Statistics

Problem Statement for "Aircraft"

Problem Statement

In aviation, a "near miss" occurs if the distance between two aircraft at some point in time is less than or equal to some threshold distance R. At a moment in time, the positions and velocities of two aircraft are known exactly. Assuming that each aircraft continues to fly with constant speed and direction, you need to work out if the aircraft will undergo a near miss now or at some point in the future.

You will be given the threshold distance R and the positions and velocities of the aircraft in 4 int[]s: p1, v1, p2 and v2. The position of the first aircraft in 3-D cartesian space is given by (p1[0] , p1[1] , p1[2]) and its velocity vector by (v1[0] , v1[1] , v1[2]) and similarly the second aircraft's position and velocity are given by (p2[0] , p2[1] , p2[2]) and (v2[0] , v2[1] , v2[2]). So, if an aircraft's initial position is the vector p and its velocity vector is v, the position of this aircraft at some future time t will be p + v * t. You should return a String containing "YES" if the aircraft will undergo a near miss now or in the future or "NO" if they won't (quotes for clarity).

Definition

Class:
Aircraft
Method:
nearMiss
Parameters:
int[], int[], int[], int[], int
Returns:
String
Method signature:
String nearMiss(int[] p1, int[] v1, int[] p2, int[] v2, int R)
(be sure your method is public)

Notes

  • The distance between two points (x1, y1, z1) and (x2, y2, z2) is given by sqrt((x1-x2)2 + (y1-y2)2 + (z1-z2)2).

Constraints

  • p1, v1, p2 and v2 will contain exactly 3 elements.
  • Each element of p1, v1, p2 and v2 will be between -10000 and 10000, inclusive.
  • R will be between 0 and 10000, inclusive.

Examples

  1. {15,50,5}

    {25,1,0}

    {161,102,9}

    {-10,-10,-1}

    10

    Returns: "YES"

    At time 4, the first aircraft will be at position {115,54,5} and the second at {121,62,5}, which is the first point in time at which they are exactly 10 distance units apart.

  2. {0,0,0}

    {2,2,0}

    {9,0,5}

    {-2,2,0}

    5

    Returns: "YES"

    At time 2.25, aircraft 1 will be at {4.5, 4.5, 0} and aircraft 2 at {4.5, 4.5, 5}, exactly a distance of 5 units apart.

  3. {0,0,0}

    {-2,2,0}

    {9,0,5}

    {2,2,0}

    5

    Returns: "NO"

    The aircraft are flying away from each other here, so the distance always increases with time.

  4. {-4921,250,5852}

    {-2,1,-2}

    {-2,-1729,-9307}

    {-2,0,0}

    9864

    Returns: "YES"

  5. {-6987,-881,-5232}

    {0,-2,-2}

    {9835,-872,8837}

    {-1,-2,-4}

    8755

    Returns: "YES"

  6. {7492,131,-2802}

    {0,1,1}

    {602,-9362,9112}

    {1,3,0}

    6444

    Returns: "YES"

  7. {-9760,-689,6267}

    {2,2,-2}

    {7881,-1423,4867}

    {0,1,-2}

    8660

    Returns: "YES"

  8. {-2838,-7940,-2936}

    {1,1,-2}

    {532,3850,9590}

    {1,0,-3}

    3410

    Returns: "YES"

    The closest approach of the aircraft occurs at time 12,158

  9. {-4921,250,5852}

    {-2,1,-2}

    {-2,-1729,-9307}

    {-2,0,0}

    9863

    Returns: "NO"

  10. {-6987,-881,-5232}

    {0,-2,-2}

    {9835,-872,8837}

    {-1,-2,-4}

    8754

    Returns: "NO"

  11. {7492,131,-2802}

    {0,1,1}

    {602,-9362,9112}

    {1,3,0}

    6443

    Returns: "NO"

  12. {-9760,-689,6267}

    {2,2,-2}

    {7881,-1423,4867}

    {0,1,-2}

    8659

    Returns: "NO"

  13. {-2838,-7940,-2936}

    {1,1,-2}

    {532,3850,9590}

    {1,0,-3}

    3409

    Returns: "NO"

