Statistics

Problem Statement for "IsoscelesTriangles"

Problem Statement

A triangle is called isosceles if it has two sides of equal length. Two triangles are considered to be different if they have different sets of vertices. You have a grid of N x M square cells. Return the number of different isosceles triangles you can form using only the centers of grid cells as vertices.

Definition

Class:
IsoscelesTriangles
Method:
count
Parameters:
int, int
Returns:
long
Method signature:
long count(int N, int M)
(be sure your method is public)

Constraints

  • N will be between 1 and 200, inclusive.
  • M will be between 1 and 200, inclusive.

Examples

  1. 1

    10

    Returns: 0

    Any three centers of grid cells will lie on the same straight line, so it's impossible to form a triangle at all.

  2. 2

    2

    Returns: 4

    We can select 4 triples of centers of grid cells, and all these triples will form isosceles triangles.

  3. 2

    3

    Returns: 10

    All 10 isosceles triangles for a 2x3 grid are listed below ('X' stands for a triangle vertex): XX. XX. .X. X.. X.X X.. .X. XX. XX. .X. .XX .XX ..X .X. .X. .X. ..X .XX .XX X.X

  4. 5

    4

    Returns: 248

  5. 10

    10

    Returns: 11284

  6. 1

    1

    Returns: 0

  7. 1

    5

    Returns: 0

  8. 1

    16

    Returns: 0

  9. 1

    76

    Returns: 0

  10. 1

    164

    Returns: 0

  11. 1

    190

    Returns: 0

  12. 1

    199

    Returns: 0

  13. 1

    200

    Returns: 0

  14. 2

    1

    Returns: 0

  15. 2

    5

    Returns: 24

  16. 4

    4

    Returns: 148

  17. 3

    11

    Returns: 444

  18. 2

    61

    Returns: 2040

  19. 3

    175

    Returns: 79328

  20. 5

    177

    Returns: 309936

  21. 2

    199

    Returns: 20394

  22. 2

    200

    Returns: 20596

  23. 17

    1

    Returns: 0

  24. 14

    5

    Returns: 3332

  25. 13

    22

    Returns: 106180

  26. 18

    18

    Returns: 156092

  27. 12

    77

    Returns: 696548

  28. 6

    144

    Returns: 328524

  29. 17

    184

    Returns: 7473948

  30. 24

    198

    Returns: 21097508

  31. 18

    200

    Returns: 9969728

  32. 32

    1

    Returns: 0

  33. 58

    3

    Returns: 9302

  34. 45

    7

    Returns: 63928

  35. 32

    83

    Returns: 11397744

  36. 50

    50

    Returns: 13245148

  37. 36

    137

    Returns: 35244912

  38. 98

    193

    Returns: 847185388

  39. 26

    196

    Returns: 25764444

  40. 90

    200

    Returns: 726073444

  41. 124

    1

    Returns: 0

  42. 156

    5

    Returns: 243592

  43. 115

    25

    Returns: 9940444

  44. 156

    49

    Returns: 99002016

  45. 154

    173

    Returns: 2012714728

  46. 131

    131

    Returns: 799471140

  47. 112

    180

    Returns: 1039961704

  48. 125

    196

    Returns: 1581379928

  49. 132

    200

    Returns: 1868961872

  50. 187

    1

    Returns: 0

  51. 189

    2

    Returns: 18424

  52. 188

    25

    Returns: 21694816

  53. 190

    39

    Returns: 73383778

  54. 179

    150

    Returns: 2032567010

  55. 182

    186

    Returns: 3350738104

  56. 176

    176

    Returns: 2779752656

  57. 190

    198

    Returns: 4182248932

  58. 193

    200

    Returns: 4415586200

  59. 199

    1

    Returns: 0

  60. 197

    5

    Returns: 380496

  61. 199

    19

    Returns: 11418400

  62. 198

    69

    Returns: 359231512

  63. 197

    103

    Returns: 994029032

  64. 198

    183

    Returns: 3857808886

  65. 197

    198

    Returns: 4516114624

  66. 198

    198

    Returns: 4564501136

  67. 199

    200

    Returns: 4711695860

  68. 200

    1

    Returns: 0

  69. 200

    3

    Returns: 103164

  70. 200

    19

    Returns: 11512660

  71. 200

    69

    Returns: 365141132

  72. 200

    159

    Returns: 2881159180

  73. 200

    188

    Returns: 4174121528

  74. 200

    198

    Returns: 4661851180

  75. 200

    200

    Returns: 4761658200

  76. 91

    198

    Returns: 734227046

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