Create solver_combinatorics.py

solver_combinatorics.py

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+from __future__ import annotations
+
+import re
+from math import comb, perm, factorial
+from typing import Optional
+
+from models import SolverResult
+
+
+def solve_combinatorics(text: str) -> Optional[SolverResult]:
+    lower = (text or "").lower()
+
+    if not any(w in lower for w in [
+        "combination", "permutation", "arrange", "arrangement",
+        "choose", "select", "committee"
+    ]):
+        return None
+
+    # "how many ways to choose r from n"
+    m = re.search(r"choose\s+(\d+)\s+from\s+(\d+)", lower)
+    if m:
+        r = int(m.group(1))
+        n = int(m.group(2))
+        if r > n or r < 0:
+            return None
+        result = comb(n, r)
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="combinations",
+            answer_value=str(result),
+            internal_answer=str(result),
+            steps=[
+                "Use combinations when order does not matter.",
+                "Compute nCr.",
+            ],
+        )
+
+    # "committee of 3 from 8"
+    m = re.search(r"committee\s+of\s+(\d+).*?from\s+(\d+)", lower)
+    if m:
+        r = int(m.group(1))
+        n = int(m.group(2))
+        if r > n or r < 0:
+            return None
+        result = comb(n, r)
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="combinations",
+            answer_value=str(result),
+            internal_answer=str(result),
+            steps=[
+                "A committee is a selection problem, so use combinations.",
+                "Compute nCr.",
+            ],
+        )
+
+    # "arrange 5 books" / "permutations of 5 items"
+    m = re.search(r"(?:arrange|arrangement|permutation).*?(\d+)", lower)
+    if m and "choose" not in lower and "committee" not in lower:
+        n = int(m.group(1))
+        result = factorial(n)
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="permutations",
+            answer_value=str(result),
+            internal_answer=str(result),
+            steps=[
+                "When arranging all distinct items, use n!.",
+            ],
+        )
+
+    # "how many ways to arrange r from n"
+    m = re.search(r"arrange\s+(\d+).*?from\s+(\d+)", lower)
+    if m:
+        r = int(m.group(1))
+        n = int(m.group(2))
+        if r > n or r < 0:
+            return None
+        result = perm(n, r)
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="permutations",
+            answer_value=str(result),
+            internal_answer=str(result),
+            steps=[
+                "Use permutations when order matters.",
+                "Compute nPr.",
+            ],
+        )
+
+    return None