Implement Efficient Prime Factorization Function with Comprehensive Testing

src/prime_factorization.py

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+from typing import List
+
+def prime_factorization(n: int) -> List[int]:
+    """
+    Compute the prime factorization of a given positive integer.
+
+    Args:
+        n (int): The positive integer to factorize.
+
+    Returns:
+        List[int]: A list of prime factors in ascending order.
+
+    Raises:
+        ValueError: If the input is less than 1.
+    """
+    # Validate input
+    if not isinstance(n, int):
+        raise TypeError("Input must be an integer")
+
+    if n < 1:
+        raise ValueError("Input must be a positive integer")
+
+    # Handle special cases
+    if n == 1:
+        return []
+
+    # Prime factorization algorithm
+    factors = []
+
+    # First, handle 2 as a special case to optimize odd number checking
+    while n % 2 == 0:
+        factors.append(2)
+        n //= 2
+
+    # Check for odd prime factors
+    factor = 3
+    while factor * factor <= n:
+        while n % factor == 0:
+            factors.append(factor)
+            n //= factor
+        factor += 2
+
+    # If n is a prime number greater than 2
+    if n > 2:
+        factors.append(n)
+
+    return factors

tests/test_prime_factorization.py

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+import pytest
+from src.prime_factorization import prime_factorization
+
+def test_prime_factorization_basic():
+    assert prime_factorization(12) == [2, 2, 3]
+    assert prime_factorization(15) == [3, 5]
+    assert prime_factorization(100) == [2, 2, 5, 5]
+
+def test_prime_factorization_prime_numbers():
+    assert prime_factorization(7) == [7]
+    assert prime_factorization(11) == [11]
+    assert prime_factorization(17) == [17]
+
+def test_prime_factorization_edge_cases():
+    assert prime_factorization(1) == []
+    assert prime_factorization(2) == [2]
+
+def test_prime_factorization_large_number():
+    result = prime_factorization(84)
+    assert result == [2, 2, 3, 7]
+    assert all(is_prime(factor) for factor in result)
+
+def test_prime_factorization_invalid_inputs():
+    with pytest.raises(ValueError):
+        prime_factorization(0)
+    with pytest.raises(ValueError):
+        prime_factorization(-5)
+    with pytest.raises(TypeError):
+        prime_factorization(3.14)
+    with pytest.raises(TypeError):
+        prime_factorization("not a number")
+
+def is_prime(n: int) -> bool:
+    """Helper function to check if a number is prime."""
+    if n < 2:
+        return False
+    for i in range(2, int(n**0.5) + 1):
+        if n % i == 0:
+            return False
+    return True