結果

問題 No.950 行列累乗
ユーザー 👑 hos.lyrichos.lyric
提出日時 2019-12-13 02:13:43
言語 D
(dmd 2.109.1)
結果
WA  
実行時間 -
コード長 7,930 bytes
コンパイル時間 1,214 ms
コンパイル使用メモリ 141,672 KB
実行使用メモリ 19,740 KB
最終ジャッジ日時 2024-06-22 03:32:15
合計ジャッジ時間 6,729 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
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ファイルパターン 結果
sample AC * 4
other AC * 55 WA * 2
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std
    .typecons;
import core.bitop;
class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens
    .popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }
bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }
int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1;
    (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }
// floor(a^(1/k))
ulong floorKthRoot(ulong a, ulong k) {
import core.bitop : bsr;
import std.algorithm : min;
if (a == 0) {
return 0;
} else if (k <= 1) {
return a;
} else if (k == 2) {
ulong b = a, x = 0, y = 0;
for (int e = bsr(a) & ~1; e >= 0; e -= 2) {
x <<= 1;
y <<= 1;
if (b >= (y | 1) << e) {
b -= (y | 1) << e;
x |= 1;
y += 2;
}
}
return x;
} else if (k <= 40) {
// min x s.t. x^k >= 2^64
enum ulong[] HIS =
[0, 0, 4294967296UL, 2642246, 65536, 7132, 1626, 566, 256, 139, 85, 57,
41, 31, 24, 20, 16, 14, 12, 11, 10, 9, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 4, 4];
ulong lo = 1UL << (bsr(a) / k);
ulong hi = min(1UL << (bsr(a) / k + 1), HIS[cast(size_t)(k)]);
for (; lo + 1 < hi; ) {
const ulong mid = (lo + hi) / 2;
ulong b = mid * mid;
foreach (i; 2 .. k) b *= mid;
((b <= a) ? lo : hi) = mid;
}
return lo;
} else if (k <= 63) {
return ((1UL << k) <= a) ? 2 : 1;
} else {
return 1;
}
}
// a^-1 (mod m)
long modInv(long a, long m)
in {
assert(m > 0, "modInv: m > 0 must hold");
}
do {
long b = m, x = 1, y = 0, t;
for (; ; ) {
t = a / b; a -= t * b;
if (a == 0) {
assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");
if (b == -1) y = -y;
return (y < 0) ? (y + m) : y;
}
x -= t * y;
t = b / a; b -= t * a;
if (b == 0) {
assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");
if (a == -1) x = -x;
return (x < 0) ? (x + m) : x;
}
y -= t * x;
}
}
Int mod(Int)(Int a, Int m) {
if ((a %= m) < 0) a += m; return a;
}
Int gcd(Int)(Int a, Int b) { return (b != 0) ? gcd(b, a % b) : a; }
Int lcm(Int)(Int a, Int b) { return a / gcd(a, b) * b; }
Int gojo(Int)(Int a, Int b, out Int x, out Int y) {
if (b != 0) { Int g = gojo(b, a % b, y, x); y -= (a / b) * x; return g; }
x = 1; y = 0; return a;
}
Int modInv(Int)(Int a, Int m) { Int x, y; gojo(a, m, x, y); return mod(x, m); }
long modLogP(long a, long b, long m) {
a = mod(a, m); b = mod(b, m);
if (m == 1) return 0;
long k, al = 1;
Tuple!(long,long)[] as;
for (k = 0; k * k < m; ++k) {
as ~= tuple(al, k);
al = (al * a) % m;
}
as.sort;
al = modInv(al, m);
for (long i = 0; i < k; ++i) {
int pos = as.lowerBound(tuple(b, 0L));
if (pos < as.length && as[pos][0] == b) return i * k + as[pos][1];
b = (b * al) % m;
}
return -1;
}
long P;
long[][] A, B;
long[][] div(long[][] a, long t) {
const invT = modInv(t, P);
