77 lines
1.9 KiB
Go
77 lines
1.9 KiB
Go
/*
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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] = Stirling1(i+k-1, k-1) for a given k, nextStirling1 updates the slice so vals[i] = Stirling1(i+k, k) using the property that Stirling1(n, k) = -(n-1)*Stirling1(n-1, k) + Stirling1(n-1, k-1)
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func nextStirling1(k int, vals []*big.Int) {
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for i := 1; i < len(vals); i++ {
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n := int64(k + i - 1)
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v := big.NewInt(-n)
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v.Mul(v, vals[i-1])
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vals[i].Add(vals[i], v)
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}
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}
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func Stirling1(n, k int) *big.Int {
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if k > n {
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return big.NewInt(0)
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}
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vals := make([]*big.Int, n-k+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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nextStirling1(i, vals)
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}
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return vals[n-k]
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}
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// given a slice where vals[i] = Stirling2(i+k-1, k-1) for a given k, nextStirling2 updates the slice so vals[i] = Stirling2(i+k, k) using the property that Stirling2(n, k) = k*Stirling2(n-1, k) + Stirling2(n-1, k-1)
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func nextStirling2(k int64, vals []*big.Int) {
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for i := 1; i < len(vals); i++ {
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v := big.NewInt(k)
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v.Mul(v, vals[i-1])
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vals[i].Add(vals[i], v)
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}
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}
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func Stirling2(n, k int) *big.Int {
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if k > n {
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return big.NewInt(0)
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}
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vals := make([]*big.Int, n-k+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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nextStirling2(int64(i), vals)
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}
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return vals[n-k]
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}
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