Segmented sieve - doctests (#9945)

* Replacing the generator with numpy vector operations from lu_decomposition.

* Revert "Replacing the generator with numpy vector operations from lu_decomposition."

This reverts commit ad217c6616.

* Added doctests.

* Update segmented_sieve.py

Removed unnecessary check.

* Update segmented_sieve.py

Added checks for 0 and negative numbers.

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* Update segmented_sieve.py

* Update segmented_sieve.py

Added float number check.

* Update segmented_sieve.py

* Update segmented_sieve.py

simplified verification

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* Update segmented_sieve.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update segmented_sieve.py

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* ValueError: Number 22.2 must instead be a positive integer

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

maths/segmented_sieve.py

@@ -4,7 +4,36 @@ import math
 
 
 def sieve(n: int) -> list[int]:
-    """Segmented Sieve."""
+    """
+    Segmented Sieve.
+
+    Examples:
+    >>> sieve(8)
+    [2, 3, 5, 7]
+
+    >>> sieve(27)
+    [2, 3, 5, 7, 11, 13, 17, 19, 23]
+
+    >>> sieve(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: Number 0 must instead be a positive integer
+
+    >>> sieve(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Number -1 must instead be a positive integer
+
+    >>> sieve(22.2)
+    Traceback (most recent call last):
+        ...
+    ValueError: Number 22.2 must instead be a positive integer
+    """
+
+    if n <= 0 or isinstance(n, float):
+        msg = f"Number {n} must instead be a positive integer"
+        raise ValueError(msg)
+
     in_prime = []
     start = 2
     end = int(math.sqrt(n))  # Size of every segment
@@ -42,4 +71,9 @@ def sieve(n: int) -> list[int]:
     return prime
 
 
-print(sieve(10**6))
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    print(f"{sieve(10**6) = }")