The following graph G is called a Petersen graph and its vertices have been numbered from 0 to 9. Some letters have also been assigned to vertices of G, as can be seen from the following picture:
Let’s consider a walk W in graph G, which consists of L vertices W1, W2, …, WL. A string S of L letters 'A' – 'E' is realized by walk W if the sequence of letters written along W is equal to S. Vertices can be visited multiple times while walking along W.
For example, S = 'ABBECCD' is realized by W = (0, 1, 6, 9, 7, 2, 3). Determine whether there is a walk W which realizes a given string S in graph G, and if so then find the lexicographically least such walk. The only line of input contains one string S. If there is no walk W which realizes S, then output -1 otherwise, you should output the least lexicographical walk W which realizes S.
Input : s = 'ABB' Output: 016 Explanation: As we can see in the graph the path from ABB is 016. Input : s = 'AABE' Output :-1 Explanation: As there is no path that exists, hence output is -1.
We apply breadth first search to visit each vertex of the graph.
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