/*
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
}