add partitions command

cmd/partitions.go

@@ -0,0 +1,103 @@
+/*
+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")
+}