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Generate values by weighted probabilities | Google Interview Question

Quick Overview

This question evaluates understanding of probabilistic sampling, numerical stability, input validation, and algorithmic trade-offs for streaming weighted random draws, including generator determinism via seeding and methods such as CDF/binary-search versus alias for performance.

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

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.
Generator interface
- Provide a generator that yields an infinite stream of draws following the specified distribution.
- Allow deterministic behavior via a random seed.
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.
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.
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.

Quick Overview

Requirements

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.

Generator interface

Provide a generator that yields an infinite stream of draws following the specified distribution.
Allow deterministic behavior via a random seed.

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.

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.

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.

Generate values by weighted probabilities

Quick Overview

Weighted Random Sampling Generator (Streaming)

Requirements

Solution

Comments (0)

Generate values by weighted probabilities

Quick Overview

Weighted Random Sampling Generator (Streaming)

Requirements

Solution

Comments (0)