2nd/10_Wiki/Topics/Frontend/Randomized-Algorithms.md

---
id: wiki-2026-0508-randomized-algorithms
title: Randomized Algorithms
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Randomized Algorithms, Random Algorithms, 확률 알고리즘]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [algorithms, randomization, probability, frontend]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: TypeScript
  framework: none
---

# Randomized Algorithms

## 매 한 줄
> **"매 randomness 의 algorithmic resource 사용"**. Randomized algorithm 은 worst-case input adversary 회피 또는 simpler logic 으로 expected-time 성능 달성. Frontend 에서 quickselect, reservoir sampling, bloom filter, A/B bucketing 등 매 광범위 응용.

## 매 핵심

### 매 두 가지 분류
- **Las Vegas**: 매 항상 correct 결과, runtime 만 random (e.g. randomized quicksort).
- **Monte Carlo**: 매 bounded runtime, 결과는 매 probability 1-ε 로 correct (e.g. Miller-Rabin, bloom filter).

### 매 왜 frontend
- 매 large dataset (virtualized list, large table) 의 sampling.
- 매 client-side A/B test bucketing — deterministic hash + random salt.
- 매 game / animation 의 procedural generation.
- 매 dedup / membership test (bloom filter) 의 memory 절약.

### 매 응용
1. Reservoir sampling — log streaming 의 fixed-size sample.
2. Quickselect — top-K 의 O(n) average.
3. Bloom filter — 매 service worker cache lookup.
4. Random shuffle — 매 Fisher-Yates 만 정답.

## 💻 패턴

### Fisher-Yates shuffle (매 in-place, uniform)
```ts
function shuffle<T>(arr: T[]): T[] {
  for (let i = arr.length - 1; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1));
    [arr[i], arr[j]] = [arr[j], arr[i]];
  }
  return arr;
}
```

### Reservoir sampling (k items from stream)
```ts
function reservoir<T>(stream: Iterable<T>, k: number): T[] {
  const reservoir: T[] = [];
  let i = 0;
  for (const item of stream) {
    if (i < k) reservoir.push(item);
    else {
      const j = Math.floor(Math.random() * (i + 1));
      if (j < k) reservoir[j] = item;
    }
    i++;
  }
  return reservoir;
}
```

### Quickselect (kth smallest, O(n) avg)
```ts
function quickselect(arr: number[], k: number, lo = 0, hi = arr.length - 1): number {
  if (lo === hi) return arr[lo];
  const pivotIdx = lo + Math.floor(Math.random() * (hi - lo + 1));
  const pivot = arr[pivotIdx];
  [arr[pivotIdx], arr[hi]] = [arr[hi], arr[pivotIdx]];
  let store = lo;
  for (let i = lo; i < hi; i++) {
    if (arr[i] < pivot) {
      [arr[i], arr[store]] = [arr[store], arr[i]];
      store++;
    }
  }
  [arr[store], arr[hi]] = [arr[hi], arr[store]];
  if (k === store) return arr[store];
  return k < store ? quickselect(arr, k, lo, store - 1) : quickselect(arr, k, store + 1, hi);
}
```

### Bloom filter (membership, frontend cache)
```ts
class BloomFilter {
  private bits: Uint8Array;
  constructor(private size: number, private k: number) {
    this.bits = new Uint8Array(Math.ceil(size / 8));
  }
  private hash(s: string, seed: number): number {
    let h = seed;
    for (let i = 0; i < s.length; i++) h = (h * 31 + s.charCodeAt(i)) >>> 0;
    return h % this.size;
  }
  add(s: string) {
    for (let i = 0; i < this.k; i++) {
      const idx = this.hash(s, i * 0x9e3779b1);
      this.bits[idx >> 3] |= 1 << (idx & 7);
    }
  }
  has(s: string): boolean {
    for (let i = 0; i < this.k; i++) {
      const idx = this.hash(s, i * 0x9e3779b1);
      if (!(this.bits[idx >> 3] & (1 << (idx & 7)))) return false;
    }
    return true; // possible false positive
  }
}
```

### A/B bucketing (매 deterministic hash + salt)
```ts
import { sha256 } from "@noble/hashes/sha256";

function bucket(userId: string, exp: string, buckets: number): number {
  const h = sha256(`${exp}:${userId}`);
  const n = (h[0] << 24) | (h[1] << 16) | (h[2] << 8) | h[3];
  return (n >>> 0) % buckets;
}
```

### Crypto-secure random (매 token, ID)
```ts
function secureId(bytes = 16): string {
  const a = new Uint8Array(bytes);
  crypto.getRandomValues(a);
  return Array.from(a, b => b.toString(16).padStart(2, "0")).join("");
}
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Top-K from large array | Quickselect (O(n) avg) |
| Sample N from stream | Reservoir sampling |
| Membership test, big set | Bloom filter |
| Token / session ID | `crypto.getRandomValues` |
| A/B bucket | SHA-256 hash + modulo |
| Shuffle | Fisher-Yates 만 |

**기본값**: deterministic algorithm 우선 — randomization 은 매 measured benefit 있을 때 만.

## 🔗 Graph
- 부모: [[Algorithms]] · [[Probability]]
- 변형: [[Las-Vegas-Algorithms]] · [[Monte-Carlo-Methods]]
- 응용: [[Bloom-Filter]] · [[Reservoir-Sampling]] · [[Quickselect]] · [[AB-Testing]]
- Adjacent: [[Hashing]] · [[Data-Sketches]]

## 🤖 LLM 활용
**언제**: large dataset 의 sampling/selection, A/B bucketing, client-side dedup, security-irrelevant random.
**언제 X**: cryptographic context 에 `Math.random` — 매 절대 X. Token, password, nonce 매 `crypto.getRandomValues` 만.

## ❌ 안티패턴
- **Math.random for security**: 매 PRNG 의 predictability — token 에 절대 X.
- **Naive shuffle (`sort(() => Math.random() - 0.5)`)**: 매 non-uniform distribution.
- **Modulo bias**: `Math.floor(Math.random() * n)` 까지는 OK, 매 `crypto` byte % n 매 bias 발생 가능.
- **Repeated bloom filter without size planning**: 매 false positive rate 폭증.

## 🧪 검증 / 중복
- Verified (CLRS Ch.5, Mitzenmacher & Upfal "Probability and Computing", MDN Web Crypto).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — Las Vegas/Monte Carlo 분류, Fisher-Yates/Reservoir/Quickselect/Bloom/AB-bucket 패턴 |