Statistics

Problem Statement for "MaxTriangle"

Problem Statement

A triangle with positive area has been positioned on the plane in such a way that all of its vertices are located at integer coordinates. The lengths of two sides of this triangle are equal to sqrt(A) and sqrt(B), where sqrt(X) denotes the square root of X. Return the maximum area this triangle can have. If there is no such triangle, return -1 instead.

Definition

Class:
MaxTriangle
Method:
calculateArea
Parameters:
int, int
Returns:
double
Method signature:
double calculateArea(int A, int B)
(be sure your method is public)

Notes

  • The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

  • A and B will each be between 1 and 2000000000, inclusive.

Examples

  1. 1

    1

    Returns: 0.5

  2. 3

    7

    Returns: -1.0

  3. 41

    85

    Returns: 29.5

    One possible triangle has vertices at (-1, 1), (6, -5) and (10, 0).

  4. 194

    881

    Returns: 202.5

  5. 1000000000

    1000000000

    Returns: 5.0E8

  6. 2000000000

    2000000000

    Returns: 1.0E9

  7. 2000000000

    1

    Returns: 22240.0

  8. 1999967841

    1999878400

    Returns: 9.9996156E8

  9. 850

    925

    Returns: 442.5

  10. 925

    725

    Returns: 408.5

  11. 325

    725

    Returns: 242.5

  12. 850

    650

    Returns: 371.0

  13. 845

    625

    Returns: 362.5

  14. 31525

    65000

    Returns: 22633.0

  15. 53300

    34225

    Returns: 21355.0

  16. 93425

    95485

    Returns: 47222.5

  17. 81925

    90625

    Returns: 43079.0

  18. 91250

    75205

    Returns: 41417.5

  19. 32045

    21025

    Returns: 12977.5

  20. 68125

    90610

    Returns: 39283.5

  21. 93425

    18125

    Returns: 20575.0

  22. 53650

    38425

    Returns: 22692.5

  23. 99025

    15725

    Returns: 19705.0

  24. 86125

    68125

    Returns: 38250.0

  25. 16900

    75725

    Returns: 17875.0

  26. 91225

    10625

    Returns: 15566.5

  27. 84500

    70850

    Returns: 38675.0

  28. 45305

    65000

    Returns: 27133.0

  29. 89050

    75205

    Returns: 40917.5

  30. 79300

    92500

    Returns: 42820.0

  31. 31525

    22100

    Returns: 13196.0

  32. 94250

    28900

    Returns: 26095.0

  33. 65000

    56425

    Returns: 30275.0

  34. 1988995850

    1987587738

    Returns: 9.92895591E8

  35. 1997433828

    1984338325

    Returns: 9.88315917E8

  36. 1994939060

    1985077097

    Returns: 9.94537511E8

  37. 1999185781

    1995219252

    Returns: 9.54664047E8

  38. 1990368553

    1998422397

    Returns: 9.559109355E8

  39. 1999999170

    1999999170

    Returns: 9.99999585E8

  40. 1999999170

    1999999625

    Returns: 9.999996825E8

  41. 1215306625

    1215306625

    Returns: 6.076533125E8

  42. 1215309770

    1215306625

    Returns: 6.076540895E8

  43. 1215300970

    1215302800

    Returns: 6.07648058E8

  44. 1215301825

    1215306625

    Returns: 6.0765193E8

  45. 1999999656

    1215307490

    Returns: 7.79517726E8

  46. 1215309770

    8450

    Returns: 1602193.0

  47. 1215304456

    4802

    Returns: 1199422.0

  48. 1568

    1999999880

    Returns: 880824.0

  49. 1215304200

    9516

    Returns: -1.0

  50. 1215303505

    1215306625

    Returns: 6.076519475E8

  51. 1215304658

    8125

    Returns: 1570277.5

  52. 1215303505

    7225

    Returns: 1481473.5

  53. 7225

    1215303505

    Returns: 1481473.5

  54. 8125

    1215304025

    Returns: 1567525.0

  55. 1215303197

    1215302800

    Returns: 6.0754498E8

  56. 1

    2

    Returns: 0.5

  57. 3

    4

    Returns: -1.0

  58. 4

    4

    Returns: 2.0

  59. 6

    6

    Returns: -1.0

  60. 1

    2000000000

    Returns: 22240.0

  61. 987654321

    123456789

    Returns: -1.0

  62. 999999999

    1

    Returns: -1.0

  63. 1999999997

    1

    Returns: 22349.5

  64. 1999967841

    1948604449

    Returns: 9.870595515E8

  65. 831910120

    1271435329

    Returns: 5.13408051E8

  66. 2

    2

    Returns: 1.0

  67. 1999967841

    1999967841

    Returns: 9.999839205E8

  68. 199999

    2000000000

    Returns: -1.0

  69. 8

    4

    Returns: 2.0

  70. 999939200

    999939200

    Returns: 4.999696E8

  71. 2

    1

    Returns: 0.5

  72. 169

    180

    Returns: 87.0

  73. 9945

    9425

    Returns: 4836.0

  74. 2

    1000000000

    Returns: 22240.0

  75. 100000000

    500000000

    Returns: 1.11759488E8

  76. 100000000

    1441557

    Returns: 6003000.0

  77. 1

    13

    Returns: 1.5

  78. 61

    442

    Returns: 79.5

  79. 1172488941

    1172401781

    Returns: 5.8622268E8

  80. 1951000578

    1951000578

    Returns: 9.75500289E8

  81. 8

    8

    Returns: 4.0

  82. 2000000000

    1999967842

    Returns: 9.9459736E8

  83. 112805732

    1120048829

    Returns: 1.77564679E8

  84. 1

    32

    Returns: 2.0

  85. 1825030001

    1600000001

    Returns: 8.120919755E8

  86. 1

    9441

    Returns: 48.0

  87. 169

    144

    Returns: 78.0

  88. 1

    72

    Returns: 3.0

  89. 1999569325

    1999569325

    Returns: 9.997846625E8

  90. 1349232625

    73652228

    Returns: 1.57615655E8

  91. 5

    25

    Returns: 5.5

  92. 800000000

    400000000

    Returns: 2.822272E8

  93. 1999999940

    1277997957

    Returns: 7.98469914E8

  94. 25

    31

    Returns: -1.0

  95. 2

    2000000000

    Returns: 31600.0

  96. 1

    1172488941

    Returns: 17089.5

  97. 101203012

    186538500

    Returns: 6.8636946E7

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