Statistics

Problem Statement for "PipeCuts"

Problem Statement

A 100 meter long pipe must be cut in two places. It can only be cut at certain places, where it was originally welded from smaller pipes. If the two cut locations are chosen at random (each potential location has equal probability of being chosen), find the probability of a resulting pipe being longer than L meters.

Create a method named probability that accepts a int[] weldLocations and int L as parameters. It should calculate the probability of one or more resulting pipes being strictly longer than L if the two cut locations are chosen at random from weldLocations. Each element in weldLocations represents the number of meters from the left end of the pipe.

Definition

Class:
PipeCuts
Method:
probability
Parameters:
int[], int
Returns:
double
Method signature:
double probability(int[] weldLocations, int L)
(be sure your method is public)

Notes

  • Your return value must have a relative or absolute error less than 1e-9.

Constraints

  • weldLocations will have between 2 and 50 elements, inclusive.
  • Each element in weldLocations will be between 1 and 99, inclusive.
  • weldLocations will not contain duplicate elements.
  • L will be between 1 and 100, inclusive.

Examples

  1. {25, 50, 75}

    25

    Returns: 1.0

    Any random set of cuts results in a pipe being longer than 25 meters.

  2. {25, 50, 75}

    50

    Returns: 0.0

    This time, it is impossible to cut the pipe such that some resulting pipe is longer than 50 meters.

  3. {25, 50, 75}

    24

    Returns: 1.0

  4. {99, 88, 77, 66, 55, 44, 33, 22, 11}

    50

    Returns: 0.7222222222222222

  5. {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    34

    Returns: 0.9974489795918368

  6. {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    95

    Returns: 0.002551020408163265

    Probably the smallest return value greater than 0.0

  7. {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    60

    Returns: 0.4362244897959184

    random test

  8. {50,51}

    50

    Returns: 0.0

  9. {50,51}

    49

    Returns: 1.0

  10. {67, 21, 90, 77, 19, 38, 85, 91, 23, 29, 42}

    71

    Returns: 0.18181818181818182

  11. {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    34

    Returns: 0.9974489795918368

    probably largest return value less than 1.0

  12. {31, 55, 22, 99, 1, 49, 21, 7, 3, 88, 89, 36, 41}

    77

    Returns: 0.2948717948717949

  13. {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    55

    Returns: 0.5892857142857143

  14. {99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    51

    Returns: 0.9208163265306123

  15. {99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

    60

    Returns: 0.6048979591836735

  16. {54,69,86,50,21,66,35,62,55,44,25,2,36,37,53,82,14,19,92,60,68,16,87,78,29,31,34,77,33,74,51,97,46,58,39,71,72,32,88,42}

    74

    Returns: 0.07307692307692308

  17. {5,92,62,69,42,11,91,24,7,78,46,44,15,90,82,71,20,39,13,96,14,19,93,38,47,12,75,45,9,2,81,73,17,64,60,26,22,84,32,67,56,30,85,66,36}

    86

    Returns: 0.04141414141414142

  18. {8,92,80,13,95,86,4,76,85,94,41,91,57,47}

    75

    Returns: 0.5274725274725275

  19. {12,30,87,77,22,46,98,64,20,71,44,45,36,33,92,68,97}

    61

    Returns: 0.45588235294117646

  20. {74,5,72,20,29,91,80,14,30,39,46,12,95,15,93,82,79,42,25,1,84,37,7,19,9,50,35,54,44,65,68,6,28,66,99,21}

    69

    Returns: 0.353968253968254

  21. {18,21,20,13,92,73,80,97,27,77,16,89,7,4,65,26,1,14,25,54,28,40,34,55,86,29,98,41,2,75,94}

    50

    Returns: 0.8451612903225807

  22. {12,43,73,82,3,85,7,67,66,6,21,71,96,28,14,1,36,60,62,61,94,9,79,84,50,65,80,76,44,59,87,88,32}

    48

    Returns: 0.8428030303030303

  23. {51,5,19,50,55,4,33,95,57,32,13,75,21,16,42,44,14,94,96,1,53,30,88,63,25,64,83,59,20,34,99,29,54}

    92

    Returns: 0.028409090909090908

  24. {36,53,89,55,63,17,85,70,60,24,58,78,14,97,52,91,64,50,44,15,4,95,46,40,82,71,88,56,77,12,41,34,75,67,57,87,2,65,69,96}

    44

    Returns: 0.8769230769230769

  25. {27,40,67,21,57,75,42,93,46,78,54,29,53,74,22,44,13,97,95,39,63,70,65,81,14,82}

    82

    Returns: 0.018461538461538463

  26. {33,96,73,72,50,76,49,41,22,39,34,6,30,65,14,40,7,43,27,99,8,78,87,36,32,15,45,23,77,20,56,35,53,31,54,66}

    36

    Returns: 0.9761904761904762

  27. {87,49,75,41,34,9,77,1,89,66,18,58,72,31,54,43,27,60,40,38,84,86,63,70,95,69,79,26,8,55,97,17}

    43

    Returns: 0.8508064516129032

  28. {85,16,97,8,52}

    71

    Returns: 0.5

  29. {92,17,21,10,4,90,52,66,58,95,53,22,99,1,63}

    61

    Returns: 0.5428571428571428

  30. {25, 50, 75 }

    50

    Returns: 0.0

  31. {30, 60, 90 }

    50

    Returns: 0.6666666666666666

  32. {99, 88, 77, 66, 55, 44, 33, 22, 11 }

    50

    Returns: 0.7222222222222222

  33. {50, 75 }

    49

    Returns: 1.0

  34. {1, 2 }

    50

    Returns: 1.0

  35. {99, 1 }

    98

    Returns: 0.0

  36. {80, 90, 10, 20 }

    50

    Returns: 1.0

  37. {24, 49 }

    50

    Returns: 1.0

  38. {20, 60, 70 }

    45

    Returns: 0.6666666666666666

  39. {15, 45, 56 }

    50

    Returns: 0.3333333333333333

  40. {25, 75 }

    70

    Returns: 0.0

  41. {25, 50, 60 }

    39

    Returns: 1.0

  42. {10, 30, 59, 1 }

    59

    Returns: 0.5

  43. {25, 75 }

    30

    Returns: 1.0

  44. {75, 76 }

    74

    Returns: 1.0

  45. {25, 26 }

    25

    Returns: 1.0

  46. {26, 40 }

    25

    Returns: 1.0

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