  14. {-8509,9560,345}

    {-89,-33,62}

    {-5185,-1417,2846}

    {-58,24,26}

    8343

    Returns: "NO"

  15. {-8509,9560,345}

    {-89,-33,62}

    {-5185,-1417,2846}

    {-58,24,26}

    8344

    Returns: "YES"

    A near miss occurs between times 111 and 112

  16. {-8837,-2570,-3892}

    {22,45,-29}

    {9503,1162,7241}

    {-95,-9,-66}

    7116

    Returns: "NO"

  17. {-8837,-2570,-3892}

    {22,45,-29}

    {9503,1162,7241}

    {-95,-9,-66}

    7117

    Returns: "YES"

  18. {872,-4636,-3909}

    {68,46,11}

    {7185,703,1529}

    {-88,-7,96}

    8890

    Returns: "NO"

  19. {872,-4636,-3909}

    {68,46,11}

    {7185,703,1529}

    {-88,-7,96}

    8891

    Returns: "YES"

  20. {-7163,-371,-2459}

    {-59,-41,-14}

    {-2398,-426,-5487}

    {-43,27,67}

    5410

    Returns: "NO"

    The aircraft almost have a near miss between times 15 and 16, but stay just outside the threshold distance.

  21. {-7163,-371,-2459}

    {-59,-41,-14}

    {-2398,-426,-5487}

    {-43,27,67}

    5411

    Returns: "YES"

  22. {7448,-4019,7503}

    {80,81,-74}

    {9487,320,7057}

    {30,-17,80}

    3643

    Returns: "NO"

  23. {7448,-4019,7503}

    {80,81,-74}

    {9487,320,7057}

    {30,-17,80}

    3644

    Returns: "YES"

  24. {-3524,-430,9848}

    {-82,-72,55}

    {-7590,-8706,9853}

    {-97,-33,37}

    7204

    Returns: "NO"

  25. {-3524,-430,9848}

    {-82,-72,55}

    {-7590,-8706,9853}

    {-97,-33,37}

    7205

    Returns: "YES"

  26. {4431,-7298,3341}

    {34,71,35}

    {906,69,2117}

    {72,-81,83}

    2010

    Returns: "NO"

  27. {4431,-7298,3341}

    {34,71,35}

    {906,69,2117}

    {72,-81,83}

    2011

    Returns: "YES"

  28. {4274,-3305,1209}

    {-19,97,-57}

    {-14,5972,857}

    {8,-47,-56}

    2521

    Returns: "NO"

  29. {4274,-3305,1209}

    {-19,97,-57}

    {-14,5972,857}

    {8,-47,-56}

    2522

    Returns: "YES"

  30. {1645,4417,6355}

    {-14,29,-85}

    {9948,3104,2174}

    {-13,-6,-3}

    8813

    Returns: "NO"

  31. {3884,-748,6705}

    {58,-52,-5}

    {-4571,-1177,6318}

    {58,-52,-5}

    8474

    Returns: "NO"

  32. {3884,-748,6705}

    {58,-52,-5}

    {-4571,-1177,6318}

    {58,-52,-5}

    8475

    Returns: "YES"

  33. {2865,-8636,-5491}

    {-72,-79,55}

    {1887,-5387,-6267}

    {-72,-79,55}

    3480

    Returns: "NO"

  34. {2865,-8636,-5491}

    {-72,-79,55}

    {1887,-5387,-6267}

    {-72,-79,55}

    3481

    Returns: "YES"

  35. {1774,-4491,7810}

    {-12,19,-24}

    {2322,3793,9897}

    {-12,19,-24}

    8560

    Returns: "NO"

  36. {1774,-4491,7810}

    {-12,19,-24}

    {2322,3793,9897}

    {-12,19,-24}

    10000

    Returns: "YES"

    The aircraft are here flying with identical velocities, so the distance between them never changes. The distance at time 0 is lower than the threshold, so a near miss is already underway.

