Code Efficiency Ratio

Problem

Compute the efficiency of a code as H / L, the ratio of the source entropy in bits to the expected codeword length. Probabilities are normalized before use and zero-probability symbols are skipped. Return 1.0 when L equals 0, which covers the single-symbol case.

Hint

Efficiency is entropy divided by expected length, never above 1 by Shannon's bound.

Test cases

case 1

in: [[0.25,0.25,0.25,0.25],[2,2,2,2]]

expected: 1

case 2

in: [[0.5,0.5],[1,2]]

expected: 0.6666666666666666

case 3

in: [[1],[0]]

expected: 1

case 4

in: [[1,3],[1,2]]

expected: 0.46358749969093305

Starter codePython

import math
def code_efficiency(probs, lengths):
    # Your code here
    pass

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