Gini Impurity for a split

The problem, from first principles

A tree needs a way to tell whether the labels arriving at a node agree. Pure nodes need no more splitting; mixed nodes may benefit from it. Gini impurity summarizes that label mixture without assuming class labels are consecutive integers.

From theory to code

Implement gini_impurity(labels) by counting each distinct label, converting counts to proportions, and applying the impurity formula. Theory also defines the empty-node convention used by later split logic.

Constraints

• labels is a one-dimensional array of arbitrary integer class labels.
• Return a Python float in [0, 1).
• Return exactly 0.0 for an empty array and for a pure node.
• Count distinct labels with np.unique(..., return_counts=True).
• Use vectorized NumPy reductions; do not loop through labels.

Hints

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