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maths/prime_factorization_fast.py

@@ -1,61 +1,121 @@
-from math import ceil, sqrt
 from __future__ import annotations
+from math import ceil, sqrt
+import time
 
 
-def primeproduct(n: int, x: list = []) -> list[int]:
+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]:
     """
     >>> 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 n < 1:
+    if not isinstance(num, int):
+        raise TypeError("Input must be an integer")
+
+    if num <= 1:
         return []
 
-    if n > 1:
+    prime_factors: list[int] = []
-        if len(x) >= 1 and x[-1] % n == 0:  # check in already factorised
+    while num > 1:
-            x.append(x[-1])
+        if len(prime_factors) >= 1 and prime_factors[-1] % num == 0:
-            n = n // x[-1]
+            prime_factors.append(prime_factors[-1])
-
         else:
-            sq = ceil(sqrt(n))
+            sq = ceil(sqrt(num))
             flag = 0
 
-            if x != []:
+            if prime_factors != []:
-                for i in range(x[-1], sq + 1, 2):
+                for i in range(prime_factors[-1], sq + 1, 2):
-                    if n % i == 0:
+                    if num % i == 0:
-                        n = n // i
+                        num = num // i
-                        x.append(i)
+                        prime_factors.append(i)
                         flag = 1
                         break
-
             else:
-                # Handle factor 2 separately
+                while num % 2 == 0:
-                while n % 2 == 0:  # only 2 is even prime
+                    num = num // 2
-                    n = n // 2
+                    prime_factors.append(2)
-                    x.append(2)
+                for i in range(3, sq + 1, 2):
-
+                    if num % i == 0:
-                # Start loop from 3 and increment by 2
+                        num = num // i
-                for i in range(3, sq + 1, 2):  # skip even numbers
+                        prime_factors.append(i)
-                    if n % i == 0:
-                        n = n // i
-                        x.append(i)
                         flag = 1
                         break
-
+            if not flag and num > 1:
-            if not flag:
+                prime_factors.append(num)
-                x.append(n)
+                num = 1
-                n = 1
+                break
-
+    return prime_factors
-        return primeproduct(n, x)
-
-    return x
 
 
-# faster than https://github.com/sourabhkv/Python/blob/master/maths/prime_factors.py approx 2x
 if __name__ == "__main__":
-    import doctest
+    n = int(input("enter number: ").strip())
-
+    primeproduct(n)
-    doctest.testmod()
+    prime_factors(n)

maths/prime_factors.py

@@ -1,9 +1,21 @@
-"""
-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.
@@ -46,7 +58,64 @@ 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()