Formula

experiments/levenshtein_split.py

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+
+def ngrams_count(l, n):
+    return l - (n - 1)
+
+def ngrams_upper_bound(l, m):
+    n = l // m
+
+    return ngrams_count(l, n) + ngrams_count(l, n + 1)
+
+def powerset(a, b):
+    return (a + 1) * (b + 1) - 1
+
+def keys_count(a, b):
+    return powerset(a, b) * 2 - a - b
+
+def formula(k):
+    if k % 2 != 0:
+        return ((k + 1) ** 2) / 2 + (k + 1)
+    else:
+        return (k ** 2) / 2 + 2 * k + 1
+
+for k in range(1, 10):
+
+    m = k + 1
+    l_max = m * 2 - 1
+    l_med = m + m // 2
+
+    a = l_med % m
+    b = m - a
+
+    print('Stats for k = %i:' % k)
+    print('  - k (distance threshold): %i' % k)
+    print('  - m (number of chunks): %i' % m)
+    print('  - min nb of keys: %i (%i with tr)' % (m, m * 2))
+    print('  - max nb of keys: %i (with formula: %i)' % (keys_count(a, b), formula(k)))
+    print('  - %s%s (%i, %i)' % ('a' * a, 'b' * b, a, b))
+    print()