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How to Perform Welch's t-Test in Python
Calculate the Welch t-statistic and degrees of freedom for two samples with unequal variances using Python's statistics module.
import math
from statistics import mean, variance
def welch_t_test(sample1, sample2):
n1, n2 = len(sample1), len(sample2)
mean1, mean2 = mean(sample1), mean(sample2)
var1, var2 = variance(sample1), variance(sample2)
# Welch's t statistic
t_stat = (mean1 - mean2) / math.sqrt(var1 / n1 + var2 / n2…How to Run a Fisher Exact Test in Python
Compute the two-sided Fisher exact test p-value for a 2x2 contingency table using pure Python and the math module.
from math import comb, factorial
from itertools import combinations
def hypergeometric_probability(a, b, c, d):
"""Probability of observing table [[a, b], [c, d]] under the null."""
row1 = a + b
row2 = c + d
col1 = a + c
col2 = b + d
total = row1 + row2
return (comb(row1, a) * comb(row2, …How to Simulate Fixed-Horizon Testing in Python
Simulate a fixed-horizon experiment by labeling data before the horizon as warmup and after as active/inactive, then summarize via CSV.
import csv
import io
def fixed_horizon_mock(data: list[tuple[float, float, float]], horizon: int) -> str:
"""Simulate fixed-horizon testing, then summarize with CSV output."""
output = io.StringIO()
writer = csv.writer(output)
writer.writerow(["day", "value", "signal", "status"])
for day, value,…How to Simulate Geo Experiments in Python
Build a mock geo experiment simulator with ramp-up/down periods, measuring weekly lift between treatment and control markets.
import random
import math
from dataclasses import dataclass
@dataclass
class GeoMarket:
name: str
base_demand: float
geo_coefficient: float
def simulate_geo_experiment(markets, weeks=12, control_weeks=6):
"""
Simulates a geo experiment with ramp-up and ramp-down periods.
Returns weekly lift p…How to create a global control holdout group in Python
This code implements a deterministic global control holdout group, randomly selecting a fraction of users to be excluded from feature rollouts for experiment validation.
import random
class GlobalControl:
def __init__(self, population_size, holdout_fraction=0.2, seed=42):
random.seed(seed)
self.population_size = population_size
self.holdout_fraction = holdout_fraction
self.holdout_size = int(population_size * holdout_fraction)
self.holdout_…How to join assignment logs with outcomes in Python
Merge submission log entries with grading outcomes using left join and full outer join patterns in pure Python.
from datetime import datetime, timedelta
class AssignmentLog:
def __init__(self):
self.logs = [
{"assignment_id": 101, "student_id": "S001", "submitted_at": "2024-03-01 10:30:00"},
{"assignment_id": 101, "student_id": "S002", "submitted_at": "2024-03-02 14:15:00"},
{"as…How to simulate a contextual bandit in Python
Simulate a contextual multi-armed bandit with random features and epsilon-greedy action selection in Python.
import random
class ContextualBandit:
def __init__(self, n_actions=3, n_features=4):
self.n_actions = n_actions
self.n_features = n_features
self.theta = [random.random() for _ in range(n_actions * n_features)]
def mock_context(self):
return [random.uniform(-1, 1) for _ in ra…Simulate a Ramp Rollout Percentage in Python
Simulates a percentage-based ramp rollout with deterministic seeding, returning success/failure/in-progress counts for a mock user population.
import random
from enum import Enum
class RolloutStatus(Enum):
SUCCESS = "success"
FAILED = "failed"
IN_PROGRESS = "in_progress"
def simulate_ramp_rollout(total_users: int, percentage: int, seed: int = 42) -> dict:
"""
Simulates a mock ramp rollout for a given percentage of users.
Returns sta…Synthetic Control in Python: Mock Example
Implements synthetic control from scratch: learns donor weights via ridge regression on pre-period data, then predicts a counterfactual for the treated unit.
import numpy as np
class SyntheticControl:
def __init__(self, data, treated_index, pre_periods, post_periods):
self.data = np.array(data, dtype=float)
self.treated_index = treated_index
self.pre_periods = pre_periods
self.post_periods = post_periods
def fit_weights(sel…Thompson Sampling Mock Bandit in Python
Implement a Thompson sampling multi-armed bandit to explore and exploit reward probabilities across multiple options, updating Beta distributions over time.
import random
class ThompsonSamplingBandit:
def __init__(self, num_arms, alpha=1.0, beta=1.0):
self.num_arms = num_arms
self.alpha = [alpha] * num_arms
self.beta = [beta] * num_arms
def select_arm(self):
samples = [random.betavariate(a, b) for a, b in zip(self.alpha, self.beta…UCB1 Bandit Algorithm in Python
This code implements the UCB1 multi-armed bandit algorithm, balancing exploration and exploitation to identify the best arm while maximizing cumulative reward.
import math
import random
def ucb1(means, n_iterations=1000, exploration_weight=2.0):
"""Run UCB1 bandit algorithm on arms with given true means."""
n_arms = len(means)
counts = [0] * n_arms
rewards = [0.0] * n_arms
for t in range(1, n_iterations + 1):
# UCB1 selection
if t <…Approximate Count with HyperLogLog in Python
A mock HyperLogLog implementation uses hash-based registers to estimate cardinality of large datasets with sublinear memory.
