mathtools/cmd/partitions.go

/*
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"
	"strconv"

	"github.com/spf13/cobra"
)

var partitionsN string
var partitionsK string

// given a slice where vals[i] = p_{k-1}(i) for a given k, nextPartition updates the slice so vals[i] = p_k(i) using the property that p_k(n) = p_k(n-k) + p_{k-1}(n)
func nextPartition(k int, vals []*big.Int) {
	for i := 1; i < len(vals); i++ {
		if i-k >= 0 {
			vals[i].Add(vals[i], vals[i-k])
		}
	}
}

func p(n, k int) *big.Int {
	if n < 0 {
		return big.NewInt(0)
	}

	if k > n {
		k = n
	}

	vals := make([]*big.Int, n+1)
	for i := range vals {
		vals[i] = big.NewInt(0)
	}
	vals[0] = big.NewInt(1)

	for i := 1; i <= k; i++ {
		nextPartition(i, vals)
	}

	return vals[n]
}

func partitions(cmd *cobra.Command, args []string) {
	n, err := strconv.Atoi(partitionsN)
	if err != nil {
		cobra.CheckErr("invalid input " + partitionsN)
	}

	var k int
	if partitionsK == "" {
		k = n
	} else {
		var err error
		k, err = strconv.Atoi(partitionsK)
		if err != nil {
			cobra.CheckErr("invalid input " + partitionsK)
		}
	}

	if n < 0 {
		cobra.CheckErr("n must be nonnegative")
	}

	if k < 0 {
		cobra.CheckErr("k must be nonnegative")
	}

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

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

For example, 4 can be partitioned into
4
3+1
2+2
2+1+1
1+1+1+1
so p(n) = 5.

To compute the number of partitions into at most k parts, provide the -k flag.`,
	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")
}