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package main | |
import ( | |
"bufio" | |
"fmt" | |
"io" | |
"log" | |
"math/big" | |
"os" | |
"strings" | |
) | |
var one = big.NewInt(1) | |
var minusOne = big.NewInt(-1) | |
var zero = big.NewInt(0) | |
type applier interface { | |
apply(n *big.Int, mod *big.Int) | |
} | |
type change struct { | |
scale *big.Int | |
shift *big.Int | |
} | |
func (chg change) mod(mod int64) { | |
chg.scale.Mod(chg.scale, big.NewInt(mod)) | |
chg.shift.Mod(chg.shift, big.NewInt(mod)) | |
} | |
func (chg change) apply(n *big.Int, mod *big.Int) { | |
n.Mul(n, chg.scale) | |
n.Add(n, chg.shift) | |
n.Mod(n, mod) | |
} | |
func (chg change) invert(mod int64) invertedChange { | |
chg.mod(mod) | |
m := big.NewInt(mod) | |
scale := big.NewInt(0) | |
if chg.scale.Cmp(zero) != 0 { | |
scale = chg.scale.ModInverse(chg.scale, m) | |
} | |
shift := chg.shift.Mul(chg.shift, minusOne) | |
shift.Mul(shift, scale) | |
shift.Mod(shift, m) | |
return invertedChange{scale, shift} | |
} | |
type invertedChange struct { | |
scale *big.Int | |
shift *big.Int | |
} | |
func (ichg invertedChange) apply(n *big.Int, mod *big.Int) { | |
n.Mul(n, ichg.scale) | |
n.Add(n, ichg.shift) | |
n.Mod(n, mod) | |
} | |
func geoSum(a, r, n, mod *big.Int) { | |
var denom big.Int | |
denom.Set(one) | |
denom.Sub(&denom, r) | |
denom.ModInverse(&denom, mod) | |
r.Exp(r, n, mod) | |
r.Mul(r, minusOne) | |
r.Add(r, one) | |
r.Mul(r, &denom) | |
r.Mul(r, a) | |
a.Set(r) | |
a.Mod(a, mod) | |
} | |
func (ichg invertedChange) pow(n *big.Int, mod *big.Int) { | |
var scale big.Int | |
scale.Set(ichg.scale) | |
geoSum(ichg.shift, &scale, n, mod) | |
ichg.scale.Exp(ichg.scale, n, mod) | |
} | |
func ReadTransformations(r io.Reader) change { | |
scan := bufio.NewScanner(r) | |
chg := change{big.NewInt(1), big.NewInt(0)} | |
var x big.Int | |
for scan.Scan() { | |
line := scan.Text() | |
switch { | |
case strings.Index(line, "deal with") == 0: | |
var d int64 | |
fmt.Sscanf(line, "deal with increment %d", &d) | |
x.SetInt64(d) | |
chg.scale.Mul(chg.scale, &x) | |
chg.shift.Mul(chg.shift, &x) | |
case strings.Index(line, "cut") == 0: | |
var d int64 | |
fmt.Sscanf(line, "cut %d", &d) | |
x.SetInt64(d) | |
chg.shift.Sub(chg.shift, &x) | |
case strings.Index(line, "deal into") == 0: | |
chg.scale.Mul(chg.scale, minusOne) | |
chg.shift.Mul(chg.shift, minusOne) | |
chg.shift.Sub(chg.shift, one) | |
default: | |
log.Fatal("bad line:", line) | |
} | |
} | |
if err := scan.Err(); err != nil { | |
log.Fatal(err) | |
} | |
return chg | |
} | |
func apply(n int64, mod int64, a applier, times int) int64 { | |
x := big.NewInt(n) | |
m := big.NewInt(mod) | |
for ; times > 0; times-- { | |
a.apply(x, m) | |
x.Mod(x, m) | |
} | |
return x.Int64() | |
} | |
func main() { | |
f, err := os.Open(os.Args[1]) | |
if err != nil { | |
log.Fatal(err) | |
} | |
defer f.Close() | |
chg := ReadTransformations(f) | |
fmt.Println(apply(2019, 10007, chg, 1)) | |
var mod int64 = 119315717514047 | |
const n = 2020 | |
const times = 101741582076661 | |
i := chg.invert(mod) | |
m := big.NewInt(mod) | |
x := big.NewInt(n) | |
i.pow(big.NewInt(times), m) | |
i.apply(x, m) | |
x.Mod(x, m) | |
fmt.Println(x) | |
} |