Information Gain for a split

The problem, from first principles

Once a node is mixed, a tree must compare proposed partitions. A useful split leaves its children more label-consistent than their parent; a useless split merely moves the same mixture around. Information gain measures that reduction while ensuring a tiny child cannot count as much as a large one.

From theory to code

Implement information_gain(parent_labels, left_labels, right_labels) using the existing gini_impurity helper and a child-size-weighted average.

Constraints

• left_labels and right_labels partition parent_labels.
• Return a Python float gain.
• Weight each child impurity by its size divided by parent_labels.size.
• Empty children remain valid because gini_impurity returns 0.0 for them.
• Reuse gini_impurity; do not reimplement its class counting.

Hints

Open one at a time. Each gives away a little more than the last.