diff --git a/DIRECTORY.md b/DIRECTORY.md
index 81d6f4c70864..95863260ae2d 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -757,6 +757,7 @@
* [Harmonic Series](maths/series/harmonic_series.py)
* [Hexagonal Numbers](maths/series/hexagonal_numbers.py)
* [P Series](maths/series/p_series.py)
+ * [Sieve Of Atkin](maths/sieve_of_atkin.py)
* [Sieve Of Eratosthenes](maths/sieve_of_eratosthenes.py)
* [Sigmoid](maths/sigmoid.py)
* [Signum](maths/signum.py)
@@ -793,6 +794,7 @@
* [Tanh](maths/tanh.py)
* [Test Factorial](maths/test_factorial.py)
* [Test Prime Check](maths/test_prime_check.py)
+ * [Test Sieve Of Atkin](maths/test_sieve_of_atkin.py)
* [Three Sum](maths/three_sum.py)
* [Trapezoidal Rule](maths/trapezoidal_rule.py)
* [Triplet Sum](maths/triplet_sum.py)
@@ -1352,6 +1354,7 @@
* [Split](strings/split.py)
* [String Switch Case](strings/string_switch_case.py)
* [Strip](strings/strip.py)
+ * [Suffix Array](strings/suffix_array.py)
* [Text Justification](strings/text_justification.py)
* [Title](strings/title.py)
* [Top K Frequent Words](strings/top_k_frequent_words.py)
diff --git a/maths/sieve_of_atkin.py b/maths/sieve_of_atkin.py
new file mode 100644
index 000000000000..e1f57706655f
--- /dev/null
+++ b/maths/sieve_of_atkin.py
@@ -0,0 +1,75 @@
+import math
+
+
+def sieve_of_atkin(limit: int) -> list[int]:
+ """
+ Compute all prime numbers up to the given limit using the Sieve of Atkin.
+
+ Parameters
+ ----------
+ limit : int
+ Upper bound of primes to generate (inclusive).
+
+ Returns
+ -------
+ list[int]
+ A list of prime numbers <= limit.
+
+ Raises
+ ------
+ ValueError
+ If limit is not an integer >= 2.
+
+ References
+ ----------
+ https://en.wikipedia.org/wiki/Sieve_of_Atkin
+
+ Examples
+ --------
+ >>> sieve_of_atkin(10)
+ [2, 3, 5, 7]
+ >>> sieve_of_atkin(1)
+ Traceback (most recent call last):
+ ...
+ ValueError: limit must be an integer >= 2
+ """
+ if not isinstance(limit, int) or limit < 2:
+ raise ValueError("limit must be an integer >= 2")
+
+ # Initialize the sieve array
+ sieve = [False] * (limit + 1)
+ results: list[int] = []
+
+ # Preliminary marking based on quadratic forms
+ sqrt_limit = int(math.sqrt(limit)) + 1
+ for x in range(1, sqrt_limit):
+ for y in range(1, sqrt_limit):
+ n = 4 * x * x + y * y
+ if n <= limit and n % 12 in (1, 5):
+ sieve[n] = not sieve[n]
+ n = 3 * x * x + y * y
+ if n <= limit and n % 12 == 7:
+ sieve[n] = not sieve[n]
+ n = 3 * x * x - y * y
+ if x > y and n <= limit and n % 12 == 11:
+ sieve[n] = not sieve[n]
+
+ # Mark all multiples of squares as non-prime
+ for n in range(5, sqrt_limit):
+ if sieve[n]:
+ step = n * n
+ for k in range(step, limit + 1, step):
+ sieve[k] = False
+
+ # Compile the list of primes
+ if limit >= 2:
+ results.extend([2, 3])
+ results.extend([i for i in range(5, limit + 1) if sieve[i]])
+ return results
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ print("All doctests passed!")
diff --git a/maths/test_sieve_of_atkin.py b/maths/test_sieve_of_atkin.py
new file mode 100644
index 000000000000..4b668aa3876b
--- /dev/null
+++ b/maths/test_sieve_of_atkin.py
@@ -0,0 +1,16 @@
+import pytest
+
+from maths.sieve_of_atkin import sieve_of_atkin
+
+
+def test_small_primes():
+ assert sieve_of_atkin(10) == [2, 3, 5, 7]
+
+
+def test_medium_primes():
+ assert sieve_of_atkin(20) == [2, 3, 5, 7, 11, 13, 17, 19]
+
+
+def test_invalid_limit():
+ with pytest.raises(ValueError):
+ sieve_of_atkin(1)
diff --git a/strings/suffix_array.py b/strings/suffix_array.py
new file mode 100644
index 000000000000..f2b786e7bd2a
--- /dev/null
+++ b/strings/suffix_array.py
@@ -0,0 +1,66 @@
+def build_suffix_array(s: str) -> list[int]:
+ # Append a sentinel that is lexicographically smaller than all other characters
+ s += "\0"
+ n = len(s)
+ # Initial ranking by character code
+ ranks = [ord(c) for c in s]
+ sa = list(range(n))
+ tmp = [0] * n
+ k = 1
+ # Doubling loop
+ while k < n:
+ # Sort by (rank[i], rank[i+k]) pairs
+ sa.sort(key=lambda i: (ranks[i], ranks[i + k] if i + k < n else -1))
+ # Temporary array for new ranks
+ tmp[sa[0]] = 0
+ for i in range(1, n):
+ prev, curr = sa[i - 1], sa[i]
+ # Compare pair (rank, next rank)
+ r_prev = (ranks[prev], ranks[prev + k] if prev + k < n else -1)
+ r_curr = (ranks[curr], ranks[curr + k] if curr + k < n else -1)
+ tmp[curr] = tmp[prev] + (1 if r_curr != r_prev else 0)
+ ranks, tmp = tmp, ranks # reuse lists to save memory
+ k <<= 1
+ if ranks[sa[-1]] == n - 1:
+ break
+ # Drop the sentinel index
+ return sa[1:]
+
+
+def build_lcp_array(s: str, sa: list[int]) -> list[int]:
+ n = len(sa)
+ # Inverse of suffix array: pos[i] gives rank of suffix at i
+ pos = [0] * n
+ for i, suf in enumerate(sa):
+ pos[suf] = i
+ lcp = [0] * n
+ k = 0
+ for i in range(len(s)):
+ if pos[i] == 0:
+ k = 0
+ continue
+ j = sa[pos[i] - 1]
+ # Compare characters starting from k
+ while i + k < len(s) and j + k < len(s) and s[i + k] == s[j + k]:
+ k += 1
+ lcp[pos[i]] = k
+ if k:
+ k -= 1
+ return lcp[1:]
+
+
+if __name__ == "__main__":
+ # Example usage and simple tests
+ test_strings = ["banana", "abracadabra", "mississippi"]
+ for s in test_strings:
+ sa = build_suffix_array(s)
+ lcp = build_lcp_array(s, sa)
+ print(f"String: {s}")
+ print(f"Suffix Array: {sa}")
+ print(f"LCP Array : {lcp}\n")
+
+ # Assertions for correctness
+ s = "banana"
+ expected_sa = [5, 3, 1, 0, 4, 2] # indices of sorted suffixes
+ assert build_suffix_array(s) == expected_sa, "SA test failed"
+ print("All tests passed!")
pFad - Phonifier reborn
Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.
Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.
Alternative Proxies:
Alternative Proxy
pFad Proxy
pFad v3 Proxy
pFad v4 Proxy