IBM Online Assessment: Make Network Connected - Union Find

You are given n nodes (0..n-1) and a list of bidirectional connections. The goal is to determine the minimum number of operations to make the entire network connected. An operation removes any existing connection and reassigns it to connect two nodes. If there are fewer than n-1 edges you should immediately return -1 since it's impossible to connect all nodes.

This problem tests graph connectivity and counting of redundant edges. A concise approach is:

1. Validate feasibility: if m < n - 1 return -1.
2. Build connectivity using Union-Find (or DFS/BFS) and count how many connected components you end up with.
3. Compute how many edges are "redundant" (extra edges you can rewire). The total minimal edges needed inside components is (n - components). So redundant = m - (n - components). If redundant >= components - 1, you can connect all components with (components - 1) operations; otherwise return -1.

You should be ready to implement Union-Find with path compression and union by rank or an iterative DFS to avoid recursion depth issues. Time complexity: O(n + m). Space: O(n + m) (or O(n) with Union-Find). Be prepared to discuss edge cases (duplicate edges, self-loops, isolated nodes) and to output the actual list of rewire operations if asked.