  37. {-4628,859,6322}

    {-64,-61,-20}

    {5633,7426,9547}

    {20,-58,75}

    8432

    Returns: "NO"

  38. {-4628,859,6322}

    {-64,-61,-20}

    {5633,7426,9547}

    {20,-58,75}

    8433

    Returns: "NO"

  39. {-7593,579,-9146}

    {56,-21,55}

    {3668,-8134,795}

    {-56,82,49}

    9451

    Returns: "NO"

  40. {-7593,579,-9146}

    {56,-21,55}

    {3668,-8134,795}

    {-56,82,49}

    9452

    Returns: "YES"

  41. {-2611,6642,4107}

    {-95,9,-53}

    {-3365,276,-9263}

    {-73,-15,52}

    9320

    Returns: "NO"

  42. {-2611,6642,4107}

    {-95,9,-53}

    {-3365,276,-9263}

    {-73,-15,52}

    9321

    Returns: "YES"

  43. {-13,-9966,-7414}

    {-64,-33,52}

    {-7920,-5123,-1713}

    {-66,45,89}

    8335

    Returns: "NO"

  44. {-13,-9966,-7414}

    {-64,-33,52}

    {-7920,-5123,-1713}

    {-66,45,89}

    8336

    Returns: "NO"

  45. {-777,2791,-952}

    {-65,98,-21}

    {6929,-7286,1573}

    {-10,-69,99}

    6257

    Returns: "NO"

  46. {-777,2791,-952}

    {-65,98,-21}

    {6929,-7286,1573}

    {-10,-69,99}

    6258

    Returns: "NO"

  47. {-748,-3746,-65}

    {41,-8,-82}

    {-3872,9801,4798}

    {-34,94,59}

    8330

    Returns: "NO"

  48. {-748,-3746,-65}

    {41,-8,-82}

    {-3872,9801,4798}

    {-34,94,59}

    8331

    Returns: "NO"

  49. {-9100,-5265,-8023}

    {73,-89,95}

    {-7372,-1078,659}

    {11,-94,-59}

    4251

    Returns: "NO"

  50. {-9100,-5265,-8023}

    {73,-89,95}

    {-7372,-1078,659}

    {11,-94,-59}

    4252

    Returns: "YES"

  51. {-1605,-7199,-4764}

    {62,-7,-89}

    {-2897,-2402,-5350}

    {-29,-72,4}

    4701

    Returns: "NO"

  52. {-1605,-7199,-4764}

    {62,-7,-89}

    {-2897,-2402,-5350}

    {-29,-72,4}

    4702

    Returns: "YES"

  53. {3731,8537,5661}

    {-70,71,32}

    {8701,-1886,-5115}

    {28,-13,7}

    9766

    Returns: "NO"

  54. {3731,8537,5661}

    {-70,71,32}

    {8701,-1886,-5115}

    {28,-13,7}

    9767

    Returns: "NO"

  55. {0,0,0}

    {1,0,0}

    {0,0,1}

    {0,1,0}

    1

    Returns: "YES"

  56. {0,0,0}

    {1,0,0}

    {0,0,1}

    {1,0,0}

    1

    Returns: "YES"

  57. {0, 1, -1}

    {3, -3, 3}

    {1, -1, 1}

    {3, 3, -3}

    1

    Returns: "YES"

  58. {0, 2856, -2856}

    {98, -9996, 9996}

    {10000, -2856, 2856}

    {98, 9996, -9996}

    10000

    Returns: "YES"

  59. {0, 10000, -10000}

    {3, -3, 3}

    {10000, -10000, 10000}

    {3, 3, -3}

    10000

    Returns: "YES"

  60. {0, 10000, -10000}

    {7, -7, 7}

    {10000, -10000, 10000}

    {7, 7, -7}

    10000

    Returns: "YES"

  61. {-2838, -7940, -2936 }

    {1, 1, -2 }

    {532, 3850, 9590 }

    {1, 0, -3 }

    3410

    Returns: "YES"

  62. {-7163, -371, -2459 }

    {-59, -41, -14 }

    {-2398, -426, -5487 }

    {-43, 27, 67 }

    5410

    Returns: "NO"