import hashlib
class HyperLogLog:
def __init__(self, precision=4):
if precision < 4 or precision > 16:
raise ValueError("precision must be between 4 and 16")
self.precision = precision
self.registers = [0] * (1 << precision)
def _hash(self, value):
return int(hashl…B-Tree Insert and In-Order Traversal in Python
Simulates a B-tree (order 2) with insert and split logic, then prints keys in sorted order via in-order traversal.
class BTreeNode:
def __init__(self, leaf=False):
self.leaf = leaf
self.keys = []
self.children = []
def is_full(self, t):
return len(self.keys) == 2 * t - 1
class BTree:
def __init__(self, t=2):
self.t = t
self.root = BTreeNode(leaf=True)
def insert(s…Broadcast a Small Reference Table in Python
Simulates SQL-style broadcasting of a small lookup table against a larger fact table in memory for mockups or load tests.
import random
def broadcast_mock(target, source, columns):
result = {}
for col in columns:
if col in target and col in source:
result[col] = target[col] + [source[col][i % len(source[col])] for i in range(len(target[col]))]
elif col in target:
result[col] = target[col]
…Build a Full Text Search Index in Python
Create a simple inverted index for full-text search with the standard library, supporting multi-word AND queries across documents.
import re
from collections import defaultdict
class SimpleTextIndex:
def __init__(self):
self.index = defaultdict(list)
self.documents = {}
def add_document(self, doc_id, text):
self.documents[doc_id] = text
words = set(re.findall(r'\w+', text.lower()))
for word in wo…Build a Partial Index Mock in Python for Database Filtering
Simulate a partial database index by filtering keys with a predicate, then return a limited mock lookup dictionary.
data = [
"alpha", "beta", "gamma", "delta", "epsilon",
"zeta", "eta", "theta", "iota", "kappa"
]
filtered_keys = [item for item in data if len(item) >= 5]
def mock_partial_index(keys, filter_func, limit=3):
result = {}
for key in keys:
if not filter_func(key):
continue
res…Composite index leftmost prefix in Python
Simulate a composite index in SQLite and check whether query columns match the leftmost prefix rule for index usage.
import sqlite3
def get_indexed_columns(table_name):
"""Simulate a composite index by reading column names that start with 'idx_'."""
conn = sqlite3.connect(":memory:")
conn.execute(f"CREATE TABLE {table_name} (id INTEGER, idx_col1 TEXT, idx_col2 INTEGER, other TEXT)")
conn.execute(f"CREATE INDEX idx_…Consistent Hashing with Virtual Buckets in Python
This code maps many virtual buckets onto a few physical buckets using a consistent hashing ring, ensuring balanced distribution with minimal remapping when physical buckets change.
import random
class VirtualBuckets:
"""Maps many virtual buckets onto few physical buckets using consistent hashing."""
def __init__(self, physical_buckets, virtual_factor=100):
self.physical = list(physical_buckets)
self.virtual_factor = virtual_factor
self.ring = []
self…Database indexing and query timing optimization in Python
Create SQLite indexes and time query performance to measure speedup for large table lookups in Python.
import sqlite3
import time
def time_query(db_path, query, params=()):
conn = sqlite3.connect(db_path)
conn.execute("PRAGMA journal_mode = WAL")
start = time.perf_counter()
result = conn.execute(query, params).fetchall()
elapsed = time.perf_counter() - start
conn.close()
return result, ela…Geo shard by region in Python
Maps users to database shards based on geographic region with a deterministic hash fallback.
import json
from collections import defaultdict
REGION_SHARD_MAP = {
"na": ["shard-01", "shard-02"],
"eu": ["shard-03", "shard-04", "shard-05"],
"ap": ["shard-06"],
"sa": ["shard-07", "shard-08"],
}
# user_id -> region (mock lookup)
USER_REGIONS = {
"u_1001": "na",
"u_1002": "eu",
"u_1003…Hash index equality mock concept in Python
A simple hash index class in Python that stores key-value pairs in buckets and demonstrates basic equality-based lookup.
class HashIndex:
def __init__(self):
self._buckets = {}
def insert(self, key, value):
"""Insert a key-value pair into the hash index."""
index = hash(key) % 10
if index not in self._buckets:
self._buckets[index] = []
self._buckets[index].append((key, value))…How to Batch Load JSON Data in Python for Database Optimization
This code parses JSON data into records and loads them in batches to simulate efficient database insertion, reducing load and improving performance.
import json
import time
def parse_and_load(data, batch_size=100):
"""
Parse JSON data and batch-load into a list of dicts.
Demonstrates batching for database efficiency.
"""
records = json.loads(data)
batches = []
for i in range(0, len(records), batch_size):
batch = records[i:i + …How to Build a Connection Pool Reuse Mock in Python
Build a mock connection pool with context manager to track connection reuse, acquires, and releases in Python.
import time
from contextlib import contextmanager
class Connection:
def __init__(self, name):
self.name = name
self.in_use = False
self.busy_since = None
def fetch(self):
return f"data from {self.name}"
class ConnectionPool:
def __init__(self, size=3):
self.conn…How to Build a Shard Map Mock Dict in Python
Implement a dictionary-like class that distributes keys across multiple shards using Python's hash() for realistic data partitioning.
class ShardMap:
def __init__(self, shard_count):
self.shards = {i: {} for i in range(shard_count)}
self.shard_count = shard_count
def _shard_for(self, key):
return hash(key) % self.shard_count
def __getitem__(self, key):
return self.shards[self._shard_for(key)][key]
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