import java.io.IOException;
import java.util.TreeSet;
import java.util.ArrayList;

public class WPtrRefClique {

	//
	// Produce the ith combination of superset, of a given size.
	//
	public static TreeSet<Integer> choose(TreeSet<Integer> superset, int size, int index) {
		if (size==0)
			return new TreeSet<Integer>();

		TreeSet<Integer> superb = new TreeSet<Integer>(superset);

		int chosen = superb.pollFirst(),
			target = nCr(superb.size(), size-1),
			lastTarget = 0;

		while (index >= target) {
			chosen = superb.pollFirst();
			lastTarget = target;
			target += nCr(superb.size(), size-1);			
		}

		TreeSet<Integer> out = new TreeSet<Integer>();
		out.add(chosen);
		out.addAll(choose(superb, size-1, index-lastTarget));

		return out;
	}

	public static int nCr (int n, int r) {
		if (n==0 || r==0 || r==n)
			return 1;
		return nCr(n-1, r) + nCr(n-1, r-1);
	}

	public static void main(String[] args) {
		if (args.length < 1) {
			System.out.println("PARAMS: ref-file");
			return;
		}

		try {
			Instance inst = Instance.fromDir(args[0]);
			int num_authors = inst.getNumAuthors();

			//System.out.println("c max-clique formulation of "+args[0]);
			System.out.println("p edge " + (15*num_authors) + " 0");

			ArrayList<ArrayList<TreeSet<Integer>>> combinations = new ArrayList<>(num_authors);

			// Calculate all combinations size 4 from each person's allowed papers.
			// Every time we calculate a set, compare it against all existing sets from previous authors.
			// This is probably very memory heavy -- I don't much feel like optimisation today.
			for (int i=0; i<num_authors; i++) {
				TreeSet<Integer> allowedPapers = inst.getAuthorPapers(i);
				ArrayList<TreeSet<Integer>> allCombos = new ArrayList<>(15);
				combinations.add(allCombos);

				for (int j=0; j<15; j++) {
					TreeSet<Integer> subset = choose(allowedPapers, 4, j);
					allCombos.add(subset);

					// Now compare against vertices for past authors.
					int myNum = 15*i + j + 1;
					
					int score = 0;
					for (Integer p : subset){
						score += inst.getScore(p);
					}
					
					System.out.println("n " + myNum + " " + score);
					
					for (int x=0; x<i; x++) {
						for (int y=0; y<15; y++) {
							int theirNum = 15*x + y + 1;

							TreeSet<Integer> isect = new TreeSet<Integer>(subset);
							isect.retainAll(combinations.get(x).get(y));

							if (isect.size()==0)
								System.out.println("e "+theirNum+" "+myNum);
						}
					}
				}	
			}

		} catch (IOException e) {
			System.err.println("Bad file!");
			System.err.println(e);
		}
	}
}