/*
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 cmd

import (
	"fmt"
	"math/big"

	"github.com/spf13/cobra"
)

var partitionsN string
var partitionsK string

// TODO: use dynamic programming
func p(n, k *big.Int) *big.Int {
	if n.Cmp(big.NewInt(0)) == -1 {
		return big.NewInt(0)
	} else if n.Cmp(big.NewInt(0)) == 0 {
		return big.NewInt(1)
	} else if k.Cmp(big.NewInt(0)) == 0 {
		return big.NewInt(0)
	}

	newN := new(big.Int).Sub(n, k)
	x := p(newN, k)

	newK := new(big.Int).Sub(k, big.NewInt(1))
	y := p(n, newK)

	z := new(big.Int).Add(x, y)
	return z
}

func partitions(cmd *cobra.Command, args []string) {
	n, ok := new(big.Int).SetString(partitionsN, 10)
	if !ok {
		cobra.CheckErr("invalid input " + partitionsN)
	}

	var k *big.Int
	if partitionsK == "" {
		k = new(big.Int).Set(n)
	} else {
		var ok bool
		k, ok = new(big.Int).SetString(partitionsK, 10)
		if !ok {
			cobra.CheckErr("invalid input " + partitionsK)
		}
	}

	if n.Cmp(big.NewInt(0)) == -1 {
		cobra.CheckErr("n must be nonnegative")
	}

	if k.Cmp(big.NewInt(0)) == -1 {
		cobra.CheckErr("k must be nonnegative")
	}

	z := p(n, k)
	fmt.Println(z)
}

// partitionsCmd represents the partitions command
var partitionsCmd = &cobra.Command{
	Use:   "partitions",
	Short: "Compute the number of partitions of an integer",
	Long:  `Compute the number of partitions of an integer.`,
	Run:   partitions,
}

func init() {
	rootCmd.AddCommand(partitionsCmd)

	// Here you will define your flags and configuration settings.

	// Cobra supports Persistent Flags which will work for this command
	// and all subcommands, e.g.:
	// partitionsCmd.PersistentFlags().String("foo", "", "A help for foo")

	// Cobra supports local flags which will only run when this command
	// is called directly, e.g.:
	// partitionsCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")

	partitionsCmd.Flags().StringVarP(&partitionsN, "number", "n", "", "number to compute partitions of")
	partitionsCmd.MarkFlagRequired("number")

	partitionsCmd.Flags().StringVarP(&partitionsK, "parts", "k", "", "maximum number of parts")
}