LLM Sampling: Temperature, Top-k, Top-p (Nucleus)

Task Implement an LLM token sampler. You are given a logits vector logits of length V and sampling parameters: temperature (>0) top_k (integer, 0 disables) top_p (0..1, 1 disables) seed (for reproducible RNG) Sample one token id as follows: If temperature != 1, divide logits by temperature. Compute softmax to obtain probabilities p (numerically stable). If top_k is enabled: keep only the top-k tokens by probability, zero out the rest, and renormalize. If top_p is enabled: sort by probability descending, keep the smallest prefix whose cumulative prob is >= top_p, zero out the rest, and renormalize. Initialize RNG with seed and sample 1 token from the final distribution; output its 0-based index. Input (stdin) Line 1: V Line 2: V floats for logits Line 3: temperature top_k top_p seed Output (stdout) One line: sampled token id (0-based integer) Constraints 1 <= V <= 5000 Logits may be large/small; use numerically stable softmax. If top_k > V, treat it as V. top_k and top_p may both be enabled (apply in order). Example Input 3 0 0 0 1 0 1 0 Output 2