Statistics

Problem Statement for "TeamPhoto"

Problem Statement

It's time to line up for the team photo. We want all the team members, plus the head coach and the two assistant coaches to be in the photo. We want the head coach in the middle and the two assistant coaches on the two ends. But we don't want to have much disparity in heights between adjacent people.

Let's line up to minimize the sum of the absolute height differences of adjacent people. If there is an even number of people, the coach can go in either center position. Create a class TeamPhoto that contains method minDiff that takes int[] height, the heights of all the people, and returns the minimum possible sum of adjacent absolute height differences.

height lists the coach first, then the two assistant coaches, then the team members.

Definition

Class:
TeamPhoto
Method:
minDiff
Parameters:
int[]
Returns:
int
Method signature:
int minDiff(int[] height)
(be sure your method is public)

Constraints

  • height has between 5 and 50 elements inclusive
  • each element of height is between 10 and 100 inclusive

Examples

  1. {80,82,81,50,90,65}

    Returns: 79

    The coach has a height of 80 and must be in one of the two middle positions, with the assistant coaches (82 and 81) on the two ends. The best lineup is 81,65,50,80,90,82 with the minDiff calculated as |81-65| + |65-50| + |50-80| + |80-90| + |90-82| = 79. There are other ways to achieve this minDiff.

  2. {70,82,91,50,50,50,50,50,50}

    Returns: 113

    Line up in the order 82,50,50,50,70,50,50,50,91

  3. {10,100,30,22,23,24,25,26,27,28,29,30,31,32}

    Returns: 110

  4. {100,30,10,22,23,24,25,26,27,28,29,30,31,32}

    Returns: 164

  5. {30,10,100,22,23,24,25,26,27,28,29,30,31,32}

    Returns: 94

  6. {13, 17, 11, 12, 10}

    Returns: 10

    One optimal way to line up is 17, 12, 13, 10, 11 making the sum of the absolute differences 5 + 1 + 3 + 1 = 10

  7. {10,10,10,25,26,26}

    Returns: 62

  8. {10,10,10,25,26,26,40}

    Returns: 92

  9. {10,12,11,25,10,26,40}

    Returns: 87

  10. {20,12,31,18,22,25,29}

    Returns: 23

  11. {30, 92, 50, 35, 36, 37, 38,39,40,52,53,54,55,60,61,62, 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,71,72,73,74,75,76,77,78,89,88,87,86,44,12,62}

    Returns: 122

  12. {17,50,60,52,30,53}

    Returns: 76

  13. {17,50,13,52,49,53}

    Returns: 107

  14. {60,30,20,13,14,15,16,17}

    Returns: 112

  15. {60,30,15,13,14,15,16,17}

    Returns: 107

  16. {50,30,70,20,60,80}

    Returns: 80

  17. {28,61,60,42,98,78,99,25,61,76,32,86,95,77,75,27,68,54,67,96,62,24,56,81,84,57,17,80,71,51,100,73,86,91,26,37,39,57,35,86,85,65,30,88,10,62,73,92,31,90}

    Returns: 193

  18. {32,92,29,34,89,33,21,56,68,66,51,22,71,59,80,79,74,66,40,38,36,51,45,46,75,71,17,92,36,91,52,85,45,45,81,50,53,29,20,67,87,13,14,61,14,39,33,77,45}

    Returns: 133

  19. {26,12,52,25,11,78,27,73,77,90,12,96,54,63,21,38,61,27,70,78,28,91,58,54,67,88,22,94,56,37,85,80,68,66,12,63,50,95,41,88,50,99,58,20,92,27,37,73,62,47}

    Returns: 200

  20. {82,32,16,77,77,79,97,16,99,30,58,89,71,11,47,33,77,23,84,81,35,100,65,62,80,64,18,50,97,16,65,32,78,28,35,44,58,75,16,46,68,59,84,34,99,48,82,95,33}

    Returns: 162

  21. {88,88,38,49,63,34,52,73,30,74,71,42,51,30,48,84,22,55,61,18,99,53,36,96,91,88,79,31,31,56,70,65,12,74,54,57,71,74,39,84,72,51,19,25,37,98,85,27,89,58}

    Returns: 186

  22. {99,83,78,34,33,28,74,76,58,65,70,42,91,96,33,85,28,16,94,70,24,60,74,69,90,65,70,23,25,95,72,43,33,99,12,56,56,59,18,70,80,24,26,26,30,52,88,38,47}

    Returns: 219

  23. {20,11,93,17,75,49,100,43,74,62,95,71,97,80,60,39,72,16,88,83,72,42,17,22,36,15,16,38,69,41,41,73,32,31,11,37,41,10,65,67,91,78,74,29,51,95,85,14,85,22}

