Statistics

Problem Statement for "Connection"

Problem Statement

An important aspect of many wireless connections is signal strength. The signal strength can affect the speed of the connection, as well as the chance that errors are introduced into the transmitted data.

In this problem, you are to write a method that models the signal strength of a connection, given the distance between two wireless components and a function that models the signal strength. The function given to you will be the sum of a number of terms of the form coeff*distexp. Each of these terms will be represented by an element of coeffs and a corresponding element of exp with the same index. Thus, the function 4*dist-1 + 3*dist2 would be represented by coeff = {4,3} and exp = {-1,2}. Your task is to evaluate the function represented by coeff and exp for the given dist and return the result.

Definition

Class:
Connection
Method:
signalStrength
Parameters:
int[], int[], int
Returns:
double
Method signature:
double signalStrength(int[] coeff, int[] exp, int dist)
(be sure your method is public)

Constraints

  • coeff and exp will each contain between 1 and 50 elements, inclusive.
  • coeff and exp will contain the same number of elements.
  • Each element of coeff will be between -100 and 100, inclusive.
  • Each element of exp will be between -10 and 10, inclusive.
  • dist will be between 1 and 1,000,000, inclusive.
  • Each element of exp will be distinct.

Examples

  1. {5,4}

    {-1,0}

    10

    Returns: 4.5

    Here, the signal strength is evaluated as: 5 * 10-1 + 4 * 100 = 5 * 0.1 + 4 * 1 = 4.5

  2. {100}

    {-2}

    13

    Returns: 0.591715976331361

    This is fairly realistic model of a wireless signal in empty space. The surface area of a sphere is proportional to the radius of the sphere squared. Thus, if the strength of a signal at a given distance is evenly distributed over the surface of a sphere, the strength at any one point is proportional to one over the radius squared.

  3. {-1,20}

    {1,0}

    25

    Returns: -5.0

    This example shows that some inputs lead to bogus results such as negative signal strength.

