Statistics

Problem Statement for "MyFriends"

Problem Statement

There is a group of n kids, numbered 0 through n-1, where n is an odd number. Each kid has some friends within the group, and each kid knows how many friends each of the other kids has. Friendship is symmetric, so if kid 0 is a friend of kid 1, then kid 1 is a friend of kid 0. Each kid i also supports exactly one other kid (i+k) % n, not necessarily a friend.


You ask each kid to answer the following question: Consider each kid in the group except yourself and the kid you support. What is the sum of the number of friends each of them has? For example, if you ask kid 0 this question, and kid 0 supports kid 1, he should tell you (the number of friends kid 2 has) + (the number of friends kid 3 has) + ... + (the number of friends kid n-1 has).


You are given a int[] sumFriends, where the i-th element (0-indexed) is the answer given to you by kid i. Some of the kids might not be telling the truth (they are just kids, forgive them). Return "IMPOSSIBLE" if it is impossible for all the given answers to be accurate. Otherwise, return "POSSIBLE" (all quotes for clarity).

Definition

Class:
MyFriends
Method:
calcFriends
Parameters:
int[], int
Returns:
String
Method signature:
String calcFriends(int[] sumFriends, int k)
(be sure your method is public)

Constraints

  • sumFriends will contain odd number of elements.
  • sumFriends will contain between 3 and 49 elements, inclusive.
  • Each element of sumFriends will be between 0 and 9999, inclusive.
  • k will be between 1 and (number of elements in sumFriends)-1, inclusive.

Examples

  1. {8, 6, 4, 7, 5}

    2

    Returns: "IMPOSSIBLE"

  2. {8, 9, 8, 8, 9}

    2

    Returns: "POSSIBLE"

    We can get such sums only if kid 1 has 2 friends and all other kids have 3 friends. Such a situation is possible. For example: Kid His/her friends 0 1, 3, 4 1 0, 2 2 1, 3, 4 3 0, 2, 4 4 0, 2, 3

  3. {7, 6, 5, 4, 4}

    2

    Returns: "IMPOSSIBLE"

  4. {5, 6, 5, 4, 4}

    1

    Returns: "POSSIBLE"

  5. {11, 10, 12, 10, 11}

    2

    Returns: "POSSIBLE"

  6. {12, 12, 12, 12, 12}

    4

    Returns: "POSSIBLE"

  7. {8, 9, 8, 9, 8, 9, 9}

    5

    Returns: "POSSIBLE"

  8. {41, 49, 46, 45, 41, 49, 49, 43, 46, 46, 49}

    4

    Returns: "POSSIBLE"

  9. {204, 201, 194, 201, 203, 203, 203, 195, 200, 201, 199, 204, 196, 203, 202, 202, 201, 200, 199, 202, 205}

    5

    Returns: "POSSIBLE"

  10. {1095, 1091, 1085, 1096, 1096, 1095, 1094, 1091, 1099, 1094, 1093, 1097, 1089, 1094, 1095, 1085, 1101, 1093, 1097, 1095, 1093, 1091, 1093, 1095, 1101, 1096, 1099, 1095, 1096, 1083, 1097, 1104, 1095, 1102, 1106, 1097, 1100, 1091, 1096, 1097, 1090, 1096, 1099, 1099, 1103, 1098, 1093}

    39

    Returns: "POSSIBLE"

  11. {1122, 1118, 1122, 1118, 1124, 1119, 1121, 1123, 1117, 1116, 1118, 1119, 1118, 1122, 1120, 1116, 1127, 1123, 1122, 1119, 1117, 1124, 1129, 1129, 1119, 1122, 1116, 1118, 1123, 1120, 1119, 1121, 1122, 1122, 1117, 1119, 1115, 1127, 1123, 1120, 1116, 1122, 1117, 1118, 1122, 1115, 1121, 1125, 1114}

    16

    Returns: "POSSIBLE"

  12. {425, 427, 428, 429, 430, 424, 437, 432, 429, 430, 423, 429, 430, 427, 427, 428, 429, 434, 430, 425, 429, 432, 433, 435, 429, 423, 429, 426, 430, 425, 418}

    11

    Returns: "POSSIBLE"