  63. {0, 0, 0 }

    {2, 2, 0 }

    {9, 0, 5 }

    {-2, 2, 0 }

    5

    Returns: "YES"

  64. {15, 50, 5 }

    {25, 1, 0 }

    {161, 102, 9 }

    {-10, -10, -1 }

    10

    Returns: "YES"

  65. {-8509, 9560, 345 }

    {-89, -33, 62 }

    {-5185, -1417, 2846 }

    {-58, 24, 26 }

    8344

    Returns: "YES"

  66. {-10000, 0, 0 }

    {10000, 0, 0 }

    {1, 0, 0 }

    {0, 0, 0 }

    0

    Returns: "YES"

  67. {-1000, 0, 0 }

    {1, 0, 1000 }

    {1000, 0, 0 }

    {-1, 0, 1000 }

    0

    Returns: "YES"

  68. {3731, 8537, 5661 }

    {-70, 71, 32 }

    {8701, -1886, -5115 }

    {28, -13, 7 }

    9766

    Returns: "NO"

  69. {0, 0, 0 }

    {1, 1, 1 }

    {10000, 10000, 10000 }

    {-1, -1, -1 }

    0

    Returns: "YES"

  70. {2, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    1

    Returns: "NO"

  71. {0, 0, 0 }

    {-2, 2, 0 }

    {9, 0, 5 }

    {2, 2, 0 }

    5

    Returns: "NO"

  72. {10, 10, 0 }

    {-1, 0, 0 }

    {-10, -10, 0 }

    {0, 0, 0 }

    1

    Returns: "NO"

  73. {0, 0, 0 }

    {0, 0, 0 }

    {2, 2, 2 }

    {0, 0, 0 }

    1

    Returns: "NO"

  74. {1, 1, 1 }

    {1, 1, 1 }

    {-1, -1, -1 }

    {-1, -1, -1 }

    10000

    Returns: "YES"

  75. {-2837, -7940, -2936 }

    {1, 1, -2 }

    {532, 3850, 9590 }

    {1, 0, -3 }

    3410

    Returns: "YES"

  76. {0, 0, 0 }

    {9999, 9999, 0 }

    {4, 0, 0 }

    {-5555, 5555, 0 }

    1

    Returns: "NO"

  77. {10000, 0, 0 }

    {-10000, 0, 0 }

    {-10000, 0, 0 }

    {1, 0, 0 }

    1

    Returns: "YES"

  78. {100, 1000, 10000 }

    {15, 9, 8 }

    {1200, 1300, 100 }

    {9, 8, 17 }

    135

    Returns: "NO"

  79. {0, 0, 0 }

    {0, 0, 1000 }

    {0, 0, 2 }

    {0, 0, 0 }

    1

    Returns: "YES"

  80. {0, 0, 0 }

    {25, 1, 0 }

    {0, 0, 0 }

    {-10, -10, -1 }

    0

    Returns: "YES"

  81. {1, 1, 0 }

    {0, 10000, 0 }

    {1, 3, 0 }

    {0, -10000, 0 }

    1

    Returns: "YES"

  82. {1, 1, 1 }

    {1, 1, 1 }

    {0, 0, 0 }

    {1, 1, 1 }

    1

    Returns: "NO"

  83. {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    5

    Returns: "YES"

  84. {0, 0, 0 }

    {1, 0, 0 }

    {0, 0, 2 }

    {1, 0, 0 }

    1

    Returns: "NO"

  85. {-7136, -371, -2459 }

    {-59, -41, -14 }

    {-2398, -426, -5487 }

    {-43, 27, 67 }

    5410

    Returns: "YES"

  86. {0, 0, 0 }

    {1, 0, 0 }

    {10, 0, 2 }

    {-1, 0, 0 }

    1

    Returns: "NO"

  87. {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    0

    Returns: "YES"

  88. {1, 1, 1 }

    {0, 0, 0 }

    {2, 1, 1 }

    {0, 0, 0 }

    10

    Returns: "YES"

  89. {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 1 }

    {0, 0, 0 }

    0

    Returns: "NO"

