mathtools/cmd/stirling.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"
	"scm.dairydemon.net/filifa/mathtools/internal/lib"
)

var firstKind bool
var secondKind bool
var stirlingTop string
var stirlingBottom string
var stirlingUnsigned bool

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

	k, err := strconv.Atoi(stirlingBottom)
	if err != nil {
		cobra.CheckErr("invalid input " + stirlingBottom)
	}

	var result *big.Int
	if firstKind {
		result = lib.Stirling1(n, k)
	} else if secondKind {
		result = lib.Stirling2(n, k)
	}

	if stirlingUnsigned {
		result.Abs(result)
	}

	fmt.Println(result)
}

// stirlingCmd represents the stirling command
var stirlingCmd = &cobra.Command{
	Use:   "stirling [-1|-2] -n N -k N",
	Short: "Compute the Stirling numbers",
	Long: `Compute the Stirling numbers.

The Stirling numbers of the first kind give the coefficients in the expansion of the falling factorial. For example,
x(x-1)(x-2) = x^3 - 3x^2 + 2x
Consequently, s(3,1) = 2, s(3,2) = -3, and s(3,3) = 3.

The Stirling numbers of the second kind count the number of ways to partition a set of n objects into k non-empty subsets. For example, there are 7 ways to partition a set of 4 objects into 2 non-empty subsets:
{1} {2,3,4}
{2} {1,3,4}
{3} {1,2,4}
{4} {1,2,3}
{1,2} {3,4}
{1,3} {2,4}
{1,4} {2,3}
Therefore S(4,2) = 7.`,
	Run: stirling,
}

func init() {
	rootCmd.AddCommand(stirlingCmd)

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

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

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

	stirlingCmd.Flags().BoolVarP(&firstKind, "first", "1", false, "Compute Stirling numbers of the first kind")
	stirlingCmd.Flags().BoolVarP(&secondKind, "second", "2", false, "Compute Stirling numbers of the second kind")

	stirlingCmd.MarkFlagsMutuallyExclusive("first", "second")
	stirlingCmd.MarkFlagsOneRequired("first", "second")

	stirlingCmd.Flags().StringVarP(&stirlingTop, "n", "n", "", "n")
	stirlingCmd.Flags().StringVarP(&stirlingBottom, "k", "k", "", "k")
	stirlingCmd.MarkFlagRequired("n")
	stirlingCmd.MarkFlagRequired("k")

	stirlingCmd.Flags().BoolVar(&stirlingUnsigned, "unsigned", false, "output the absolute value of the number (only relevant for first kind)")
}