  13. {8, 8, 8, 8, 10, 9, 9}

    5

    Returns: "POSSIBLE"

  14. {16, 16, 18, 20, 23, 20, 16, 19, 20}

    1

    Returns: "POSSIBLE"

  15. {434, 437, 444, 438, 434, 448, 441, 435, 440, 440, 440, 437, 436, 441, 439, 440, 438, 439, 445, 441, 441, 443, 433, 442, 440, 431, 436, 440, 436, 433, 444, 430, 439, 442, 437, 439, 438, 442, 436, 439, 435, 438, 439}

    3

    Returns: "POSSIBLE"

  16. {186, 187, 180, 190, 182, 187, 184, 186, 190, 186, 186, 185, 193, 183, 187, 182, 189, 186, 186, 185, 186, 192, 181, 188, 184, 189, 187, 186, 187}

    20

    Returns: "POSSIBLE"

  17. {578, 572, 569, 564, 560, 572, 570, 574, 580, 566, 567, 573, 573, 571, 567, 570, 575, 570, 570, 569, 565, 569, 573, 571, 567, 565, 568, 573, 570, 568, 573, 557, 568, 570, 574, 576, 566, 571, 572, 573, 571, 570, 564, 572, 570, 565, 567, 570, 570}

    22

    Returns: "POSSIBLE"

  18. {188, 193, 184, 190, 190, 190, 185, 190, 185, 186, 187, 187, 192, 189, 191, 192, 188, 193, 189, 186, 184, 190, 194, 187, 188, 191, 190, 187, 193, 186, 185, 190, 185, 188, 187}

    14

    Returns: "POSSIBLE"

  19. {67, 69, 68, 68, 71, 71, 72, 69, 70, 73, 72, 69, 71, 71, 73, 74, 66, 69, 70, 72, 70, 66, 67, 69, 71}

    20

    Returns: "POSSIBLE"

  20. {177, 182, 178, 181, 176, 179, 183, 182, 177, 177, 180, 178, 175, 179, 178, 181, 176, 175, 183, 178, 172, 180, 173, 181, 177, 176, 186, 176, 178, 178, 176, 181, 181}

    8

    Returns: "POSSIBLE"

  21. {173, 174, 174, 172, 173, 171, 170, 170, 174, 169, 176, 169, 171, 174, 173, 170, 174, 166, 167, 173, 176, 169, 168, 172, 171, 171, 177, 171, 168, 174, 175, 169, 170, 173, 169}

    25

    Returns: "POSSIBLE"

  22. {197, 191, 193, 192, 194, 192, 190, 196, 188, 197, 195, 196, 196, 192, 196, 194, 195, 198, 197, 193, 197, 196, 195, 192, 196, 194, 191, 195, 192, 188, 193, 191, 194, 196, 193, 193, 189, 191, 190}

    32

    Returns: "POSSIBLE"

  23. {38, 33, 36, 39, 37, 39, 38, 39, 35, 38, 34, 34, 35, 32, 38, 32, 35, 36, 32}

    3

    Returns: "POSSIBLE"

  24. {135, 139, 137, 138, 134, 138, 135, 136, 135, 138, 135, 137, 136, 140, 138, 133, 140, 140, 138, 131, 140, 138, 135, 138, 137, 132, 133, 135, 137, 135, 136, 133, 137, 140, 139, 137, 137, 137, 139}

    4

    Returns: "POSSIBLE"

  25. {13, 15, 14, 14, 14, 13, 12, 12, 13, 13, 11}

    10

    Returns: "POSSIBLE"

  26. {223, 228, 225, 235, 226, 227, 234, 227, 227, 228, 230, 222, 227, 225, 223, 219, 232, 224, 228, 231, 226, 228, 226, 233, 228, 232, 230, 224, 219, 230, 226, 227, 227, 227, 230, 231, 232, 232, 233, 228, 226, 223, 228, 224, 223}

    13

    Returns: "POSSIBLE"

  27. {4, 2, 4, 2, 4, 3, 3, 4, 2}

    7

    Returns: "POSSIBLE"

  28. {1,1,1}

    1

    Returns: "IMPOSSIBLE"

