maths/prime_factorization_fast.py

@@ -1,121 +1,61 @@
-from __future__ import annotations
 from math import ceil, sqrt
-import time
+from __future__ import annotations
 
 
-def timer(func):
-    def wrapper(*args, **kwargs):
-        start = time.time()
-        result = func(*args, **kwargs)
-        print(result)
-        end = time.time()
-        print(f"{func.__name__} took {end - start:.6f} seconds to execute.")
-        return result
-
-    return wrapper
-
-
-@timer
-def prime_factors(n: int) -> list[int]:
-    """
-    Returns prime factors of n as a list.
-
-    >>> prime_factors(0)
-    []
-    >>> prime_factors(100)
-    [2, 2, 5, 5]
-    >>> prime_factors(2560)
-    [2, 2, 2, 2, 2, 2, 2, 2, 2, 5]
-    >>> prime_factors(10**-2)
-    []
-    >>> prime_factors(0.02)
-    []
-    >>> x = prime_factors(10**241) # doctest: +NORMALIZE_WHITESPACE
-    >>> x == [2]*241 + [5]*241
-    True
-    >>> prime_factors(10**-354)
-    []
-    >>> prime_factors('hello')
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'str'
-    >>> prime_factors([1,2,'hello'])
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'list'
-
-    """
-    if not isinstance(n, int):
-        raise TypeError("Input must be an integer")
-
-    if n <= 0:
-        return []
-
-    i = 2
-    factors = []
-    while i * i <= n:
-        if n % i:
-            i += 1
-        else:
-            n //= i
-            factors.append(i)
-    if n > 1:
-        factors.append(n)
-    return factors
-
-
-@timer
-def primeproduct(num: int) -> list[int]:
+def primeproduct(n: int, x: list = []) -> list[int]:
     """
     >>> primeproduct(868)
     [2, 2, 7, 31]
     >>> primeproduct(9039423423423743)
     [2, 2, 7, 31, 719, 12572216166097]
     >>> primeproduct(0.02)
-    Traceback (most recent call last):
-    ValueError: invalid literal for int() with base 10: '0.02'
-    >>> primeproduct(-2342)
     []
     """
-    if not isinstance(num, int):
-        raise TypeError("Input must be an integer")
-
-    if num <= 1:
+    if n < 1:
         return []
 
-    prime_factors: list[int] = []
-    while num > 1:
-        if len(prime_factors) >= 1 and prime_factors[-1] % num == 0:
-            prime_factors.append(prime_factors[-1])
+    if n > 1:
+        if len(x) >= 1 and x[-1] % n == 0:  # check in already factorised
+            x.append(x[-1])
+            n = n // x[-1]
+
         else:
-            sq = ceil(sqrt(num))
+            sq = ceil(sqrt(n))
             flag = 0
 
-            if prime_factors != []:
-                for i in range(prime_factors[-1], sq + 1, 2):
-                    if num % i == 0:
-                        num = num // i
-                        prime_factors.append(i)
+            if x != []:
+                for i in range(x[-1], sq + 1, 2):
+                    if n % i == 0:
+                        n = n // i
+                        x.append(i)
                         flag = 1
                         break
+
             else:
-                while num % 2 == 0:
-                    num = num // 2
-                    prime_factors.append(2)
-                for i in range(3, sq + 1, 2):
-                    if num % i == 0:
-                        num = num // i
-                        prime_factors.append(i)
+                # Handle factor 2 separately
+                while n % 2 == 0:  # only 2 is even prime
+                    n = n // 2
+                    x.append(2)
+
+                # Start loop from 3 and increment by 2
+                for i in range(3, sq + 1, 2):  # skip even numbers
+                    if n % i == 0:
+                        n = n // i
+                        x.append(i)
                         flag = 1
                         break
-            if not flag and num > 1:
-                prime_factors.append(num)
-                num = 1
-                break
-    return prime_factors
+
+            if not flag:
+                x.append(n)
+                n = 1
+
+        return primeproduct(n, x)
+
+    return x
 
 
+# faster than https://github.com/sourabhkv/Python/blob/master/maths/prime_factors.py approx 2x
 if __name__ == "__main__":
-    n = int(input("enter number: ").strip())
-    primeproduct(n)
-    prime_factors(n)
+    import doctest
+
+    doctest.testmod()

maths/prime_factors.py

@@ -1,21 +1,9 @@
+"""
+python/black : True
+"""
 from __future__ import annotations
-from math import ceil, sqrt
-import time
 
 
-def timer(func):
-    def wrapper(*args, **kwargs):
-        start = time.time()
-        result = func(*args, **kwargs)
-        print(result)
-        end = time.time()
-        print(f"{func.__name__} took {end - start:.6f} seconds to execute.")
-        return result
-
-    return wrapper
-
-
-@timer
 def prime_factors(n: int) -> list[int]:
     """
     Returns prime factors of n as a list.
@@ -58,64 +46,7 @@ def prime_factors(n: int) -> list[int]:
     return factors
 
 
-@timer
-def primeproduct(num: int) -> list[int]:
-    """
-    >>> primeproduct(868)
-    [2, 2, 7, 31]
-    >>> primeproduct(9039423423423743)
-    [2, 2, 7, 31, 719, 12572216166097]
-    >>> primeproduct(0.02)
-    Traceback (most recent call last):
-    ValueError: invalid literal for int() with base 10: '0.02'
-    >>> primeproduct(-2342)
-    []
-    """
-
-    if num <= 1:
-        return []
-
-    prime_factors: list[int] = []
-    while num > 1:
-        if len(prime_factors) >= 1 and prime_factors[-1] % num == 0:
-            prime_factors.append(prime_factors[-1])
-
-        else:
-            sq = ceil(sqrt(num))
-            flag = 0
-
-            if prime_factors != []:
-                for i in range(prime_factors[-1], sq + 1, 2):
-                    if num % i == 0:
-                        num = num // i
-                        prime_factors.append(i)
-                        flag = 1
-                        break
-
-            else:
-                while num % 2 == 0:
-                    num = num // 2
-                    prime_factors.append(2)
-
-                for i in range(3, sq + 1, 2):
-                    if num % i == 0:
-                        num = num // i
-                        prime_factors.append(i)
-                        flag = 1
-                        break
-
-            if not flag and num > 1:
-                prime_factors.append(num)
-                num = 1
-                break
-
-    return prime_factors
-
-
 if __name__ == "__main__":
-    n = int(input("enter number: "))
-    primeproduct(n)
-    prime_factors(n)
     import doctest
 
     doctest.testmod()