Quiz: Path Compression

You call find(x) on a chain of $1{,}000$ nodes: $x \to a_1 \to a_2 \to \cdots \to \text{root}$. After this single call, what is the depth of node $x$?

1. A.$1{,}000$, unchanged
2. B.$500$, because compression halves the chain
3. C.$\log(1{,}000) \approx 10$
4. D.$1$, because $x$ now points directly to the root