  29. {625, 622, 622, 625, 621, 615, 619, 620, 616, 621, 620, 618, 623, 625, 624, 624, 626, 625, 624, 622, 612, 611, 621, 630, 630, 622, 626, 632, 628, 624, 624, 622, 623, 622, 620, 623, 630, 630, 625, 632, 626, 618, 621, 622, 625}

    1

    Returns: "POSSIBLE"

  30. {659, 658, 666, 661, 664, 676, 667, 670, 674, 671, 673, 671, 677, 676, 668, 681, 677, 666, 670, 680, 673, 665, 680, 675, 673, 671, 676, 673, 669, 674, 675, 666, 676, 676, 668, 678, 674, 671, 676, 668, 669, 671, 662, 662, 660}

    3

    Returns: "POSSIBLE"

  31. {699, 697, 696, 696, 697, 701, 692, 695, 697, 693, 701, 693, 704, 705, 693, 695, 699, 709, 700, 693, 691, 698, 702, 694, 697, 700, 694, 701, 698, 701, 697, 698, 703, 702, 703, 695, 699, 695, 690, 701, 697, 696, 695, 688, 700}

    5

    Returns: "POSSIBLE"

  32. {538, 537, 524, 537, 536, 554, 533, 540, 543, 535, 546, 541, 541, 530, 539, 535, 540, 533, 528, 540, 553, 537, 535, 539, 536, 554, 539, 542, 536, 542, 539, 541, 529, 535, 542, 555, 534, 541, 542, 533, 548, 538, 535, 536, 541}

    15

    Returns: "POSSIBLE"

  33. {596, 603, 601, 603, 597, 597, 596, 598, 596, 603, 599, 606, 603, 595, 593, 598, 599, 596, 603, 592, 598, 599, 600, 600, 593, 597, 604, 598, 592, 600, 598, 602, 599, 598, 595, 591, 601, 598, 590, 602, 598, 608, 595, 595, 593}

    30

    Returns: "POSSIBLE"

  34. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    48

    Returns: "POSSIBLE"

  35. {381, 369, 372, 373, 376, 371, 369, 371, 374, 373, 374, 377, 384, 371, 373, 375, 375, 368, 370, 376, 380, 379, 371, 376, 380, 372, 375, 375, 375, 371, 371, 379, 376, 381, 373, 371, 375, 373, 373, 376, 371, 377, 369, 377, 368, 378, 371, 372, 373}

    12

    Returns: "POSSIBLE"

  36. {27, 28, 28, 28, 28, 28, 27, 29, 26, 27, 27, 27, 25, 26, 29, 27, 26, 26, 27, 28, 26}

    18

    Returns: "POSSIBLE"

  37. {63, 65, 62, 68, 64, 65, 65, 64, 66, 64, 67, 59, 64, 64, 65, 64, 63, 63, 63, 68, 67, 62, 64, 64, 67}

    4

    Returns: "POSSIBLE"

  38. {22, 19, 20, 19, 22, 19, 20, 22, 21, 23, 21, 21, 23, 22, 22, 21, 23}

    3

    Returns: "POSSIBLE"

  39. {2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256, 2256}

    7

    Returns: "POSSIBLE"

  40. {1869, 1868, 1869, 1871, 1868, 1865, 1869, 1867, 1871, 1870, 1875, 1871, 1859, 1866, 1874, 1872, 1868, 1873, 1868, 1864, 1860, 1877, 1875, 1864, 1870, 1869, 1869, 1868, 1870, 1870, 1864, 1867, 1869, 1871, 1874, 1868, 1869, 1861, 1864, 1871, 1872, 1869, 1869, 1867, 1862, 1864, 1872, 1872, 1862}

    7

    Returns: "POSSIBLE"

  41. {354, 356, 356, 354, 354, 353, 356, 353, 355, 353, 358, 354, 354, 354, 357, 356, 353, 353, 353, 356, 356}

    9

    Returns: "POSSIBLE"

  42. {492, 489, 490, 490, 496, 488, 493, 493, 495, 490, 489, 489, 490, 495, 488, 491, 494, 492, 490, 490, 493, 490, 494, 489, 492}

    9

    Returns: "POSSIBLE"

