Weighted Random Sampling Generator (Streaming)

You are given:

• A list of distinct integers values.
• A matching list of nonnegative probabilities (weights) that should sum to 1 within a small tolerance.

Implement a Python solution that supports streaming (potentially infinite) weighted draws, validates inputs, and is numerically robust.

Requirements

1. Input validation
   • values and weights must be the same nonzero length.
   • values must contain distinct integers.
   • weights must be nonnegative; zero-weight items are allowed and must never be sampled.
   • The sum of weights should be 1 within a small tolerance; handle floating-point rounding and renormalize when needed.
2. Generator interface
   • Provide a generator that yields an infinite stream of draws following the specified distribution.
   • Allow deterministic behavior via a random seed.
3. Efficient sampling methods
   • Implement at least one efficient method and optionally both:
     • Prefix sums with binary search (CDF + bisect): O(n) preprocess, O(log n) per sample, O(n) space.
     • Alias method (Vose/Walker): O(n) preprocess, O(1) per sample, O(n) space.
   • Explain time/space trade-offs and when to use each.
4. Numerical robustness
   • Clamp tiny negative weights caused by rounding to zero.
   • Renormalize weights if their sum differs from 1 by more than a tolerance.
   • Ensure the final CDF ends at exactly 1.0 to avoid edge-case misses.
5. Tests
   • Unit tests with:
     • Deterministic checks via random seeding (same seed → same sequence; different seeds → different sequences with high probability).
     • Statistical verification over many samples (e.g., 50k–200k) that empirical frequencies are close to target probabilities.
     • Edge-case validation (zeros, invalid inputs).

Provide clean, well-documented code and explain the design choices and trade-offs.