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Based on @Julian's idea, the solution can be based on union-find method. union all connected nodes. count total groups number M. if there's a group which the good node is the root, than return M-1, else return M.
An optimised union-find algorithms takes almost o(n) to union all nodes. So the time and space complexity of this algorithms is o(n)
- snail914 December 13, 2015