Create solver_factorial.py

solver_factorial.py

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+from __future__ import annotations
+
+import math
+import re
+from typing import Optional
+
+from models import SolverResult
+
+
+def solve_factorial(text: str) -> Optional[SolverResult]:
+    lower = (text or "").lower()
+
+    if "!" not in text and "factorial" not in lower:
+        return None
+
+    # n!
+    m = re.search(r"(\d+)\s*!", text)
+    if m:
+        n = int(m.group(1))
+        if n < 0:
+            return None
+        result = math.factorial(n)
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="factorial",
+            answer_value=str(result),
+            internal_answer=str(result),
+            steps=[
+                "Use n! = n × (n−1) × ... × 1.",
+            ],
+        )
+
+    # "how many trailing zeros in 100!"
+    m = re.search(r"trailing zeros.*?(\d+)\s*!", lower)
+    if m:
+        n = int(m.group(1))
+        count = 0
+        power = 5
+        while power <= n:
+            count += n // power
+            power *= 5
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="factorial_trailing_zeros",
+            answer_value=str(count),
+            internal_answer=str(count),
+            steps=[
+                "Trailing zeros come from factors of 10 = 2×5.",
+                "There are always more 2s than 5s in a factorial.",
+                "Count factors of 5 using n//5 + n//25 + n//125 + ...",
+            ],
+        )
+
+    return None