  90. {-2838, -7940, -2936 }

    {1, 1, -2 }

    {5323, 3850, 9590 }

    {1, 0, -3 }

    3

    Returns: "NO"

  91. {0, 0, 0 }

    {2001, 2000, 0 }

    {9000, 0, 5000 }

    {-2000, 2000, 0 }

    5000

    Returns: "YES"

  92. {0, 0, 0 }

    {0, 1, 0 }

    {2, 0, 0 }

    {0, 1, 0 }

    1

    Returns: "NO"

  93. {-10000, 0, 0 }

    {0, 0, 0 }

    {10000, 0, 0 }

    {-1, 0, 0 }

    0

    Returns: "YES"

  94. {10000, 10000, 10000 }

    {-10000, -10000, -10000 }

    {-10000, -10000, -10000 }

    {10000, 10000, 10000 }

    10000

    Returns: "YES"

  95. {0, 0, 0 }

    {-2, 2, 0 }

    {9, 0, 5 }

    {2, 2, 0 }

    100

    Returns: "YES"

  96. {0, 0, 0 }

    {0, 0, 0 }

    {-2, 0, 0 }

    {10000, 0, 0 }

    1

    Returns: "YES"

  97. {3731, 8537, 5661 }

    {70, 71, 32 }

    {8701, -1886, -5115 }

    {28, 80, 7 }

    10000

    Returns: "NO"

  98. {15, 50, 5 }

    {25, 1, 0 }

    {161, 102, 9 }

    {25, 1, 0 }

    10

    Returns: "NO"

  99. {1, 0, 0 }

    {1, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    1

    Returns: "YES"

  100. {1, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    1

    Returns: "YES"

  101. {0, 0, 0 }

    {-5, 0, 0 }

    {5, 0, 0 }

    {5, 0, 0 }

    5

    Returns: "YES"

  102. {0, 0, 0 }

    {1, 1, 1 }

    {10, 0, 0 }

    {1, 1, 1 }

    5

    Returns: "NO"

  103. {-10000, 0, 0 }

    {1, 0, 0 }

    {10000, 0, 0 }

    {0, 0, 0 }

    0

    Returns: "YES"

  104. {0, 0, 0 }

    {10000, 0, 0 }

    {10, 0, 0 }

    {-10000, 0, 0 }

    1

    Returns: "YES"

  105. {0, 0, 0 }

    {0, 1, 0 }

    {4, 11, 0 }

    {0, -1, 0 }

    2

    Returns: "NO"

  106. {0, 0, 0 }

    {0, 0, 0 }

    {10, 10, 10 }

    {-1, -1, -1 }

    2

    Returns: "YES"

  107. {0, 0, 0 }

    {0, 1, 0 }

    {10, 0, 0 }

    {1, 0, 0 }

    10

    Returns: "YES"

  108. {1, 2, 3 }

    {1, 2, 3 }

    {100, 200, 300 }

    {1, 2, 3 }

    1

    Returns: "NO"

  109. {0, 0, 0 }

    {10000, 0, 0 }

    {1000, 0, 0 }

    {-10000, 0, 0 }

    1

    Returns: "YES"

  110. {1, 1, 1 }

    {1, 1, 1 }

    {2, 2, 2 }

    {1, 1, 1 }

    1

    Returns: "NO"

  111. {0, 0, 0 }

    {0, 0, 0 }

    {2, -1, 0 }

    {0, 2, 0 }

    2

    Returns: "YES"

  112. {0, 0, 0 }

    {0, 0, 0 }

    {-1, 1, 0 }

    {10000, 0, 0 }

    1

    Returns: "YES"

  113. {0, 0, 0 }

    {0, 0, 0 }

    {1, 0, 0 }

    {1, 0, 0 }

    1

    Returns: "YES"

  114. {0, 0, 0 }

    {0, 1, 0 }

    {0, -100, 0 }

    {0, 4000, 0 }

    1

    Returns: "YES"

  115. {0, 0, 0 }

    {10000, 0, 0 }

    {10, 0, 0 }

    {0, 0, 0 }

    2

    Returns: "YES"