  4. {-7,40,-10,1}

    {-4,-2,-1,0}

    160

    Returns: 0.9390624893188476

  5. {100}

    {10}

    1000000

    Returns: 9.999999999999999E61

  6. {1}

    {-10}

    1000000

    Returns: 1.0E-60

  7. {9,-88,95,86,-49,97,58,76,11}

    {-2,8,6,3,1,5,10,-3,9}

    461291

    Returns: 2.5303347867871016E58

  8. {92,-16,9,62,31,-64,-23,63,46,91,55,-36,-8,69,30}

    {7,-5,5,9,-9,10,2,8,1,4,-7,-6,-1,-4,-8}

    612313

    Returns: -4.7414817921128495E59

  9. {50,-95,-63,76,19,61,70,-40,95,-65,20,85,-64,-28,61}

    {6,8,5,-10,9,7,4,-1,-4,3,-7,-5,0,10,-8}

    823196

    Returns: -4.0011993363278854E60

  10. {-34}

    {0}

    848507

    Returns: -34.0

  11. {82,98,-11,-43,-89,23,-6,16,3,90,-87,39,-74,-87,-31,-17}

    {3,-3,-2,6,-6,-10,-7,0,1,10,7,-1,9,-4,2,4}

    624735

    Returns: 8.150801415579656E59

  12. {-84,40,-57,56,-6,24,77,-40,-66}

    {1,5,8,0,4,-8,-7,-6,-4}

    193466

    Returns: -1.1186959755687171E44

  13. {-87,-88,9,92,82,-47}

    {-4,9,8,2,1,6}

    117958

    Returns: -3.8907103402220025E47

  14. {57,58,-63,0,51,72,54,-89,92}

    {6,-6,-8,-10,-3,2,-7,5,7}

    393849

    Returns: 1.3523737747451952E41

  15. {-65,-60,-99,-71,91,-62,58,58,45,-98,-90,-27}

    {9,6,-7,2,-3,-10,3,-1,7,-8,4,1}

    203031

    Returns: -3.8104348431727925E49

  16. {8,7,-43,92,47,-94,-27,46,-35,5,89,54,-61}

    {7,-10,4,-5,-3,1,5,-2,6,-8,3,-7,9}

    377652

    Returns: -9.531383327838629E51

  17. {-47,38,-90,61,-42,16}

    {-7,7,-3,-10,1,4}

    854959

    Returns: 1.2688217524341418E43

  18. {94,-59,-16,1,-59,77,20,-46,15,84}

    {-7,1,2,-8,10,7,8,4,0,5}

    175466

    Returns: -1.6322315563155113E54

  19. {80,71,-97,-83,-21,-55,-79,83,-19}

    {3,9,6,-7,-2,-9,-10,-4,-5}

    523034

    Returns: 2.079829049936733E53

  20. {-87,5,-10,-45,32,-34,-100,20,14,2,69,-61,-26,2,70,46,-62,10,23}

    {7,4,-9,-10,-5,-7,-2,9,8,-4,-3,6,2,-8,0,5,3,1,10}

    405393

    Returns: 2.7573457157340942E57

  21. {-28,97,-70,5,37,-40,-14,-52,82}

    {8,-10,10,-1,-6,-2,2,0,6}

    275459

    Returns: -1.7606284094103215E56

  22. {86,29,67,94,7,50}

    {-9,3,7,-10,0,-7}

    840372

    Returns: 1.983242497295197E43

  23. {15,-31,-77,-4,22,-41,69,-80,-95,10,-53,-44,93,-50}

    {7,2,10,5,-4,-8,-3,-2,-1,0,-7,6,8,9}

    251507

    Returns: -7.798168515068407E55

  24. {87,19,9,-1,-29,67,56,29,35,86,-86,19,64,-23,93,-14,-68}

    {10,-8,-7,-1,3,7,1,-2,-5,-9,-3,0,-10,5,9,2,4}

    67046

    Returns: 1.5968161047538277E50

  25. {12,-86,-51,63,21,-12,-55}

    {-4,-1,2,9,-10,7,1}

    783845

    Returns: 7.037400719808777E54

  26. {64,-6,21,70,79}

    {10,7,-2,1,-8}

    205635

    Returns: 8.652673748573099E54

  27. {-1,61,88,-20,-29,-3,-64,-6,-43,16,-77}

    {2,-1,8,4,10,6,1,-6,0,-5,-7}

    38740

    Returns: -2.2079750462952473E47

  28. {-67,-11,-36,-88,59,-95,70,36,-7,51,32,86,27,25,-51,-47}

    {-9,9,8,-7,0,-5,6,2,-3,5,3,1,-1,-2,7,-8}

    919908

    Returns: -5.189120929110706E54

  29. {-29,60,72,-89,-77,43}

    {0,6,7,-8,3,-2}

    772403

    Returns: 1.18097479374735E43

  30. {-57,-47,49,-19,21}

    {-6,-4,2,8,-2}

    112120

    Returns: -4.744804398896554E41

  31. {-44,-63,-24,79,70,1,69,-15,-53,-81,-11,-4,70,64,77}

    {-1,1,-4,4,-7,5,3,9,-6,7,-3,8,2,-5,-10}

    261337

    Returns: -8.529033383711312E49

  32. {-57,64,-2,-95,21,-73,-51,-33,99,-85,25,82,-50,-80,81}

    {-4,-6,10,-1,1,-7,-8,-9,-3,2,9,-5,3,5,0}

    900023

    Returns: -6.9752542638076E59

  33. {5,-84,-100,-35,-56,-75,88,-66,35,14,-81,-16,-48,45,-56,26}

    {5,-4,-6,8,-3,-10,1,-7,-5,-8,3,-2,0,-9,9,7}

    629720

    Returns: -8.719987031537303E53

  34. {54,93,-22,62}

    {9,10,1,6}

    779205

    Returns: 7.67362511997115E60

