UVa 10843 - Anne's game

10843 - Anne's game

 * http://acm.uva.es/p/v108/10843.html

Summary
For this problem, we have to find the number of labeled trees on N vertices, modulo 2000000011.

Explanation
Each circle is a vertex and each line drawn is an edge. Clearly after N steps we have a connected graph with N vertices and N-1 edges. Thus the resulting graph is a tree. It can be proved that there are exactly $$N^{N-2}$$ labeled trees on N vertices. Since we only have to print the answer modulo 2000000011, this can be safely calculated without the use of BigNum.

Gotchas
While the answer fits into a 32-bit signed integer, using 64-bit integers is recommended when computing the result to avoid overflow.

Input
3 1 2 3

Output
Case #1: 1 Case #2: 1 Case #3: 3