Compute information gain for a candidate split in a decision tree, which tells you how much uncertainty about the labels is reduced after splitting. You’ll implement entropy and use it to score a split given arrays of labels and feature values.

The Information Gain for a binary split is defined as:

where $H(Y)$ is the entropy of the labels.

Requirements

Implement the function

Rules:

• Use entropy $H(S) = -\sum_{c} p(c)\log_2 p(c)$ (ignore terms where $p(c)=0$).
• Split into left group $L=\{i: x_i \le t\}$ and right group $R=\{i: x_i > t\}$.
• Use only NumPy.
• Return a single float.

Example

Output: