/*
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"
	"log"
	"math/big"

	"github.com/spf13/cobra"
)

var remainders []string
var moduli []string

func crtSolve(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
	// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
	m1 := new(big.Int)
	m2 := new(big.Int)
	tmp := new(big.Int)
	tmp.GCD(m1, m2, n1, n2)

	// x = a1*m2*n2 + a2*m1*n1
	x := new(big.Int).Set(a1)
	x.Mul(x, m2)
	x.Mul(x, n2)

	tmp.Set(a2)
	tmp.Mul(tmp, m1)
	tmp.Mul(tmp, n1)

	x.Add(x, tmp)

	N := new(big.Int).Set(n1)
	N.Mul(N, n2)

	x.Mod(x, N)

	return x, N
}

func arePairwiseCoprime(moduli []*big.Int) bool {
	z := new(big.Int)
	for i, a := range moduli {
		for _, b := range moduli[i+1:] {
			z.GCD(nil, nil, a, b)
			if z.Cmp(big.NewInt(1)) != 0 {
				return false
			}
		}
	}

	return true
}

func crt(cmd *cobra.Command, args []string) {
	if len(remainders) != len(moduli) {
		log.Fatal("number of remainders and moduli do not match")
	}

	ns := make([]*big.Int, len(moduli))
	for i := range moduli {
		n, ok := new(big.Int).SetString(moduli[i], 10)
		if !ok {
			log.Fatal("invalid input " + moduli[i])
		}

		ns[i] = new(big.Int).Set(n)
	}

	// TODO: support non-pairwise coprime moduli
	if !arePairwiseCoprime(ns) {
		log.Fatalf("moduli %v are not pairwise coprime", moduli)
	}

	n1 := new(big.Int)
	a1 := new(big.Int)
	for i, n2 := range ns {
		a2, ok := new(big.Int).SetString(remainders[i], 10)
		if !ok {
			log.Fatal("invalid input " + remainders[i])
		}

		if i != 0 {
			x, N := crtSolve(a1, n1, a2, n2)
			n1.Set(N)
			a1.Set(x)
		} else {
			a1.Set(a2)
			n1.Set(n2)
		}
	}

	fmt.Println(a1)
	fmt.Println(n1)
}

// crtCmd represents the crt command
var crtCmd = &cobra.Command{
	Use:   "crt -r R R [R ...] -m M M [M ...]",
	Short: "Solve a system of linear congruences",
	Long: `Solve a system of linear congruences.`,
	Run: crt,
}

func init() {
	rootCmd.AddCommand(crtCmd)

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

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

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

	crtCmd.Flags().StringSliceVarP(&remainders, "remainders", "r", make([]string, 0), "remainders of congruences")
	crtCmd.MarkFlagRequired("remainders")

	crtCmd.Flags().StringSliceVarP(&moduli, "moduli", "m", make([]string, 0), "moduli of congruences")
	crtCmd.MarkFlagRequired("moduli")
}