    Returns: 156

  24. {57,62,75,78,69,39,46,25,86,16,79,38,92,90,86,37,36,39,72,58,43,34,81,53,65,63,48,60,96,99,65,52,35,38,43,54,84,14,88,12,71,17,59,50,85,16,61,57,24}

    Returns: 161

  25. {54,54,25,46,45,35,82,46,17,62,76,86,60,19,54,12,23,38,11,45,22,24,14,24,34,25,90,96,82,21,18,62,76,61,55,98,92,86,92,55,34,42,81,92,38,23,40,34,80,94}

    Returns: 161

  26. {52,57,98,44,22,47,88,54,84,70,58,33,75,90,55,59,26,47,13,18,86,43,15,45,96,73,60,52,56,21,55,19,55,88,19,89,48,64,59,54,32,67,44,10,55,76,16,92,86}

    Returns: 135

  27. {56,23,64,43,13,12,99,35,76,25,13,95,48,71,54,32,98,23,28,41,62,93,11,16,77,12,29,97,51,11,35,27,13,72,97,25,97,96,10,89,63,75,77,22,16,35,84,63,100,98}

    Returns: 149

  28. {40,96,93,23,78,50,45,99,33,55,54,95,97,48,56,56,19,31,17,67,99,37,40,79,28,76,78,81,69,71,66,16,13,42,14,92,48,39,95,11,14,89,26,52,74,86,36,46,86}

    Returns: 173

  29. {62,28,93,50,42,17,52,97,22,77,37,27,72,26,28,68,67,78,61,34,34,52,90,40,25,86,58,78,75,86,86,76,15,55,13,59,93,87,46,82,63,23,93,58,83,24,40,93,82,84}

    Returns: 105

  30. {65,78,60,75,34,19,86,94,81,19,55,37,13,16,70,45,25,84,28,73,71,46,40,29,39,98,59,83,75,36,20,17,39,61,51,45,11,50,13,67,49,15,18,33,26,33,84,66,28}

    Returns: 196

  31. {46,29,15,32,30,21,10,75,79,24,16,43,33,65,57,78,84,88,63,65,52,35,65,24,12,64,85,10,41,21,63,86,32,46,45,56,65,96,35,88,97,55,81,70,22,92,83,83,58,13}

    Returns: 180

  32. {61,84,64,33,12,47,55,18,94,55,87,30,89,87,86,68,100,23,26,98,69,53,62,97,19,33,93,31,96,81,37,78,74,76,14,97,82,89,44,88,85,11,83,100,24,73,95,48,23}

    Returns: 168

  33. {28,49,84,99,90,13,80,21,30,55,76,35,98,42,61,80,95,63,10,19,27,55,73,98,53,19,98,30,33,78,33,52,47,70,12,98,87,81,55,88,54,24,98,68,68,74,48,42,99,59}

    Returns: 155

  34. {33,27,11,46,65,98,94,14,99,39,96,30,52,53,82,14,78,21,74,29,81,45,47,24,80,84,27,67,49,71,17,14,71,40,29,45,68,98,38,21,16,77,11,70,11,59,58,13,80}

    Returns: 192

  35. {88,74,86,43,36,79,78,29,39,60,48,11,55,19,59,48,24,42,79,15,24,53,22,72,69,15,62,82,93,97,10,75,88,71,69,42,36,82,43,95,31,98,39,22,48,79,57,28,21,51}

    Returns: 234

  36. {46,72,59,53,52,16,24,88,77,13,23,12,15,59,83,86,87,75,30,76,99,75,57,82,80,96,38,15,57,90,36,11,56,61,15,16,71,95,67,52,66,99,67,80,31,30,24,10,71}

    Returns: 165

  37. {15,27,40,93,28,44,82,88,60,18,16,46,41,43,26,72,88,84,57,34,44,40,48,89,92,59,30,88,82,46,85,67,65,96,87,70,97,14,54,13,23,73,82,86,59,94,40,25,94,71}

    Returns: 219

  38. {63,83,14,25,46,31,29,91,52,21,58,43,59,85,54,67,21,24,83,71,89,19,33,37,53,15,94,98,77,45,82,11,85,27,60,87,97,66,97,92,100,13,48,90,78,75,30,70,16}

    Returns: 117

  39. {25,38,61,43,49,43,86,10,87,10,70,66,77,72,84,20,32,20,23,69,54,57,66,33,54,95,76,61,92,55,91,29,12,65,66,94,49,76,72,67,84,26,43,41,67,99,95,48,56,57}

