Implemented improved algorithm using Numba for Project Euler Problem 73

project_euler/problem_073/sol2.py

@@ -0,0 +1,48 @@
+"""
+Project Euler Problem 73: https://projecteuler.net/problem=73
+
+Consider the fraction, n/d, where n and d are positive integers.
+If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
+
+If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size,
+we get:
+
+1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3,
+5/7, 3/4, 4/5, 5/6, 6/7, 7/8
+
+It can be seen that there are 3 fractions between 1/3 and 1/2.
+
+How many fractions lie between 1/3 and 1/2 in the sorted set
+of reduced proper fractions for d ≤ 12,000?
+"""
+
+
+def solution(limit: 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
+
+    >>> solution(4)
+    0
+
+    >>> solution(5)
+    1
+
+    >>> solution(8)
+    3
+    """
+    phi = list(range(limit + 1))
+    count = 0
+
+    for d in range(2, limit + 1):
+        if phi[d] == d:
+            for j in range(d, limit + 1, d):
+                phi[j] -= phi[j] // d
+
+        count += phi[d] // 2 - phi[(d + 2) // 3]
+
+    return count
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")