Computing Gini Impurity for Classification Labels

Gini impurity is a fundamental metric used in supervised machine learning to quantify the disorder or heterogeneity within a dataset's class distribution. This measure is central to decision tree algorithms, where it guides the selection of optimal splitting criteria to create the most informative partitions.

The Gini impurity for a node containing samples from multiple classes is calculated using the following formula:

$$\text{Gini Impurity} = 1 - \sum_{k=1}^{K} p_k^2$$

Where:

• K is the total number of distinct classes
• p_k represents the probability (relative frequency) of class k in the dataset

Intuition Behind Gini Impurity:

• A Gini impurity of 0 indicates perfect purity — all samples belong to a single class. This is the ideal outcome after splitting in a decision tree.
• The maximum impurity occurs when classes are evenly distributed. For a binary classification problem, this maximum is 0.5 (when both classes have equal probability of 0.5 each).
• For multi-class problems with K classes, the maximum Gini impurity is (K-1)/K, achieved when all classes are equally represented.

Your Task:

Implement a function that computes the Gini impurity for a given list of class labels. The function should:

• Count the frequency of each unique class in the input
• Calculate the probability of each class
• Apply the Gini impurity formula
• Return the result rounded to 2 decimal places