    Returns: 193

  40. {57,33,42,60,81,60,70,98,70,99,46,26,17,73,56,47,15,62,32,49,75,95,88,92,91,95,78,40,71,82,39,32,94,46,77,23,94,17,69,19,95,56,96,59,55,41,16,39,43}

    Returns: 165

  41. {99,77,75,51,17,99,99,15,85,63,14,59,75,21,94,93,37,27,39,76,35,38,12,86,10,78,84,93,22,35,45,51,51,78,61,68,26,29,26,44,88,32,74,41,60,12,95,93,91,70}

    Returns: 212

  42. {75,67,47,50,37,68,85,40,93,77,80,55,86,28,19,54,53,93,21,93,21,24,54,52,14,50,41,64,44,90,18,17,57,75,49,19,43,77,25,72,51,50,70,82,25,16,36,40,66}

    Returns: 170

  43. {83,48,35,41,74,36,91,24,40,89,100,31,15,41,31,69,83,13,34,73,11,74,77,14,32,11,26,50,21,34,76,15,99,58,12,69,91,80,64,78,50,91,26,78,20,51,84,32,82,100}

    Returns: 165

  44. {73,42,54,52,97,75,11,32,12,80,27,22,52,46,79,31,55,79,90,31,94,93,22,69,62,22,46,67,84,38,37,82,17,68,30,91,33,81,51,69,76,26,41,13,21,62,80,45,83}

    Returns: 164

  45. {18,26,23,48,92,16,73,85,50,67,81,16,76,55,47,45,23,52,38,27,79,61,35,73,60,63,60,80,94,12,89,49,95,87,61,31,39,74,89,89,81,65,18,23,46,34,48,54,95,12}

    Returns: 227

  46. {49,40,72,30,19,53,14,84,48,100,56,16,83,90,79,18,88,59,55,21,67,34,71,43,85,47,71,54,43,16,12,92,41,95,62,28,45,34,56,13,48,12,74,59,11,81,84,98,82}

    Returns: 156

  47. {45,21,15,55,76,81,53,43,46,22,74,36,75,22,32,55,88,33,36,46,59,42,81,66,40,100,89,78,13,11,51,71,76,21,28,91,99,79,69,57,44,51,100,65,39,68,46,27,73,36}

    Returns: 188

  48. {74,31,12,60,90,76,29,13,33,66,47,12,69,92,70,81,77,23,83,53,58,18,29,68,10,27,72,84,42,20,27,36,84,10,87,96,39,85,88,14,96,85,30,64,42,72,100,24,26}

    Returns: 161

  49. {79,38,45,81,71,51,50,45,73,46,37,46,33,94,48,12,31,12,82,59,37,59,35,69,67,45,27,81,16,13,72,44,97,63,30,50,76,73,20,47,23,10,87,98,10,26,21,98,57,22}

    Returns: 169

  50. {58,85,100,14,94,42,12,66,85,68,22,64,19,85,48,47,93,56,86,22,36,77,82,37,34,84,56,20,25,91,46,31,86,14,69,53,21,31,80,10,27,40,55,36,57,32,40,47,74}

    Returns: 187

  51. {73,40,53,30,67,24,14,73,45,38,26,90,46,59,15,93,63,65,22,41,96,58,69,97,55,19,15,89,36,72,37,68,65,14,97,28,35,49,80,13,53,31,79,72,35,18,52,12,61,73}

    Returns: 157

  52. {82,91,18,45,84,51,84,23,98,53,76,76,56,24,10,44,79,35,42,10,95,74,21,49,20,85,80,46,21,38,36,53,24,82,96,55,13,50,98,45,31,11,66,84,96,16,47,64,58}

    Returns: 165

  53. {28,99,39,39,65,76,86,53,46,96,85,51,80,97,64,62,83,51,23,73,33,93,61,54,62,94,46,16,73,93,50,37,64,78,100,65,42,51,78,55,65,42,97,83,67,63,58,11,83,51}

    Returns: 166

  54. {86,80,25,51,29,38,16,38,38,29,33,36,87,58,50,19,20,38,78,91,70,93,32,100,100,91,83,33,54,34,36,26,88,84,97,94,65,16,92,22,34,26,62,36,17,54,77,100,84}

    Returns: 171

  55. {86,58,94,50,50,55,52,44,56,77,60,63,51,31,98,97,30,82,35,14,88,83,86,69,98,98,31,99,82,53,71,25,94,40,90,71,94,95,45,75,50,49,34,37,73,27,36,36,75,39}

