Statistics

Problem Statement for "CircleDance"

Problem Statement

Given a group of dancers' heights, arrange a circle formation that minimizes the maximum height difference between each pair of neighboring dancers. Write a class CircleDance with a method arrangeDancers that takes a int[], heights, and returns the maximum height difference between neighboring dancers.

Definition

Class:
CircleDance
Method:
arrangeDancers
Parameters:
int[]
Returns:
int
Method signature:
int arrangeDancers(int[] heights)
(be sure your method is public)

Constraints

  • heights will contain between 3 and 20 elements inclusive.
  • Each element of heights will be between 150 and 210 inclusive.

Examples

  1. {180,183,178,185}

    Returns: 5

    The dancers may be arranged in a circle like this: 180 / \ 185 178 \ / 183 Their height differences are shown below: 180 (5)/ \(2) 185 178 (2)\ /(5) 183 The maximum difference is 5. Other arrangements may not lead to an optimal solution. For example, the following one has a maximum difference of 7: 180 (3)/ \(2) 183 178 (2)\ /(7) 185

  2. {170,180,190}

    Returns: 20

    Any arrangement is equivalent to the following one: 180 (10)/ \(10) 170 - 190 (20) So the result is 20.

  3. {180,180,180,180,180}

    Returns: 0

  4. {184,165,175,186,192,200,176,192,194,168,205,201}

    Returns: 10

  5. {155,192,169,162,174,155,180,184,150,180,192,198,199}

    Returns: 14

  6. {171,189,206,164,196,205,168,175,202,170,159,151,173,153,198,184,169,168,153}

    Returns: 14

  7. {173,163,156,199,156,193,206}

    Returns: 30

  8. {179,189,156,150,186,199,170,171,202,208,205,151,207,172,193}

    Returns: 19

  9. {161,154,164}

    Returns: 10

  10. {159,171,183,154}

    Returns: 24

  11. {152,158,179,187,174,206,165,195,161,167,186,182,174,153,203}

    Returns: 16

  12. {188,181,196,183,167,175,189,181,168,210}

    Returns: 21

  13. {204,161,207,165,179,164,151,178,160,180,194,157,173}

    Returns: 24

  14. {209,171,182,180,165,190,199,151,153,207,169,177}

    Returns: 17

  15. {154,208,160,204,190,206,210,156,169,208,197}

    Returns: 30

  16. {151,173,151}

    Returns: 22

  17. {179,151,168,157}

    Returns: 22

  18. {189,155,191,203,155,169,175,175,205,183,185,200,171,198}

    Returns: 16

  19. {162,151,187,209,197,172,159,189,194,163,186}

    Returns: 23

  20. {172,208,153,176,197,205,206,165,156,172,189,210}

    Returns: 21

  21. {159,168,175,209,203,153,207,159,198}

    Returns: 30

  22. {195,190,190,201,210,168}

    Returns: 22

  23. {201,169,150,163,161,171}

    Returns: 32

  24. {182,198,208,164,209,185,204,157,199,164,169,179,166,158,190,152}

    Returns: 13

  25. {210,209,208,207,206,205,204,203,202,201,200,199,198,197,195}

    Returns: 3

  26. {210,209,208,207,206,205,204,203,202,201,200,199,198,197,195,194}

    Returns: 3

  27. {170, 180, 190 }

    Returns: 20

  28. {184, 165, 175, 186, 192, 200, 176, 192, 194, 168, 205, 201 }

    Returns: 10

  29. {180, 183, 178, 185 }

    Returns: 5

  30. {156, 200, 197, 203, 199, 198, 186, 196, 189, 205, 190, 156, 189, 190, 191, 192, 193, 194, 200, 210 }

    Returns: 33

  31. {150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150 }

    Returns: 0

  32. {151, 161, 171, 210, 198, 167, 188, 197, 190, 200, 209, 208, 150, 152, 187, 199, 201, 205, 153, 154 }

    Returns: 20

  33. {150, 150, 151, 151, 152, 152, 153, 153, 154, 154, 155, 155, 156, 156, 157, 157, 158, 158, 159, 159 }

    Returns: 1

  34. {184, 165, 175, 186, 192, 200, 176, 192, 194, 168, 205, 201, 201, 201, 201, 201, 201, 201, 201, 201 }

    Returns: 10

  35. {150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 169, 168, 167, 166, 165, 164, 163, 162, 161, 160 }

    Returns: 2

  36. {202, 192, 152, 198, 152, 173, 203, 174, 166, 195, 200, 168, 193, 202, 163, 187, 189, 185, 157, 166 }

    Returns: 13

  37. {200, 199, 197, 194, 190, 185, 179, 172, 160, 159, 157, 157, 190, 160, 159, 158, 157, 156, 155, 154 }

    Returns: 19

  38. {184, 165, 175, 186, 192, 200, 176, 192, 194, 168, 205, 201, 176, 195, 205, 201, 194, 184, 181, 199 }

    Returns: 10

  39. {184, 165, 175, 186, 192, 200, 176, 192, 194, 168, 205, 201, 175, 185, 186, 194, 195, 195, 187, 193 }

    Returns: 10

  40. {151, 152, 153, 160, 171, 184, 192, 193, 194, 195 }

    Returns: 24

  41. {161, 204, 187, 155, 199, 201, 165, 188, 174, 150, 191, 159, 163, 209, 187, 185, 162, 159, 173, 191 }

    Returns: 13

  42. {184, 165, 175, 186, 192, 200, 176, 192, 194, 168, 205, 201, 180, 180, 180, 180, 180, 180, 180, 180 }

    Returns: 10

  43. {184, 165, 175, 186, 192, 200, 176, 192, 194, 168, 186, 162, 177, 182, 199, 209, 179, 199, 192, 166 }

    Returns: 10

  44. {177, 196, 157, 195, 172, 182, 154, 207, 179, 164, 152, 186, 160, 162, 160, 192, 196, 178, 192, 153 }

    Returns: 13

  45. {155, 155, 155, 167, 194, 185, 175, 201, 193, 167, 201, 209, 168, 183, 192, 183, 164, 193, 200, 192 }

    Returns: 15

  46. {157, 210, 201, 170, 191, 195, 181, 200, 163, 188, 191, 166, 206, 177, 184, 174, 204, 206, 163, 202 }

    Returns: 9

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