  43. {232, 233, 233, 234, 232, 232, 234, 233, 233, 232, 233, 234, 233, 232, 233, 233, 234}

    4

    Returns: "POSSIBLE"

  44. {1097, 1095, 1102, 1096, 1085, 1102, 1090, 1084, 1094, 1090, 1094, 1090, 1095, 1098, 1087, 1094, 1091, 1088, 1088, 1093, 1093, 1090, 1100, 1095, 1086, 1102, 1095, 1085, 1100, 1094, 1094, 1098, 1095, 1102, 1096, 1096, 1097, 1096, 1093, 1096, 1096, 1089, 1095, 1090, 1087, 1090, 1088, 1094, 1095}

    3

    Returns: "POSSIBLE"

  45. {324, 327, 326, 326, 326, 328, 328, 327, 329, 330, 330, 321, 322, 321, 324, 325, 326, 328, 327, 327, 324, 329, 330, 320, 326, 322, 327, 322, 326, 329, 323, 324, 324, 328, 329, 327, 324, 328, 328, 326, 323, 332, 323, 324, 327, 330, 329, 329, 325}

    12

    Returns: "POSSIBLE"

  46. {424, 420, 416, 412, 421, 420, 416, 414, 413, 408, 416, 419, 413, 420, 411, 419, 418, 411, 413, 415, 421, 420, 421, 421, 413, 414, 420, 419, 419, 416, 414, 416, 420, 412, 418, 413, 415, 415, 412, 415, 412, 421, 415, 418, 420, 414, 410, 416, 419}

    21

    Returns: "POSSIBLE"

  47. {125, 126, 124, 121, 127, 123, 126, 127, 125, 126, 125, 124, 128, 125, 126, 127, 122, 127, 126, 124, 123, 122, 125, 125, 122, 123, 125, 124, 126, 123, 123, 128, 123, 127, 122, 121, 123, 126, 120, 124, 124, 125, 127, 123, 126, 127, 125, 127, 127}

    35

    Returns: "POSSIBLE"

  48. {82, 82, 82, 84, 83, 82, 81, 83, 84, 80, 84, 81, 84, 84, 83, 84, 81, 83, 81, 81, 83, 79, 83, 85, 82, 85, 83, 84, 83, 81, 83, 82, 81, 79, 81, 83, 80, 83, 86, 83, 85, 84, 83, 81, 82, 82, 83, 82, 82}

    15

    Returns: "POSSIBLE"

  49. {2634, 6063, 7989, 5509, 5787, 1844, 4858, 3077, 7181, 7176, 3202, 1926, 8307, 257, 182, 6762, 3298, 4144, 485, 9866, 8229, 9332, 2851, 6434, 6402, 1771, 7171, 4237, 7948, 3915, 1160, 8083, 6506, 5792, 6137, 5728, 1305, 4150, 3076, 6183, 173, 9610, 5412, 6422, 4590}

    1

    Returns: "IMPOSSIBLE"

  50. {6924, 37, 9324, 6112, 2760, 3591, 1433, 2723, 101, 577, 4005, 861, 8604, 1481, 9316, 5684, 9389, 1249, 599, 5345, 9296, 1860, 4214, 5649, 9080, 5041, 5966, 5981, 2284, 390, 5541, 1613, 4328, 2193, 7606, 1129, 7313, 804, 4921, 9184, 9016, 1271, 5537, 3148, 8353}

    3

    Returns: "IMPOSSIBLE"

  51. {162, 6381, 8933, 4533, 3707, 1879, 9653, 7717, 1613, 7025, 6077, 8591, 5834, 4306, 6086, 7254, 8465, 6491, 2554, 1133, 6083, 3198, 6227, 3428, 1747, 3041, 7668, 5174, 6909, 7759, 8503, 98, 1401, 144, 7287, 8761, 8479, 9211, 9152, 7320, 3724, 3529, 2675, 614, 7094}

    5

    Returns: "IMPOSSIBLE"

