCDDBAACACCBBACBAADCCB"

    Returns: 15

  79. "AADDDDDDDDDDADDCADAABDBDDDDDABBDDDAABDABBDDDDCBDBD"

    Returns: 25

  80. "CCACACCBBCCCCCCCC"

    Returns: 6

  81. "AAABCAACCAABBABDCCCCCCDDACCACBCCC"

    Returns: 14

  82. "ADBABDBADACADA"

    Returns: 7

  83. "AADDBBBBBBDACBACACCBCABCDA"

    Returns: 13

  84. "AAAACAAAAAACACCAABAAABCAACCBACA"

    Returns: 12

  85. "CCABBCABBBCBCDBCDAABDAAAACBDDCDDBBDDCC"

    Returns: 20

  86. "ADBDBBDDDDBCBDAAAAABADDBADDBB"

    Returns: 14

  87. "ACDDBDBDCBDDCDCCDCDBD"

    Returns: 10

  88. "CBBBABADBDBBDDBBCABBABBBDD"

    Returns: 13

  89. "BADBBADACDAAABBABDAABDCDBCBDCADBBADBAA"

    Returns: 23

  90. "CCDCACBDCDCCBDCDCCDD"

    Returns: 10

  91. "DDBCDDCDCDDDB"

    Returns: 5

  92. "BBCBABCC"

    Returns: 3

  93. "DAAAADAC"

    Returns: 3

  94. "CDBDADACCABD"

    Returns: 6

  95. "ADABAAAAAAADAABAABBAAABAABADBBAAAAB"

    Returns: 14

  96. "CCB"

    Returns: 0

  97. "CAAACCDDDDDAADDACDACADCADBDCAAADDDDDDDDDD"

    Returns: 21

  98. "BBDDDDDDBCBDDDDCBDBBC"

    Returns: 9

  99. "CAADCDDDBAACDDAACDAACAAADBDABBADAAAAAACDCBDAADCDCD"

    Returns: 27

  100. "ACABBCACCBCABCAACCCBBCACCCA"

    Returns: 14

  101. "BBADABDAA"

    Returns: 4

  102. "DCDADCCD"

    Returns: 3

  103. "BAADABBBBBBBDBBBDB"

    Returns: 5

  104. "CCCCACADCCCAAC"

    Returns: 6

  105. "CCCDDBCDDBCDCCCDDDCDCBACDBDC"

    Returns: 16

  106. "BCDCADADCD"

    Returns: 5

  107. "DDDABCBADBBBCBCCABCAAAADDAABDDDCABBBCBBD"

    Returns: 21

  108. "AAAAACAAADACBDDBBCBABACCDBBAACCDBDDACCDBACDABACA"

    Returns: 27

  109. "BBCCCCBCBBCCBBBCCCCBC"

    Returns: 10

  110. "ADDDDBD"

    Returns: 2

  111. "DDCBCDCDCDCDDACCBDDDDBBDDDDC"

    Returns: 14

  112. "ABBABAAACBBBAAABBBCDBBDBBBABDBBAAABBDDBDDBACABBBBA"

    Returns: 26

  113. "CBBCDADDBBCBDDABDDDBBDCDCDDABBDDDDDBCDDCDACBBDBAD"

    Returns: 27

  114. "DAADADDBAD"

    Returns: 4

  115. "DCDACCCAACA"

    Returns: 5

  116. "BDCCDDD"

    Returns: 2

  117. "ADDDDDDDBAADBDDADDDDDAD"

    Returns: 11

  118. "ADBCDBDDADCBDADDCAADDCBDD"

    Returns: 15

  119. "DDACDCDDCDDCCDD"

    Returns: 7

  120. "CBAD"

    Returns: 0

  121. "DCBAADBBACABAADCAD"

    Returns: 10

  122. "CABCACAABABB"

    Returns: 6

  123. "BBDDBDBBDADDDBDDDD"

    Returns: 7

  124. "CCCCCBDCCBBC"

    Returns: 4

  125. "ADCDAADBCAABBCDCAADABDCDBDDABCADDDDBBDDDDDCADBBDDC"

    Returns: 28

  126. "DDAADDBDADDBDB"

    Returns: 6

  127. "BDABBBBCCBACBBABDDCCBCBBADCBAABCABC"

    Returns: 18

  128. "AADBDBBBCBABBDDDADDDDDDDBDBDCBABCAABBA"

    Returns: 16

  129. "DAAADBCDAAACCDDDAADDBACCADDAACBBAAD"

    Returns: 20

  130. "DDDDC"

    Returns: 0

  131. "CDDADBBADBBADDDBAACAD"

    Returns: 11

  132. "AACCCBBCCAAC"

    Returns: 5

  133. "ABAABB"

    Returns: 2

  134. "BADACADABD"

    Returns: 5

  135. "CAAAADCADDACCCACDACAABDAACCAAACCCCAACCCCCCADADAC"

    Returns: 23

  136. "CBCDCCBCDBDDB"

    Returns: 6

  137. "ACCADCAAABAAABAAABAACA"

    Returns: 9

  138. "CDDDADBACDADADA"

    Returns: 7

  139. "CABAACA"

    Returns: 3

  140. "AAABBBA"

    Returns: 1

  141. "AAAABAAAABBBBDBBBBCCCCACCCCDDDDCDDDD"

    Returns: 5

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