Need help with travelling salesman problem using breadth first search .

Quote:

only need the shortest path with out calculating the lowest cost.

In your case, The shortest path is the lowest cost.
Cost is how the algorithm compares possible solutions.
Imagine, you want the fastest solution which is not the shortest path because there is highways between a few cities.
If cost is distances between cities, best path is shortest.
If cost is traveling time bztween cities, best path is fastest.

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