  52. {1083, 1182, 6159, 141, 8718, 6187, 275, 4931, 2926, 5736, 777, 1757, 1817, 8295, 872, 490, 4326, 311, 8039, 5252, 5862, 402, 226, 9300, 7881, 8, 5024, 2235, 6404, 2829, 4580, 3182, 9266, 2878, 5761, 7793, 520, 8586, 7889, 2984, 2238, 430, 5223, 2506, 5050}

    15

    Returns: "IMPOSSIBLE"

  53. {6785, 2676, 1575, 4127, 6706, 7031, 6411, 2102, 1839, 8584, 8163, 4571, 375, 7335, 7520, 8876, 593, 1424, 5017, 9822, 303, 7938, 1206, 737, 6958, 8848, 2747, 6276, 5839, 9448, 8609, 8155, 6155, 354, 2443, 7440, 2273, 8747, 2519, 2441, 4148, 9459, 852, 121, 7620, 5875, 2899, 4712, 9017}

    28

    Returns: "IMPOSSIBLE"

  54. {5841, 7268, 1507, 1708, 4365, 5431, 6755, 4546, 9504, 3027, 4723, 699, 7930, 4230, 8388, 6023, 717, 8158, 8705, 3139, 7774, 5191, 1028, 3329, 5597, 2913, 5628, 9253, 7880, 2213, 7102, 6178, 3405, 5385, 7162, 8501, 9247, 2483, 9440, 6943, 7371}

    30

    Returns: "IMPOSSIBLE"

  55. {2137, 7740, 4147, 8684, 9955, 5563, 2971, 8017, 9869, 107, 1488, 6264, 7210, 6068, 5909, 87, 4002, 1102, 9093, 8302, 4791, 2656, 119, 9623, 1514, 1082, 8611, 1244, 5070}

    12

    Returns: "IMPOSSIBLE"

  56. {3178, 9166, 8552, 6656, 9493, 4715, 2518, 4468, 3341, 3768, 9797, 818, 3695, 1689, 8729, 7615, 4718, 8249, 4082}

    2

    Returns: "IMPOSSIBLE"

  57. {1452, 3908, 1494, 4243, 1812, 8709, 3794, 9360, 5544, 7623, 3130, 8115, 4193, 4102, 7043, 376, 1511, 1684, 7762, 5834, 2316, 8132, 9206, 6209, 759, 5331, 1592, 8105, 4436, 2157, 1207, 6294, 2825, 2591, 1405, 5220, 7756, 4169, 4565, 5139, 4195, 2887, 8273}

    16

    Returns: "IMPOSSIBLE"

  58. {4096, 1623, 6124, 767, 6590, 9836, 7202, 289, 3439, 5396, 9159, 9322, 6587, 504, 6609, 3369, 9400, 9065, 1597, 4790, 6490, 4692, 7300, 3304, 1006, 5719, 2398, 537, 393, 307, 7300, 2038, 2509, 4962, 154}

    25

    Returns: "IMPOSSIBLE"

  59. {64, 207, 340, 147, 172, 218, 41, 277, 434, 144, 255, 204, 209, 88, 124, 332, 347, 324, 182, 265, 373, 91, 362, 80, 5, 196, 458, 0, 125, 216, 29, 297, 482, 112, 175, 430, 317, 289, 97, 357, 233}

    28

    Returns: "IMPOSSIBLE"

  60. {131, 217, 227, 213, 255, 275, 100, 240, 247, 229, 428, 325, 361, 158, 244, 242, 424, 305, 181, 119, 208, 110, 469, 342, 45, 357, 54, 302, 2, 263, 220, 466, 289, 398, 381, 342, 238, 120, 300, 426, 126, 303, 154, 62, 201, 243, 185, 404, 230}

    17

    Returns: "IMPOSSIBLE"

  61. {108, 497, 479, 410, 209, 205, 116, 303, 240, 261, 1, 308, 486, 257, 311}

    5

    Returns: "IMPOSSIBLE"

  62. {141, 263, 244, 239, 201, 156, 477, 139, 157, 236, 357, 92, 399, 185, 249, 307, 119, 281, 479, 67, 298, 424, 430, 391, 474, 350, 305, 312, 184, 365, 486, 31, 347, 475, 5, 265, 145}

    2

    Returns: "IMPOSSIBLE"

