UVa 10959 - The Party, Part I

10959 - The Party, Part I

 * http://acm.uva.es/p/v109/10959.html

Summary
Given an unweighted undirected graph, we're asked the find the distance from a single node (Don Giovanni) to everyone else. This is a simple Single Source Shortest Path (Shortest Path) problem.

Explanation
Since $$ N \leq 1000$$, a $$O( N^2 )$$ is optimal in terms of $$N$$ - the input can be $$O( N^2 )$$ - and that is all that is necessary for this problem, though we can do better if we consider the complexity in terms of $$V$$ and $$E$$ - the edges and vertices. We can get the running time to $$O( E + V )$$ using simply breadth-first search.

Input
2

5 6 0 1 0 2 3 2 2 4 4 3 1 2

5 6 0 1 0 2 3 2 2 4 4 3 1 2

Output
1 1 2 2

1 1 2 2