add stirling subcommand

internal/lib/stirling.go

@@ -0,0 +1,68 @@
+/*
+Copyright © 2025 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package lib
+
+import (
+	"math/big"
+)
+
+// TODO: implement both of these with dynamic programming
+
+func Stirling1(n, k *big.Int) *big.Int {
+	if n.Cmp(big.NewInt(0)) == 0 && k.Cmp(big.NewInt(0)) == 0 {
+		return big.NewInt(1)
+	}
+
+	if n.Cmp(big.NewInt(0)) == 0 || k.Cmp(big.NewInt(0)) == 0 {
+		return big.NewInt(0)
+	}
+
+	newN := new(big.Int).Set(n)
+	newN.Sub(newN, big.NewInt(1))
+
+	result := Stirling1(newN, k)
+	result.Mul(result, newN)
+	result.Neg(result)
+
+	newK := new(big.Int).Set(k)
+	newK.Sub(newK, big.NewInt(1))
+
+	result.Add(result, Stirling1(newN, newK))
+	return result
+}
+
+func Stirling2(n, k *big.Int) *big.Int {
+	if n.Cmp(k) == 0 {
+		return big.NewInt(1)
+	}
+
+	if n.Cmp(big.NewInt(0)) == 0 || k.Cmp(big.NewInt(0)) == 0 {
+		return big.NewInt(0)
+	}
+
+	newN := new(big.Int).Set(n)
+	newN.Sub(newN, big.NewInt(1))
+
+	result := Stirling2(newN, k)
+	result.Mul(result, k)
+
+	newK := new(big.Int).Set(k)
+	newK.Sub(newK, big.NewInt(1))
+
+	result.Add(result, Stirling2(newN, newK))
+	return result
+}