# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement Implement consistent hashing for routing keys to servers. Provide APIs addNode(nodeId, weight), removeNode(nodeId), and getNode(key). Use virtual nodes to balance load and ensure minimal key remapping when nodes join/leave. Explain hash choice, collision handling, and how you pick the number of virtual nodes. Analyze time/space complexity and compare with modulo hashing. ## Recommended Approach Start with a brute-force baseline to confirm correctness, then identify the repeated work or ordering property that enables a better data structure such as a hash map, heap, stack, queue, two pointers, prefix sums, BFS/DFS, or dynamic programming. Write the implementation around a small invariant and test that invariant directly. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity State the baseline complexity and the optimized complexity. For most interview constraints, justify why the optimized approach meets the expected input size. ## Edge Cases and Tests Empty and singleton inputs, duplicates, ties, invalid inputs, boundary values, and tests that exercise the main invariant.