  116. {0, 0, 0 }

    {0, 0, 0 }

    {1, 0, 0 }

    {1, 0, 0 }

    2

    Returns: "YES"

  117. {0, 0, 0 }

    {0, 0, 0 }

    {1, 1, 0 }

    {-200, 0, 0 }

    1

    Returns: "YES"

  118. {1771, -1491, 7830 }

    {-12, 19, -24 }

    {2322, 3793, 9897 }

    {-12, 19, -24 }

    1000

    Returns: "NO"

  119. {-10000, -10000, -10000 }

    {0, 0, 1 }

    {10000, 10000, 10000 }

    {0, 0, 1 }

    10000

    Returns: "NO"

  120. {10, 10, 10 }

    {10, 10, 10 }

    {0, 0, 0 }

    {0, 0, 0 }

    100

    Returns: "YES"

  121. {-8509, 9560, 345 }

    {1, 2, 3 }

    {-5185, -1417, 2846 }

    {1, 2, 3 }

    8344

    Returns: "NO"

  122. {1774, -4491, 7810 }

    {-12, 19, -24 }

    {2322, 3793, 9897 }

    {-12, 19, -24 }

    10

    Returns: "NO"

  123. {5, 5, 5 }

    {1, 0, 0 }

    {0, 0, 0 }

    {1, 0, 0 }

    1

    Returns: "NO"

  124. {3, 2, 3 }

    {1, 2, 3 }

    {1, 2, 3 }

    {1, 2, 3 }

    1

    Returns: "NO"

  125. {0, 0, 0 }

    {1, 0, 0 }

    {0, 1, 0 }

    {1, 1, 0 }

    2

    Returns: "YES"

  126. {50, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    10

    Returns: "NO"

  127. {0, 0, 0 }

    {4, 2, 0 }

    {2, 0, 0 }

    {0, 2, 0 }

    1

    Returns: "YES"

  128. {0, 0, 0 }

    {0, 0, 0 }

    {3, 0, 0 }

    {0, 0, 0 }

    2

    Returns: "NO"

  129. {0, 0, 0 }

    {0, 1, 1 }

    {0, 0, 1 }

    {0, 1, -1 }

    0

    Returns: "YES"

  130. {0, 0, 0 }

    {0, 2, 0 }

    {2, 0, 0 }

    {-5, 2, 0 }

    1

    Returns: "YES"

  131. {0, 0, 0 }

    {2, 2, 0 }

    {9, 0, 5 }

    {2, 2, 0 }

    5

    Returns: "NO"

  132. {1774, -4491, 7810 }

    {-12, 19, -24 }

    {2322, 3793, 9897 }

    {-12, 19, -24 }

    5000

    Returns: "NO"

  133. {0, 0, 0 }

    {0, 0, 0 }

    {10, 0, 2 }

    {0, 0, 0 }

    1

    Returns: "NO"

  134. {1, 1, 1 }

    {1, 1, 1 }

    {22, 22, 22 }

    {1, 1, 1 }

    1

    Returns: "NO"

  135. {10, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 0 }

    1

    Returns: "NO"

  136. {31, 87, -51 }

    {121, 23, -323 }

    {23, -45, -10 }

    {28, -13, 7 }

    10000

    Returns: "YES"

  137. {-5000, -5000, 0 }

    {1, 1, 1 }

    {5000, -5000, 0 }

    {1, 1, 1 }

    10

    Returns: "NO"

  138. {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 10 }

    {0, 0, 0 }

    2

    Returns: "NO"

  139. {10000, 10000, 10000 }

    {-9999, -9999, -9999 }

    {-10000, -10000, -10000 }

    {9998, 9998, 9998 }

    100

    Returns: "YES"

  140. {0, 0, 0 }

    {0, 0, 0 }

    {0, 0, 10 }

    {0, 0, 0 }

    1

    Returns: "NO"

  141. {1, 1, 1 }

    {1, 1, 1 }

    {2, 2, 2 }

    {1, 1, 1 }

    10

    Returns: "YES"

  142. {-2838, -7940, -2936 }

    {1, 1, -2 }

    {532, 3850, 9590 }

    {1, 0, -3 }

    5410

    Returns: "YES"

