THE DATA LEAKAGE DETECTOR

Difficulty: Medium Tags: ML Evaluation, Data Leakage, Time Series

Story

A demand forecasting model is evaluated on trip records. A preprocessing change randomly shuffled rows before splitting, letting future observations leak into training. Given timestamps and a proposed cutoff, partition the records strictly by time and compute the resulting counts and mean target values.

The Math

Each record has timestamp t_i and target y_i. A record belongs to training iff t_i < C; otherwise it belongs to test. Compute training count, test count, and each partition's arithmetic mean target. If a partition is empty, its mean is None. Never shuffle the records.

Input Format

records (list of (timestamp, target) pairs), cutoff (number).

Output Format

(train_count, test_count, train_mean_or_none, test_mean_or_none).

Constraints

• 1 <= n <= 10^5, timestamps are integers, |y_i| <= 10^9.
• Time limit: 1.0 second.

Example

Input

records = [(8,100), (10,200), (12,300), (9,150)], cutoff = 10

Output

train_count = 2, test_count = 2
train_mean = 125.000000, test_mean = 250.000000

Explanation: Only timestamps strictly less than 10 enter training (8 and 9). Timestamp 10 and 12 belong to test.