auto b = new long[][](2, 2);
foreach (i; 0 .. 2) foreach (j; 0 .. 2) {
b[i][j] = mod(invT * a[i][j], P);
}
return b;
}
long[][] inv(long[][] a) {
const det = mod(a[0][0] * a[1][1] - a[0][1] * a[1][0], P);
return div([[a[1][1], -a[0][1]], [-a[1][0], a[0][0]]], det);
}
long[][] mul(long[][] a, long[][] b) {
auto c = new long[][](2, 2);
foreach (i; 0 .. 2) foreach (k; 0 .. 2) foreach (j; 0 .. 2) {
c[i][j] = mod(c[i][j] + a[i][k] * b[k][j], P);
}
return c;
}
long[][] power(long[][] a, long e) {
long[][] b = a, c = [[1, 0], [0, 1]];
for (; e; e >>= 1) {
if (e & 1) c = mul(c, b);
b = mul(b, b);
}
return c;
}
long solveBSGS(long[][] a, long[][] b) {
const m = cast(int)(floorKthRoot(2 * P, 2) + 2);
auto als = new Tuple!(long[][], int)[m];
long[][] al = [[1, 0], [0, 1]];
foreach (l; 0 .. m) {
als[l] = tuple(al, l);
al = mul(al, a);
}
als.sort;
al = inv(al);
long[][] amk = b;
foreach (k; 0 .. m) {
const pos = als.lowerBound(tuple(amk, 0));
if (pos < m && als[pos][0] == amk) {
return k * cast(long)(m) + als[pos][1];
}
amk = mul(amk, al);
}
return -1;
}
void main() {
try {
for (; ; ) {
P = readLong();
A = new long[][](2, 2);
foreach (i; 0 .. 2) foreach (j; 0 .. 2) {
A[i][j] = readLong();
}
B = new long[][](2, 2);
foreach (i; 0 .. 2) foreach (j; 0 .. 2) {
B[i][j] = readLong();
}
long ans;
const detA = mod(A[0][0] * A[1][1] - A[0][1] * A[1][0], P);
const detB = mod(B[0][0] * B[1][1] - B[0][1] * B[1][0], P);
if (detA == 0) {
if (detB == 0) {
if (A == [[0, 0], [0, 0]]) {
if (B == [[0, 0], [0, 0]]) {
ans = 1;
} else {
ans = -1;
}
} else {
/*
C^-1 A C = [[r, 0], [0, 0]]
a00 c00 + a01 c10 = r c00
a10 c00 + a11 c10 = r c10
a00 c01 + a01 c11 = 0
a10 c01 + a11 c11 = 0
*/
const r = mod(A[0][0] + A[1][1], P);
assert(r != 0);
auto c = new long[][](2, 2);
c[0][0] = mod(-A[0][1], P);
c[1][0] = mod(A[0][0] - r, P);
if (c[0][0] == 0 && c[1][0] == 0) {
c[0][0] = mod(-(A[1][1] - r), P);
c[1][0] = mod(A[1][0], P);
}
if (c[0][0] == 0 && c[1][0] == 0) {
assert(false);
}
c[0][1] = mod(-A[0][1], P);
c[1][1] = mod(A[0][0], P);
if (c[0][1] == 0 && c[1][1] == 0) {
c[0][1] = mod(-A[1][1], P);
c[1][1] = mod(A[1][0], P);
}
if (c[0][1] == 0 && c[1][1] == 0) {
assert(false);
}
debug {
writeln("r = ", r);
writeln("c = ", c);
}
auto a = mul(mul(inv(c), A), c);
auto b = mul(mul(inv(c), B), c);
debug {
writeln("a = ", a);
writeln("b = ", b);
}
if (b[0][1] == 0 && b[1][0] == 0 && b[1][1] == 0) {
ans = modLogP(a[0][0], mod(b[0][0] * modInv(a[0][0], P), P), P) + 1;
} else {
ans = -1;
}
}
} else {
ans = -1;
}
} else {
const period = modLogP(detA, modInv(detA, P), P) + 1;
long e0 = modLogP(detA, detB, P);
debug {
writeln("detA = ", detA, ", detB = ", detB);
writeln("period = ", period);
writeln("e0 = ", e0);
}
if (e0 == -1) {
ans = -1;
} else {
if (e0 == 0) {
e0 += period;
}
auto a = power(A, period);
auto b = mul(B, inv(power(A, e0)));
debug {
writeln("a = ", a);
writeln("b = ", b);
}
const res = solveBSGS(a, b);
if (res == -1) {
ans = -1;
} else {
ans = e0 + period * res;
}
}
}
writeln(ans);
}
} catch (EOFException e) {
}
}
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