# Seismically Active Island: Official Solution

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

All-Russian School Olympiad in Informatics 2025–2026, Final Stage<br>
“Artificial Intelligence” profile, Tour 2, Moscow, 25 March 2026<br>
Task B

*Translator's note: the official solution is the authors' Jupyter notebook exported to PDF. Code cells are marked “In [n]”, their results “Out [n]”, and printed output follows the cell. Lines that the PDF wrapped are joined again. Comments, docstrings and messages are translated; the code itself is unchanged. Figures are described in words; see the original PDF for the images.*

In [ ]:

```python
import numpy as np
import pandas as pd

data = np.load('data_B.npy')
N = data.shape[0]
m = np.nanmean(data, axis=1)

# Pairwise correlation
sim = np.zeros((N, N))
for i in range(N):
    for j in range(i, N):
        mask = ~np.isnan(m[i]) & ~np.isnan(m[j])
        a, b = m[i, mask] - m[i, mask].mean(), m[j, mask] - m[j, mask].mean()
        d = np.sqrt((a**2).sum() * (b**2).sum())
        if d > 0:
            sim[i, j] = sim[j, i] = (a * b).sum() / d

# Each sample goes to the cluster with the highest mean correlation
# Initialisation: greedy
labels = np.full(N, -1)
reps = []
for i in range(N):
    best_sim, best_c = -1, -1
    for c, r in enumerate(reps):
        if sim[i, r] > best_sim:
            best_sim = sim[i, r]
            best_c = c
    if best_sim > 0.35:
        labels[i] = best_c
    else:
        labels[i] = len(reps)
        reps.append(i)

# Refinement: reassign by mean correlation with the cluster
for _ in range(10):
    clusters = [np.where(labels == c)[0] for c in range(max(labels) + 1)]
    changed = False
    for i in range(N):
        best_score, best_c = -2, labels[i]
        for c, members in enumerate(clusters):
            others = members[members != i]
            score = sim[i, others].mean() if len(others) > 0 else sim[i, members[0]]
            if score > best_score:
                best_score = score
                best_c = c
        if best_c != labels[i]:
            labels[i] = best_c
            changed = True
    if not changed:
        break
    # Update the clusters
    clusters = [np.where(labels == c)[0] for c in range(max(labels) + 1)]

y = pd.read_csv('y.csv')['cluster'].values
from sklearn.metrics import adjusted_rand_score
print(f"Clusters: {len(set(labels))}, ARI = {adjusted_rand_score(y, labels):.6f}")

pd.DataFrame({'ID': range(N), 'target': labels}).to_csv('submission_B.csv', index=False)
```

*(Translator's note: in the original, this cell has not been run and shows no output.)*