Entropy of Letter Counts

Problem

Given a dictionary mapping letters to counts, normalize the counts into probabilities and return the Shannon entropy in bits:

H = -sum(p * log2(p)), p = count / total

Skip zero counts and return 0.0 when the total count is zero.

Hint

The counts only matter through their ratios, so any normalization works.

case 1

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

expected: 1

case 2

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

expected: 0.8112781244591328

case 3

in: [{"a":1,"b":2,"c":3,"d":4}]

expected: 1.8464393446710154

case 4

in: [{"a":10}]

expected: 0

case 5

in: [{"a":0,"b":4}]

expected: 0

Starter codePython

import math
def letter_entropy(counts):
    # Your code here
    pass

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