HardNLPnlp-253

nDCG at k

Problem

Compute normalized discounted cumulative gain at k. DCG sums gain(document) / log2(position + 1) over the first k retrieved positions using the gains in relevance, and IDCG uses the same formula on the gains sorted in descending order.

Return DCG / IDCG, or 0.0 when k is not positive or IDCG is 0. Missing documents have gain 0.

Hint

Discounts use log2(i + 2) for 0-based position i; build IDCG from all graded documents.

Test cases

case 1

in: [["a","b","c"],{"a":3,"b":2,"c":1},3]

expected: 1

case 2

in: [["b","a","c"],{"a":3,"b":2,"c":1},3]

expected: 0.9224945116765986

case 3

in: [["a"],{"a":3},0]

expected: 0

case 4

in: [["a"],{"a":0},1]

expected: 0

case 5

in: [["c","a"],{"a":2,"b":1,"c":3},2]

expected: 1

case 6

in: [[],{"a":5},3]

expected: 0

Starter codePython

import math
def ndcg_at_k(retrieved, relevance, k):
    # Your code here
    pass

6 test cases · run your code against them in the editor