  35. {27,-87,8,-42,-37,-16,51,-27,55,-11,68,81}

    {5,-4,-7,1,-6,8,4,9,-5,-3,-2,7}

    44002

    Returns: -1.6696343172378647E43

  36. {35,29,57,86,70,-19,75,83,8,-92,-20,5,-7,38,-24,45,76,81,-100,-25}

    {5,-2,-4,-5,9,-8,-9,10,-1,6,-6,-3,0,7,8,4,1,-10,-7,3}

    3192

    Returns: 9.116363606400812E36

  37. {65,-79,-43,-11,-11,-87,-99,-72,20,7,-86,84,-64,94,59,74,93}

    {-1,0,4,-3,7,10,-2,3,-7,1,-10,-5,-8,-6,8,6,-9}

    708786

    Returns: -2.784008520132413E60

  38. {-36}

    {1}

    817727

    Returns: -2.9438172E7

  39. {-41,-13,47,-7,-96,45,-11,-11,53,0,10,-3,54,85,-7}

    {2,4,-4,-3,9,8,-9,1,-10,-5,-1,-7,-8,3,5}

    649187

    Returns: -1.966071237323582E54

  40. {72,-59}

    {2,-2}

    287344

    Returns: 5.944793352192E12

  41. {-91,-7,-23,-47,23,1,-7,-52}

    {3,1,9,8,-8,-10,7,-5}

    244975

    Returns: -7.308484929588386E49

  42. {-64,80,62,50,-80,-26,-21,12,36,20,-88,72,45,6,64,36,-71,16,95,92,8}

    {-6,4,2,-10,6,8,9,10,-2,-4,-9,-8,-3,1,0,3,5,-1,-5,-7,7}

    987941

    Returns: 1.0628955015045036E61

  43. {22,-96,74,-43,6,10,50,67,41,20,-5,24}

    {3,0,-5,10,7,-10,8,-7,-9,9,-4,5}

    166976

    Returns: -7.244489322492785E53

  44. {28,21,-30,32,57,85,58,-42,8,90,-30,6,95,5,31,66,-35,31,-57}

    {9,-8,4,10,-9,6,-7,8,1,2,-6,-1,3,-3,-2,5,-10,-4,0}

    835471

    Returns: 5.302299196095304E60

  45. {88,0,-20,90,17,46,-23}

    {4,-2,2,8,9,1,-8}

    748739

    Returns: 1.2572628634459434E54

  46. {-77,16,80,38,83,-70,-10,73,8,6,-29,-100,-21,42,-1}

    {1,-3,3,7,0,10,6,-10,-9,-7,-4,-5,2,4,8}

    999448

    Returns: -6.961455840611339E61

  47. {29,-64,-42,46,3,100,12,-53,-86,-58,31}

    {-7,-10,0,1,-1,8,6,7,-4,-6,-2}

    756441

    Returns: 1.0720133072042169E49

  48. {55}

    {6}

    770402

    Returns: 1.1499186003353288E37

  49. {-69,11,72,-96,-20,42,-34,-55,-97,-67,27,-56,-5}

    {4,6,8,-6,-7,-5,-10,1,0,-8,3,7,5}

    205713

    Returns: 2.3090043774826188E44

  50. {59,-96,-73,93,-67,-19,-3,-24,53,59,80,84}

    {4,10,-4,-10,-8,-7,3,9,-3,-9,0,1}

    809105

    Returns: -1.1543040435228476E61

  51. {73,92,-49,6,-39,14,10}

    {-6,0,-2,-1,9,-7,6}

    300784

    Returns: -7.858817106906519E50

  52. {-47,21,68,-59,-19,84,24,66,-66,-27,-33,-81,-43,27,78,-91,-59}

    {-2,-8,2,-5,3,-3,5,-1,-9,1,10,-10,7,-7,6,0,-6}

    826365

    Returns: -4.9004175560835495E60

  53. {-48,76,-84,-25,-36,-82,-15}

    {8,-1,2,10,-9,-5,0}

    958812

    Returns: -1.641627492639277E61

  54. {56,-80,66,5,79,7,46,56,-71,80,-24}

    {4,-3,-4,6,5,7,-9,8,-7,1,9}

    328757

    Returns: -1.0766715513252542E51

  55. {62,81,-66,-36}

    {10,-10,5,0}

    162226

    Returns: 7.827017211762239E53

  56. {-53,-16,87,-59,-49,-77,-55,73,1,-96}

    {-7,-1,-8,10,6,-3,9,-4,4,8}

    528852

    Returns: -1.009704491481508E59

  57. {-7, 40, -10, 1 }

    {-4, -2, -1, 0 }

    160

    Returns: 0.9390624893188476

  58. {5, 4, 3 }

    {1, 2, 3 }

    10

    Returns: 3450.0

  59. {100 }

    {-2 }

    13

    Returns: 0.591715976331361

  60. {1, 1 }

    {9, 10 }

    1000000

    Returns: 1.0000009999999999E60

  61. {5, 4 }

    {-1, 0 }

    10

    Returns: 4.5

  62. {2, 23, 22, 2, 2 }

    {-5, -4, 4, 3, -2 }

    19

    Returns: 2880780.005717461

  63. {4, 5, 6 }

    {-1, 4, 8 }

    90

    Returns: 2.582803292805E16

  64. {10, 20, 30, 40 }

    {2, 3, 4, 5 }

    3

    Returns: 12780.0

  65. {24 }

    {5 }

    100

    Returns: 2.4E11

  66. {1, 8, 7 }

    {8, 7, 9 }

    10

    Returns: 7.18E9

  67. {-100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100 }

    {-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

    1000000

    Returns: -1.0000010000009999E62

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