  63. {289, 352, 235, 78, 110, 318, 166, 92, 34, 388, 441, 437, 62, 83, 195, 157, 310, 4, 410, 105, 119, 430, 242, 9, 456, 497, 28, 297, 438, 37, 31, 15, 52, 159, 74, 386, 41, 248, 303, 366, 71, 304, 238, 258, 456, 193, 152}

    22

    Returns: "IMPOSSIBLE"

  64. {39, 12, 44, 42, 10, 13, 38}

    5

    Returns: "IMPOSSIBLE"

  65. {36, 39, 25}

    2

    Returns: "IMPOSSIBLE"

  66. {46, 6, 32, 34, 3, 9, 28, 32, 21}

    2

    Returns: "IMPOSSIBLE"

  67. {47, 41, 16, 6, 11, 43, 39, 43, 22, 10, 47, 36, 36, 20, 33, 11, 49, 24, 12, 31, 10, 4, 0, 23, 39, 23, 27, 47, 41, 16, 7, 19, 20, 1, 9, 24, 47, 16, 28, 30, 17, 39, 30, 10, 44, 20, 5}

    24

    Returns: "IMPOSSIBLE"

  68. {4, 15, 33, 18, 32, 29, 33, 31, 40, 33, 9}

    5

    Returns: "IMPOSSIBLE"

  69. {4, 4, 4, 3, 2}

    1

    Returns: "IMPOSSIBLE"

    If in the solution of ivan_metelsky, line if (tot % (N - 2) != 0) return "IMPOSSIBLE"; is commented this example passes.

  70. {6, 0, 0, 0, 0}

    1

    Returns: "IMPOSSIBLE"

    if (res[0] != 0) return "IMPOSSIBLE"; for (int i=0; i<N; i++) if (res[i] < 0 || res[i] >= N) return "IMPOSSIBLE"; if (sum[i] > tot) return "IMPOSSIBLE";

  71. {4, 4, 0}

    1

    Returns: "IMPOSSIBLE"

  72. {6, 6, 6, 6, 6}

    1

    Returns: "POSSIBLE"

    With only one sort in Havel-Hakimi this examples give IMPOSSIBLE, but it should give POSSIBLE - 2-regular graph with 5 vertices; cycle.

  73. {15, 15, 15, 15, 15}

    3

    Returns: "IMPOSSIBLE"

    if (res[i] < 0 || res[i] >= N) return "IMPOSSIBLE"; into if (res[i] < 0 || res[i] > N) return "IMPOSSIBLE"; and without if (res[i] > i) return "IMPOSSIBLE"; "solution" fails

  74. {2, 1, 2}

    1

    Returns: "IMPOSSIBLE"

    Without if (res[0] != 0) return "IMPOSSIBLE"; and if (res[j] == 0) return "IMPOSSIBLE"; fails

  75. {16, 17, 15, 15, 18, 17, 10, 16, 17}

    6

    Returns: "IMPOSSIBLE"

    without if (res[j] == 0) return "IMPOSSIBLE"; and check about is something divisible if (tot % 2 != 0) return "IMPOSSIBLE"; if (tot % (N - 2) != 0) return "IMPOSSIBLE"; it fails

  76. {16, 15, 15, 12, 16, 17, 10, 16, 16}

    6

    Returns: "IMPOSSIBLE"

    without if (tot % 2 != 0) return "IMPOSSIBLE"; if (res[j] == 0) return "IMPOSSIBLE"; fails

  77. {12, 11, 11, 11, 12, 14, 10, 13, 11}

    6

    Returns: "IMPOSSIBLE"

    Without only if (tot % 2 != 0) return "IMPOSSIBLE"; it fails

  78. {9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999, 9999}

    35

    Returns: "IMPOSSIBLE"

  79. {1, 2, 3}

    1

    Returns: "IMPOSSIBLE"

    Here kid 2 supports kid 0, so he tells us the number of friends of kid 1. But it's obviously impossible for kid 1 to have 3 friends.

