move to lib

internal/lib/partitions.go

@@ -0,0 +1,52 @@
+/*
+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 lib
+
+import (
+	"math/big"
+)
+
+// 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 Partitions(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]
+}