Confusion Matrix Builder

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You are given lists of predictions and ground truth labels, and need to build a confusion matrix.

A confusion matrix C is a square matrix where:

C[i][j] = count of samples with true class i that were predicted as class j
Diagonal entries C[i][i] are correct predictions
Off-diagonal entries are misclassifications

The matrix provides detailed insight into which classes are being confused with each other.

For a 3-class problem, the structure is: $C = \begin{bmatrix} TP_0 & E_{0\to1} & E_{0\to2} \\ E_{1\to0} & TP_1 & E_{1\to2} \\ E_{2\to0} & E_{2\to1} & TP_2 \end{bmatrix}$

Where $TP_i$ is true positives for class i, and $E_{i\to j}$ is errors where class i was predicted as class j.

Example

Input

predictions = [0, 1, 0, 1]
ground_truth = [0, 0, 0, 1]
num_classes = 2

Output

[[2, 1], [0, 1]]

Reasoning

Inputs: predictions and ground_truth are read side by side as (true, predicted) pairs, one per sample: $(0,0)$ , $(0,1)$ , $(0,0)$ , $(1,1)$ . With num_classes $=2$ the matrix is $2 \times 2$ ; row $i$ is the true class, column $j$ the predicted class.
Row 0 (true class 0): samples 0, 1 and 2 are truly class 0. Two were predicted 0 and one was predicted 1, so $C_{00}=2$ and $C_{01}=1$ . The row sums to 3, the number of class-0 samples.
Row 1 (true class 1): only sample 3, predicted correctly, so $C_{10}=0$ and $C_{11}=1$ .
Output: [[2, 1], [0, 1]]. The diagonal holds $2+1=3$ correct predictions out of 4 (75% accuracy); the single off-diagonal count $E_{0\to1}=1$ is a class-0 sample mistaken for class 1.
Notice: orientation matters. Sample 1 has truth 0 and prediction 1, so it belongs in row 0, column 1; mixing up the roles gives the transpose $\begin{bmatrix}2&0\\1&1\end{bmatrix}$ . All entries always add up to the number of samples, and a class that never occurs keeps a row of zeros.

Constraints

predictions and ground_truth are lists of class indices of the same length
num_classes is the total number of classes
All class indices are in range [0, num_classes-1]
Return the confusion matrix as a 2D list

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Concept primerPREVIEW

You are building a counting data structure: given true labels and predicted labels for a multi-class classifier, you must tally how often each true–predicted pair occurs and store it in a square matrix.

1. Background Knowledge

In multi-class classification, each sample belongs to exactly one of $K$ classes (e.g., 0, 1, 2 for a 3-class problem). A trained model outputs a predicted class for each input. To evaluate how well the model performs per class, you use a confusion matrix instead of just overall accuracy.

A confusion matrix $C \in \mathbb{R}^{K \times K}$ is defined so that:

Rows correspond to true (ground-truth) classes.
Columns correspond to predicted classes.
Entry $C[i][j]$ is the number of samples whose true class is $i$ and predicted class is $j$ .

Thus:

Diagonal entries $C[i][i]$ = correct predictions (true positives for class $i$ ).
Off-diagonal entries show which classes are being confused (e.g., many counts in $C$ means class 0 is often predicted as class 2).

2. Algorithm / Approach

General pattern:

Determine the number of classes $K$ .
Initialize a $K \times K$ matrix of zeros.
Iterate once over all samples:

Let t = true_label[i], p = pred_label[i].
Increment C[t][p] by 1.

Return the matrix.

This is essentially frequency counting over pairs (true, pred) using array indices.

3. Step-by-Step Strategy

Identify class index range

Often labels are integers from 0 to K-1.
You may be given num_classes, or you may compute:

K = max(max(true_labels), max(pred_labels)) + 1

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