53 lines
1.2 KiB
Go
53 lines
1.2 KiB
Go
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/*
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Copyright © 2025 filifa
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package lib
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import (
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"math/big"
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)
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// 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)
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func nextPartition(k int, vals []*big.Int) {
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for i := 1; i < len(vals); i++ {
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if i-k >= 0 {
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vals[i].Add(vals[i], vals[i-k])
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}
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}
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}
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func Partitions(n, k int) *big.Int {
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if n < 0 {
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return big.NewInt(0)
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}
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if k > n {
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k = n
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}
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vals := make([]*big.Int, n+1)
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for i := range vals {
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vals[i] = big.NewInt(0)
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}
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vals[0] = big.NewInt(1)
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for i := 1; i <= k; i++ {
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nextPartition(i, vals)
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}
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return vals[n]
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}
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