  143. {0, 0, 0 }

    {0, 0, 0 }

    {100, 0, 0 }

    {100, 0, 0 }

    100

    Returns: "YES"

  144. {0, 0, 1 }

    {0, 0, 2 }

    {0, 0, 5 }

    {0, 0, 1 }

    1

    Returns: "YES"

  145. {0, 0, 0 }

    {0, 0, 0 }

    {1, 1, 1 }

    {0, 0, 0 }

    1

    Returns: "NO"

  146. {10000, 10000, 1000 }

    {10000, -10000, 10000 }

    {10000, 10000, -1000 }

    {10000, -10000, -10000 }

    1999

    Returns: "NO"

  147. {0, 0, 0 }

    {0, 0, 10000 }

    {0, 0, 500 }

    {0, 0, -10000 }

    1

    Returns: "YES"

  148. {0, 0, 0 }

    {2, 2, 0 }

    {9, 0, 5 }

    {0, 2, 0 }

    5

    Returns: "YES"

  149. {1774, 4491, 7810 }

    {0, 0, 0 }

    {-2322, 5793, 9897 }

    {0, 0, 0 }

    10000

    Returns: "YES"

  150. {0, 0, 0 }

    {0, 0, 0 }

    {1000, 0, 0 }

    {0, 0, 0 }

    1

    Returns: "NO"

  151. {0, 0, 0 }

    {1000, 1000, 1000 }

    {0, 0, 0 }

    {-1000, -1000, -1000 }

    1

    Returns: "YES"

  152. {0, 0, 0 }

    {-10000, -10000, -10000 }

    {0, 0, 0 }

    {10000, 10000, 10000 }

    10000

    Returns: "YES"

  153. {4336, 46, -2571 }

    {5882, 3100, 9715 }

    {121, 1734, -5770 }

    {5593, 7870, 6705 }

    9755

    Returns: "YES"

  154. {0, 0, 0 }

    {1, 1, 1 }

    {0, 0, 100 }

    {1, 1, 1 }

    1

    Returns: "NO"

  155. {0, 0, 0 }

    {100, 100, 0 }

    {442, 0, 10 }

    {-100, 100, 0 }

    10

    Returns: "YES"

  156. {10000, 10000, 10000 }

    {-10000, -10000, -10000 }

    {-10000, -10000, -10000 }

    {10000, 10000, 10000 }

    0

    Returns: "YES"

  157. {-579, -553, -631 }

    {-782, -729, -833 }

    {-784, -774, -588 }

    {-605, -962, -701 }

    309

    Returns: "YES"

  158. {0, 0, 0 }

    {5, 5, 5 }

    {4, 4, 0 }

    {5, 5, 5 }

    5

    Returns: "NO"

  159. {5, 7, 8 }

    {4, 1, -7 }

    {-4, 5, 7 }

    {4, 1, -7 }

    4

    Returns: "NO"

  160. {10000, 10000, 1000 }

    {10000, -10000, 10000 }

    {10000, 10000, -1000 }

    {10000, -10000, -10000 }

    2000

    Returns: "YES"

  161. {-1, -1, 0 }

    {10000, 10000, 0 }

    {1, -1, 0 }

    {-10000, 10000, 0 }

    0

    Returns: "YES"

  162. {-2838, -7940, -2936 }

    {1, -21, -2 }

    {5, 3890, 9590 }

    {9, -32, -3 }

    341

    Returns: "NO"

  163. {1, 1, 1 }

    {1, 2, 3 }

    {2, 3, 3 }

    {-1, -2, -3 }

    3

    Returns: "YES"

  164. {0, 0, 0 }

    {0, 0, 0 }

    {0, 10, 0 }

    {10, -10, 0 }

    9

    Returns: "YES"

  165. {0, 0, 0 }

    {1, 1, 0 }

    {1, 2, 0 }

    {0, 0, 0 }

    0

    Returns: "NO"

  166. {0, 0, 0 }

    {500, 0, 0 }

    {1, 0, 0 }

    {-500, 0, 0 }

    0

    Returns: "YES"

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: