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Discussion of Problem 1182. Team Them Up!

Sorry, the test is not small. Now I will give a description of the test. There 5 groups with sizes: (6 1) (5 1) (4 1) (4 1) (4 1). The right answer for this test is 14:14. But the greedy program gives 15:13. I think moderators shall add this test to the test data and many solutions will be rejected.

28
21 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 2 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
22 1 2 3 4 5 6 7 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0
23 1 2 3 4 5 6 7 8 9 10 11 12 13 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 18 19 20 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 19 20 21 22 23 24 25 26 27 28 0
23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 22 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 23 24 25 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27 28 0
23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 26 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25 27 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25 26 28 0
26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25 26 27 0
up
 Do judges want to break greedy wrong solutions? Or it is OK that they are accepted?
 It is strange, that NEERC problem has poor set of tests.
Vladimir Yakovlev (USU) Testset won't be altered (-) // Problem 1182. Team Them Up! 13 Nov 2005 00:38
DO NOT MISLEAD OTHERS WITH YOUR WRONG SAMPLE!!!
MY AC program says NO SOLUTION!
take care of the following nodes
1st group: 1 8 14 19 24! 26
2nd group: 2 3 4 5 6 7 9 10 11 12 13 15 16 17 18 20 21 22 23 24! 25 27 28

when you start deducting from 24 to other non connected with 24 nodes and so on, you will get a contradiction.
My AC prog says

14 24 19 14 9 10 11 12 13 2 3 4 5 6 7
14 1 8 15 16 17 18 20 21 22 23 25 26 27 28