Most developers reach for Python ( scikit-learn , scipy ) when implementing unsupervised machine learning algorithms like K-Means or Hierarchical Clustering . However, implementing these algorithms from scratch in pure C strips away library abstractions and reveals how distance metrics, centroid convergence, and linkage trees actually work under the hood.

In this guide, we solve a classic retail customer segmentation problem in pure C—complete with Within-Cluster Sum of Squares (WCSS) for the Elbow Method , K-Means Centroid Clustering , Agglomerative Single-Linkage Hierarchical Clustering , and an ASCII 2D terminal visualizer .

The Problem Statement

A retail company wants to segment its customers based on:

Purchasing Behavior ($X$): Store visits / purchase frequency per month.

Spending Patterns ($Y$): Average spending score (in thousands).

Demographic Information: Customer Age.

Our goal is to:

Determine the optimal number of clusters ($K$) using the Elbow Method (WCSS) .

Implement K-Means Clustering…