Problem
Entropy measures the uncertainty of a set of labels: H(S) = -Σ pₖ × log₂(pₖ), where pₖ is the fraction of labels of class k. Information gain is how much entropy drops when you split the set by a feature:
IG = H(labels) - Σ (|Sᵥ| / |S|) × H(Sᵥ)
where Sᵥ contains the labels of the samples whose feature equals v. Decision trees pick the feature with the highest gain.
Implement information_gain(feature, labels).
Input
feature: The feature value of each sample.
labels: The class label of each sample (same length).
Output
Return the information gain in bits, as a decimal number.
Constraints
1 ≤ length ≤ 10,000
Each value and label is 1 to 20 characters
Examples
Input:
labels = ["no", "no", "yes", "yes"]
feature = ["sunny", "sunny", "rain", "rain"]
Expected output:
expected = 1.0Input:
std::vector<std::string> labels = {"no", "no", "yes", "yes"};
std::vector<std::string> feature = {"sunny", "sunny", "rain", "rain"};
Expected output:
double expected = 1.0;Input:
string[] labels = new string[] {"no", "no", "yes", "yes"};
string[] feature = new string[] {"sunny", "sunny", "rain", "rain"};
Expected output:
double expected = 1.0;Explanation
The labels are half yes and half no, so H = 1 bit. Splitting by weather gives two pure groups (H = 0 each), so the gain is 1 - 0 = 1: the feature tells you everything.
Input:
labels = ["yes", "yes", "no", "no"]
feature = ["a", "b", "a", "b"]
Expected output:
expected = 0.0Input:
std::vector<std::string> labels = {"yes", "yes", "no", "no"};
std::vector<std::string> feature = {"a", "b", "a", "b"};
Expected output:
double expected = 0.0;Input:
string[] labels = new string[] {"yes", "yes", "no", "no"};
string[] feature = new string[] {"a", "b", "a", "b"};
Expected output:
double expected = 0.0;Explanation
Each group a and b still has one yes and one no (H = 1), so the remainder is 0.5 × 1 + 0.5 × 1 = 1 and the gain is 1 - 1 = 0: the feature is useless.
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.