  80. {6, 7, 7, 7, 6}

    1

    Returns: "IMPOSSIBLE"

    Breaks max-flow algorithm (that is for directed graphs) described http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=maxFlow2

  81. {12, 12, 12, 12, 9, 5, 8 }

    1

    Returns: "IMPOSSIBLE"

  82. {4, 4, 4, 4, 4, 4, 4 }

    2

    Returns: "IMPOSSIBLE"

  83. {4, 4, 8, 4, 4 }

    2

    Returns: "IMPOSSIBLE"

  84. {0, 2, 4, 4, 4, 4, 4, 4, 2 }

    1

    Returns: "IMPOSSIBLE"

  85. {1, 2, 3 }

    1

    Returns: "IMPOSSIBLE"

  86. {64, 64, 64, 64, 64, 64, 68, 72, 72, 73, 69 }

    1

    Returns: "IMPOSSIBLE"

  87. {2, 0, 0 }

    1

    Returns: "IMPOSSIBLE"

  88. {2, 0, 2 }

    1

    Returns: "IMPOSSIBLE"

  89. {1, 1, 1 }

    2

    Returns: "IMPOSSIBLE"

  90. {6, 5, 5, 4, 4 }

    1

    Returns: "POSSIBLE"

  91. {0, 0, 2 }

    1

    Returns: "IMPOSSIBLE"

  92. {5, 6, 7, 8, 7 }

    1

    Returns: "IMPOSSIBLE"

  93. {0, 2, 0 }

    1

    Returns: "IMPOSSIBLE"

  94. {0, 0, 0, 0, 0, 0, 1 }

    1

    Returns: "IMPOSSIBLE"

  95. {6, 7, 9, 7, 7 }

    2

    Returns: "IMPOSSIBLE"

  96. {6, 6, 6, 6, 3, 0, 3 }

    1

    Returns: "IMPOSSIBLE"

  97. {4, 7, 10, 9, 6 }

    1

    Returns: "IMPOSSIBLE"

  98. {8, 9, 8, 8, 9 }

    2

    Returns: "POSSIBLE"

  99. {2, 2, 0, 3, 2 }

    1

    Returns: "IMPOSSIBLE"

  100. {0, 0, 0, 0, 0 }

    1

    Returns: "POSSIBLE"

  101. {0, 0, 1 }

    1

    Returns: "IMPOSSIBLE"

  102. {2, 5, 5, 6, 3 }

    1

    Returns: "IMPOSSIBLE"

  103. {0, 0, 0 }

    1

    Returns: "POSSIBLE"

  104. {6, 6, 9, 12, 9 }

    1

    Returns: "IMPOSSIBLE"

  105. {14, 14, 14, 14, 13 }

    1

    Returns: "IMPOSSIBLE"

  106. {0, 4, 8, 8, 4 }

    1

    Returns: "IMPOSSIBLE"

  107. {2, 4, 6, 7, 5 }

    1

    Returns: "IMPOSSIBLE"

  108. {11, 9, 7, 6, 9 }

    1

    Returns: "IMPOSSIBLE"

  109. {10, 9, 6, 4, 7 }

    1

    Returns: "IMPOSSIBLE"

  110. {3, 3, 3, 3, 3 }

    1

    Returns: "IMPOSSIBLE"

  111. {0, 2, 2 }

    1

    Returns: "IMPOSSIBLE"

  112. {7, 10, 10, 10, 10, 10, 10, 10, 7 }

    1

    Returns: "POSSIBLE"

  113. {7, 7, 7, 7, 7, 7, 7, 7, 7 }

    3

    Returns: "IMPOSSIBLE"

  114. {6, 7, 6, 5, 5 }

    1

    Returns: "IMPOSSIBLE"

  115. {30, 0, 0, 0, 0, 0, 0 }

    1

    Returns: "IMPOSSIBLE"

  116. {642, 646, 638, 641, 639, 640, 641, 643, 639, 647, 644, 637, 653, 641, 637, 645, 647, 643, 635, 649, 647, 646, 646, 645, 649, 642, 642, 639, 646, 645, 644, 652, 641, 647, 653, 638, 650, 653, 640, 648, 649, 644, 642, 645, 652, 650, 644, 652, 646 }

    3

    Returns: "POSSIBLE"

  117. {56, 56, 56, 56, 56, 56, 56, 56, 56 }

    3

    Returns: "POSSIBLE"

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