Metrics · Medium

NDCG

Normalize discounted gain against the best possible ranking.

Task

Implement ndcg(relevance: list[float], scores: list[float], k: int) -> float. Rank examples by descending score, compute discounted cumulative gain through rank k, and normalize it by the ideal ranking of the same relevance labels.

Requirements

Use gain 2^relevance - 1 and discount log2(rank + 1), with ranks starting at 1.
Return 0.0 when k <= 0 or the ideal DCG is zero.
When k exceeds the dataset size, use every example.
Preserve original input order when scores tie.

Example

relevance = [3, 2, 0, 1]
scores = [0.8, 0.9, 0.7, 0.6]

ndcg(relevance, scores, 3)
# 0.7895959410