Problem E
Travelling Salesperson 2D


Your program should take as input a single TSP instance. It will be run several times, once for every test case. The time limit is per test case.

The first line of standard input contains an integer $1 \le N \le 1000$, the number of points. The following $N$ lines each contain a pair of real numbers $x, y$ giving the coordinates of the $N$ points. All numbers in the input have absolute value bounded by $10^{6}$.

The distance between two points is computed as the Euclidean distance between the two points, rounded to the nearest integer.


Standard output should consist of $N$ lines, the $i$’th of which should contain the (0-based) index of the $i$’th point visited.


Let $\text {Opt}$ be the length of an optimal tour, $\text {Val}$ be the length of the tour found by your solution, and $\text {Naive}$ be the length of the tour found by the algorithm below. Define $x = (\text {Val} - \text {Opt}) / (\text {Naive} - \text {Opt})$. (In the special case that $\text {Naive} = \text {Opt}$, define $x = 0$ if $\text {Val} = \text {Opt}$, and $x = \infty $ if $\text {Val} > \text {Opt}$.)

The score on a test case is $0.02^{x}$. Thus, if your tour is optimal, you will get $1$ point on this test case. If your score is halfway between $\text {Naive}$ and $\text {Opt}$, you get roughly $0.14$ points. The total score of your submission is the sum of your score over all test cases. There will be a total of $50$ test cases. Thus, an implementation of the algorithm below should give a score of at least $1$ (it will get $0.02$ points on most test cases, and $1.0$ points on some easy cases where it manages to find an optimal solution).

The algorithm giving the value $\text {Naive}$ is as follows:

   tour[0] = 0
   used[0] = true
   for i = 1 to n-1
      best = -1
      for j = 0 to n-1
         if not used[j] and (best = -1 or dist(tour[i-1],j) < dist(tour[i-1],best))
            best = j
      tour[i] = best
      used[best] = true
   return tour

The sample output gives the tour found by GreedyTour on the sample input. The length of the tour is 323.

Sample Input 1 Sample Output 1
95.0129 61.5432
23.1139 79.1937
60.6843 92.1813
48.5982 73.8207
89.1299 17.6266
76.2097 40.5706
45.6468 93.5470
1.8504 91.6904
82.1407 41.0270
44.4703 89.3650

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