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Problem Statement for "ConvexHull"

Problem Statement

You have a rectangle with corners at (0, 0) and (m, n). You would like to place a convex polygon inside it such that the polygon's vertices are at integer coordinates. The vertices may lie anywhere inside the rectangle or on its boundary.
You are given m and n, the dimensions of the rectangle. Return the maximal number of vertices contained by the convex polygon.

Definition

Class:
ConvexHull
Method:
intHull
Parameters:
int, int
Returns:
int
Method signature:
int intHull(int m, int n)
(be sure your method is public)

Constraints

  • m and n will be between 3 and 200, inclusive.

Examples

  1. 3

    3

    Returns: 8

  2. 3

    50

    Returns: 8

  3. 4

    4

    Returns: 9

  4. 4

    5

    Returns: 10

  5. 50

    200

    Returns: 74

  6. 200

    3

    Returns: 8

  7. 200

    5

    Returns: 12

  8. 200

    10

    Returns: 22

  9. 200

    20

    Returns: 42

  10. 200

    30

    Returns: 60

  11. 200

    40

    Returns: 68

  12. 200

    50

    Returns: 74

  13. 60

    200

    Returns: 80

  14. 70

    200

    Returns: 84

  15. 100

    200

    Returns: 95

  16. 200

    200

    Returns: 121

  17. 151

    163

    Returns: 103

  18. 163

    128

    Returns: 97

  19. 150

    184

    Returns: 107

  20. 37

    45

    Returns: 42

  21. 84

    130

    Returns: 78

  22. 66

    128

    Returns: 71

  23. 157

    145

    Returns: 100

  24. 159

    193

    Returns: 111

  25. 144

    18

    Returns: 38

  26. 180

    131

    Returns: 101

  27. 149

    57

    Returns: 71

  28. 192

    133

    Returns: 104

  29. 53

    22

    Returns: 36

  30. 100

    75

    Returns: 69

  31. 167

    81

    Returns: 84

  32. 124

    98

    Returns: 81

  33. 76

    93

    Returns: 68

  34. 25

    68

    Returns: 41

  35. 73

    96

    Returns: 67

  36. 185

    52

    Returns: 74

  37. 78

    176

    Returns: 84

  38. 7

    192

    Returns: 16

  39. 153

    124

    Returns: 94

  40. 195

    20

    Returns: 42

  41. 182

    128

    Returns: 101

  42. 106

    70

    Returns: 69

  43. 144

    28

    Returns: 53

  44. 26

    176

    Returns: 54

  45. 49

    82

    Returns: 56

  46. 50

    179

    Returns: 72

  47. 55

    57

    Returns: 52

  48. 160

    114

    Returns: 93

  49. 151

    93

    Returns: 85

  50. 16

    154

    Returns: 34

  51. 11

    72

    Returns: 24

  52. 194

    52

    Returns: 75

  53. 91

    28

    Returns: 47

  54. 115

    32

    Returns: 53

  55. 117

    21

    Returns: 44

  56. 23

    24

    Returns: 29

  57. 99

    130

    Returns: 83

  58. 6

    62

    Returns: 14

  59. 121

    80

    Returns: 75

  60. 142

    26

    Returns: 51

  61. 164

    45

    Returns: 67

  62. 194

    88

    Returns: 90

  63. 93

    62

    Returns: 63

  64. 89

    115

    Returns: 76

  65. 168

    96

    Returns: 89

  66. 81

    87

    Returns: 68

  67. 197

    168

    Returns: 113

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