LeetCode 133 Clone Graph - Handling Cycles

Suppose node $1$ connects to node $2$, and node $2$ connects back to node $1$. When you clone node $1$, you recurse into node $2$. Cloning node $2$ tries to recurse back into node $1$. Without protection, this loops forever.

The fix: use a hash map from original nodes to their copies. Before cloning any node, check the map first. If the node already has a copy, return it immediately. This breaks the cycle. You must add each node to the map before recursing into its neighbors.