Find bad GPU nodes with group tests

A cluster has n GPU nodes with ids 0 to n - 1. Each node is either good or bad, and you do not know which in advance. The only way to learn anything is a test service:

class TestServer:
    def test(self, nodes: list[int]) -> bool:
        # True if every node in `nodes` is good; False if at least one is bad.
        ...

A failing test does not say which node is bad or how many are bad. Each call runs a real health job on the hardware, so calls are expensive.

Implement find_bad_nodes(n: int, server: TestServer) -> list[int]. It returns the ids of all bad nodes in ascending order and uses as few test calls as you can.

Constraints

• 0 <= n <= 10^5
• Any number of nodes may be bad, including none or all of them. In practice bad nodes are rare.
• Testing every node on its own (n calls) is correct but too slow when n is large. Aim for a call count that depends mainly on the number of bad nodes k.

Example 1

n = 8, bad nodes = {2, 5}
output: [2, 5]

Testing [0..7] fails, so split. [0..3] fails and [4..7] fails, so keep splitting each half until single nodes remain. Halves that pass, such as [0, 1] and [6, 7], are cleared with one call each.

Example 2

n = 6, bad nodes = {}
output: []

One call on [0..5] passes, so every node is good.

Be ready for follow-ups: there is exactly one bad node, tests run in parallel rounds, you know an upper bound on the number of bad nodes, or tests are sometimes wrong.