    Returns: 186

  56. {39,37,88,98,46,63,96,52,89,61,40,83,88,31,32,90,92,34,77,80,17,94,70,77,39,21,22,60,95,67,20,11,29,45,86,54,27,21,16,21,46,83,37,57,15,45,33,60,67}

    Returns: 149

  57. {40,53,40,54,64,80,90,13,57,20,24,59,88,39,81,36,60,94,93,11,86,55,80,84,72,60,75,27,95,43,11,17,39,85,91,39,75,73,35,58,16,70,19,36,71,62,84,11,56,69}

    Returns: 193

  58. {28,45,61,45,92,60,56,30,79,52,94,36,33,77,42,77,65,60,54,65,60,49,97,29,86,92,56,99,75,36,97,34,84,20,49,100,88,28,53,59,53,51,34,70,83,12,88,88,87}

    Returns: 190

  59. {100,58,20,84,89,63,63,49,94,82,27,83,94,36,27,20,13,24,91,27,73,52,97,66,54,13,96,28,91,51,22,67,38,34,75,33,67,61,25,27,23,48,54,79,54,64,90,99,23,57}

    Returns: 138

  60. {71,44,61,18,51,55,33,15,58,74,76,13,78,48,22,62,55,89,69,87,51,54,40,44,98,50,31,95,85,76,85,29,67,75,60,11,25,13,70,81,22,40,54,24,37,24,54,71,10}

    Returns: 173

  61. {61,73,28,71,81,37,85,20,13,48,81,82,29,49,81,92,57,49,55,28,87,94,42,46,100,19,72,26,53,56,36,59,43,38,86,87,100,13,29,52,42,83,84,51,30,18,98,79,52,19}

    Returns: 145

  62. {30,79,79,97,93,81,16,19,63,29,28,37,12,54,14,15,45,97,13,33,82,71,54,48,89,15,19,74,27,26,39,90,38,54,56,98,31,71,16,58,23,65,27,26,16,19,88,94,17}

    Returns: 172

  63. {48,70,23,39,76,65,63,30,59,71,39,40,68,87,21,71,11,68,39,60,84,65,15,30,20,32,13,13,42,63,17,22,84,59,35,10,54,21,27,13,82,38,66,81,26,94,12,59,89,76}

    Returns: 121

  64. {69,64,86,74,46,100,44,48,13,21,29,87,81,54,89,58,94,76,44,99,26,24,24,44,75,72,79,13,74,35,57,87,30,11,33,25,95,74,68,59,59,61,100,66,65,72,70,38,55}

    Returns: 176

  65. {56,52,37,41,13,33,86,34,54,80,88,61,47,78,31,57,92,52,45,66,89,69,94,35,29,21,14,90,18,16,25,36,30,67,32,39,17,100,21,73,72,90,33,83,100,32,32,24,67,30}

    Returns: 169

  66. {36,19,64,82,48,80,51,12,50,48,37,59,17,53,60,22,14,92,11,85,37,81,88,17,42,39,19,50,60,95,99,29,61,24,30,57,69,11,47,39,69,52,87,11,13,41,26,39,52}

    Returns: 155

  67. { 40, 80, 100, 30, 91, 92, 95, 96, 81, 82, 83, 84, 85, 86, 87, 88, 89, 71, 55, 57, 60, 62, 63, 64, 65, 66, 67, 68, 69, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    Returns: 120

  68. { 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60 }

    Returns: 145

  69. { 10, 100, 12, 98, 14, 96, 16, 94, 18, 92, 20, 90, 22, 88, 54, 36, 96, 84, 28, 82, 30, 80, 32, 78, 34, 76, 36, 74, 38, 72, 40, 70, 42, 68, 44, 66, 46, 64, 48, 62, 50, 60, 52, 58, 54, 86, 52, 54, 56, 58 }

    Returns: 176

  70. { 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58 }

    Returns: 143

  71. { 10, 11, 12, 13, 15, 10, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 34, 54, 32, 53, 52, 53, 54, 52, 53, 42, 32, 53, 54, 54 }

    Returns: 115

  72. { 10, 10, 10, 10, 10, 10, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 24, 65, 23, 76, 87, 23, 54, 23, 65, 87, 98, 23, 12, 45, 65, 98, 45, 23, 54, 12, 43, 34, 54, 67, 78, 89, 87, 76 }

    Returns: 202

  73. { 10, 100, 100, 40, 50, 60, 70, 80, 90 }

    Returns: 180

  74. { 56, 46, 18, 78, 54, 15, 28, 82, 36, 36, 64, 87, 45, 30, 60, 85, 68, 50, 86, 50, 58, 29, 33, 29, 83, 19, 13, 33, 59, 70, 63, 70, 11, 61, 34, 63, 96, 98, 84, 82, 92, 44, 51, 49, 66, 98, 29, 50, 78, 20 }

