c coding for this program

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Sam is a tourist, One day he plans to go one country where there are N cities and each pair of city is connected to each other by a bidirectional road. Sam want to visit each city exactly once and he wants to start in one city and end in another city after traveling exactly N-1 roads. You have given a String[] path. If the j-th column of the i-th row of paths is '1', he must travel the road that connects city i and city j.


Suppose there are three cities(A,B,C), and Sam want to travel path between city A to city C. So there are 6 possible paths P(3,2)=6. For this example String[]path is {"001","000","100"} But only 4 paths allowed for Sam that are (B->A->C),(A->C->B),(B->C->A),(C->A->B) and paths( A->B->C) and (C->B->A) are not allowed because path A->C or C->A is not covered.