Performance: 25% faster Project Euler 73 #10503

project_euler/problem_073/sol1.py

@@ -19,6 +19,29 @@
 from math import gcd
 
 
+def slow_solution(max_d: int = 12_000) -> int:
+    """
+    Returns number of fractions lie between 1/3 and 1/2 in the sorted set
+    of reduced proper fractions for d ≤ max_d
+
+    >>> slow_solution(4)
+    0
+
+    >>> slow_solution(5)
+    1
+
+    >>> slow_solution(8)
+    3
+    """
+
+    fractions_number = 0
+    for d in range(max_d + 1):
+        for n in range(d // 3 + 1, (d + 1) // 2):
+            if gcd(n, d) == 1:
+                fractions_number += 1
+    return fractions_number
+
+
 def solution(max_d: int = 12_000) -> int:
     """
     Returns number of fractions lie between 1/3 and 1/2 in the sorted set
@@ -36,11 +59,34 @@ def solution(max_d: int = 12_000) -> int:
 
     fractions_number = 0
     for d in range(max_d + 1):
-        for n in range(d // 3 + 1, (d + 1) // 2):
-            if gcd(n, d) == 1:
-                fractions_number += 1
+        if d % 2 == 0:
+            n_start = d // 3 + 2 if (d // 3 + 1) % 2 == 0 else d // 3 + 1
+            for n in range(n_start, (d + 1) // 2, 2):
+                if gcd(n, d) == 1:
+                    fractions_number += 1
+        else:
+            for n in range(d // 3 + 1, (d + 1) // 2):
+                if gcd(n, d) == 1:
+                    fractions_number += 1
     return fractions_number
 
 
+def benchmark() -> None:
+    """
+    Benchmarks
+    """
+    # Running performance benchmarks...
+    # slow_solution : 21.02750190000006
+    # solution      : 15.79036830000041
+
+    from timeit import timeit
+
+    print("Running performance benchmarks...")
+
+    print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
+    print(f"solution      : {timeit('solution()', globals=globals(), number=10)}")
+
+
 if __name__ == "__main__":
     print(f"{solution() = }")
+    benchmark()