    Returns: 146

  75. { 51, 27, 44, 50, 99, 74, 58, 28, 62, 84, 45, 75, 71, 97, 71, 51, 35, 72, 67, 46, 91, 34, 42, 73, 32, 62, 61, 96, 18, 15, 57, 46, 21, 28, 79, 32, 27, 29, 35, 94, 93, 61, 12, 13, 43, 84, 31, 71, 93, 38 }

    Returns: 157

  76. { 80, 82, 81, 50, 90, 80, 82, 81, 50, 90, 80, 82, 81, 50, 90, 80, 82, 81, 33, 90, 80, 82, 81, 50, 90, 80, 82, 81, 50, 90, 80, 82, 81, 50, 90, 80, 82, 81, 50, 90, 80, 82, 43, 50, 90, 80, 82, 81, 50, 90 }

    Returns: 113

  77. { 51, 50, 53, 50, 50, 52 }

    Returns: 3

  78. { 40, 30, 70, 25, 33, 47, 79, 91, 11, 13, 15, 16, 18, 20, 22, 24, 36, 40, 45, 47, 50, 52, 53, 55, 59, 62, 83, 81, 75, 92, 95, 99, 24, 14, 19 }

    Returns: 146

  79. { 13, 12, 16, 11, 18, 14, 17, 15 }

    Returns: 12

  80. { 50, 60, 70, 12, 34, 56, 67, 78, 89, 32, 45, 54, 32, 76, 87, 98, 32, 43, 54, 65, 76, 87, 98, 11, 22, 33, 44, 55, 66, 77, 88, 99, 21, 32, 12, 45, 54, 76, 54, 32, 34, 56, 76, 54, 32, 34 }

    Returns: 166

  81. { 13, 17, 11, 12, 10, 23, 32, 55, 43, 44, 67, 78, 45, 36, 66, 76, 88 }

    Returns: 212

  82. { 10, 30, 30, 10, 10, 20, 20, 30, 30 }

    Returns: 40

  83. { 20, 10, 10, 11, 12, 13, 14 }

    Returns: 20

  84. { 70, 10, 13, 10, 45, 50, 60, 56, 45, 12, 13, 14, 65, 45, 48, 87, 67, 56, 45, 53, 45, 33, 45, 76, 87, 65, 45, 33, 13, 15, 16, 17, 84, 83, 82, 90, 91, 26, 54, 54, 53, 56, 57, 52 }

    Returns: 159

  85. { 50, 60, 70, 11, 22, 33, 44, 55, 66, 77, 88, 99, 12, 23, 34, 45, 56, 67, 78, 89, 98, 87, 76, 65, 54, 43, 32, 21, 13, 25, 36, 47, 58, 59, 35, 43, 21, 64, 75, 86, 23, 42, 74, 42, 64 }

    Returns: 166

  86. { 100, 74, 92, 24, 64, 35, 75, 87, 35, 78, 36, 77, 37, 75, 58, 86, 26, 87, 96, 36, 36, 75, 36, 47, 38, 85, 64, 74, 47, 36, 75, 74, 36, 85, 87, 36, 23, 64, 86, 98, 24, 53, 35, 67, 87, 89, 64, 35, 57, 57 }

    Returns: 192

  87. { 80, 70, 56, 36, 66, 80, 54, 32, 88, 77, 34, 65, 87, 80, 54, 76, 87, 78, 74, 34, 56, 78, 66, 34, 56, 88, 12, 23, 34, 45, 56, 67, 34, 78, 34, 90, 34, 68, 89, 34, 68, 34, 59, 39, 10, 95, 49, 48, 34, 74 }

    Returns: 178

  88. { 10, 50, 10, 70, 49, 48, 10, 10, 10, 10 }

    Returns: 80

  89. { 44, 15, 35, 99, 87, 78, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 51, 52, 53, 54, 55, 56, 57 }

    Returns: 160

  90. { 45, 10, 60, 20, 30, 40, 50 }

    Returns: 60

  91. { 50, 60, 40, 70, 59, 58, 10, 20, 30 }

    Returns: 100

  92. { 50, 100, 45, 45, 49, 60 }

    Returns: 55

  93. { 10, 100, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50, 10, 70, 80, 90, 100, 10, 20, 30, 40, 50, 10, 70, 80, 90, 100, 10, 20, 30, 40, 50, 10, 70, 80, 90, 100 }

    Returns: 170

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