結果
| 問題 | No.950 行列累乗 |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2019-12-13 01:28:41 |
| 言語 | D (dmd 2.106.1) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 9,723 bytes |
| コンパイル時間 | 1,394 ms |
| コンパイル使用メモリ | 131,440 KB |
| 実行使用メモリ | 11,496 KB |
| 最終ジャッジ日時 | 2023-09-04 03:52:33 |
| 合計ジャッジ時間 | 6,586 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge15 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | RE | - |
| testcase_01 | RE | - |
| testcase_02 | RE | - |
| testcase_03 | RE | - |
| testcase_04 | RE | - |
| testcase_05 | AC | 45 ms
7,520 KB |
| testcase_06 | RE | - |
| testcase_07 | AC | 2 ms
4,376 KB |
| testcase_08 | RE | - |
| testcase_09 | RE | - |
| testcase_10 | RE | - |
| testcase_11 | AC | 2 ms
4,380 KB |
| testcase_12 | AC | 2 ms
4,380 KB |
| testcase_13 | RE | - |
| testcase_14 | RE | - |
| testcase_15 | RE | - |
| testcase_16 | RE | - |
| testcase_17 | RE | - |
| testcase_18 | RE | - |
| testcase_19 | RE | - |
| testcase_20 | RE | - |
| testcase_21 | RE | - |
| testcase_22 | RE | - |
| testcase_23 | AC | 73 ms
11,496 KB |
| testcase_24 | RE | - |
| testcase_25 | AC | 49 ms
9,276 KB |
| testcase_26 | AC | 68 ms
9,796 KB |
| testcase_27 | AC | 94 ms
11,244 KB |
| testcase_28 | RE | - |
| testcase_29 | RE | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | RE | - |
| testcase_34 | RE | - |
| testcase_35 | RE | - |
| testcase_36 | RE | - |
| testcase_37 | RE | - |
| testcase_38 | RE | - |
| testcase_39 | RE | - |
| testcase_40 | AC | 73 ms
9,988 KB |
| testcase_41 | AC | 72 ms
9,868 KB |
| testcase_42 | RE | - |
| testcase_43 | RE | - |
| testcase_44 | RE | - |
| testcase_45 | RE | - |
| testcase_46 | RE | - |
| testcase_47 | RE | - |
| testcase_48 | RE | - |
| testcase_49 | RE | - |
| testcase_50 | RE | - |
| testcase_51 | RE | - |
| testcase_52 | RE | - |
| testcase_53 | RE | - |
| testcase_54 | RE | - |
| testcase_55 | RE | - |
| testcase_56 | RE | - |
| testcase_57 | AC | 61 ms
10,880 KB |
| testcase_58 | RE | - |
| testcase_59 | RE | - |
| testcase_60 | RE | - |
コンパイルメッセージ
Main.d(359): Warning: statement is not reachable Main.d(359): Warning: statement is not reachable
ソースコード
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;
}
}
// xorshift
uint xrand() {
static uint x = 314159265, y = 358979323, z = 846264338, w = 327950288;
uint t = x ^ x << 11; x = y; y = z; z = w; return w = w ^ w >> 19 ^ t ^ t >> 8;
}
// 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;
}
}
// (a / 2) mod m
long div2(long a, long m)
in {
assert(1 <= m && m < 1L << 62, "div2: 1 <= m < 2^62 must hold");
assert(m % 2 != 0, "div2: m must not be divisibly by 3");
assert(0 <= a && a < m, "div2: 0 <= a < m must hold");
}
do {
return (a + (a % 2) * m) / 2;
}
// (a / 3) mod m
long div3(long a, long m)
in {
assert(1 <= m && m < 1L << 61, "div3: 1 <= m < 2^61 must hold");
assert(m % 3 != 0, "div3: m must not be divisibly by 3");
assert(0 <= a && a < m, "div3: 0 <= a < m must hold");
}
do {
return (a + (((3 - a % 3) * (m % 3)) % 3) * m) / 3;
}
// Jacobi symbol (a/m)
int jacobi(long a, long m)
in {
assert(m > 0, "jacobi: m > 0 must hold");
assert(m & 1, "jacobi: m must be odd");
}
do {
import core.bitop : bsf;
import std.algorithm.mutation : swap;
int s = 1;
if (a < 0) a = a % m + m;
for (; m > 1; ) {
a %= m;
if (a == 0) return 0;
const r = bsf(a);
if ((r & 1) && ((m + 2) & 4)) s = -s;
a >>= r;
if (a & m & 2) s = -s;
swap(a, m);
}
return s;
}
// sqrt(a) (mod p)
// p: be prime
// (b + sqrt(b^2 - a))^((p+1)/2) in F_p(sqrt(b^2 - a))
long[] modSqrt(long a, long p)
in {
assert(p < 1L << 31, "modSqrt: p < 2^31 must hold");
assert(-p * p <= a && a <= p * p, "modSqrt: -p^2 <= a <= p^2 must hold");
}
do {
if (p == 2) return [a & 1];
const j = jacobi(a, p);
if (j == 0) return [0];
if (j == -1) return [];
long b, d;
for (; ; ) {
b = xrand() % p;
d = (b * b - a) % p;
if (d < 0) d += p;
if (jacobi(d, p) == -1) break;
}
long[2] mul(in long[2] x, in long[2] y) {
return [(x[0] * y[0] + d * ((x[1] * y[1]) % p)) % p,
(x[0] * y[1] + x[1] * y[0]) % p];
}
long[2] f = [b, 1], g = [1, 0];
for (long e = (p + 1) >> 1; e; e >>= 1) {
if (e & 1) g = mul(g, f);
f = mul(f, f);
}
assert(g[1] == 0);
return (g[0] < p - g[0]) ? [g[0], p - g[0]] : [p - g[0], g[0]];
}
// Roots of f0 + f1 T + T^2 in F_p[T] with multiplicity
// p: prime
long[] modRoots2(long f0, long f1, long p)
in {
assert(2 <= p && p < 1L << 31, "modRoots2: 2 <= p < 2^31 must hold");
assert(0 <= f0 && f0 < p, "modRoots2: 0 <= f0 < p must hold");
assert(0 <= f1 && f1 < p, "modRoots2: 0 <= f1 < p must hold");
}
do {
import std.algorithm : sort;
if (p == 2) {
if (f0 == 0 && f1 == 0) return [0, 0];
if (f0 == 0 && f1 == 1) return [0, 1];
if (f0 == 1 && f1 == 0) return [1, 1];
return [];
} else {
const f12 = f1.div2(p);
auto ts = modSqrt(f12 * f12 - f0, p);
foreach (ref t; ts) {
if ((t -= f12) < 0) t += p;
}
sort(ts);
switch (ts.length) {
case 0: return [];
case 1: return [ts[0], ts[0]];
case 2: return ts;
default: assert(false);
}
}
}
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 modLog(long a, long b, long m) {
a = mod(a, m); b = mod(b, m);
long f, g, r = 1 % m;
for (f = 0; (g = gcd(a, m)) > 1; ++f) {
if (b % g != 0) return (r == b) ? f : -1;
b /= g; m /= g;
r = (r * (a / g)) % m;
}
long res = modLogP(a, b * modInv(r, m) % m, m);
return (res != -1) ? (f + res) : -1;
}
long P;
long[][] A, B;
long detA;
long[][] inv(long[][] a) {
const det = mod(a[0][0] * a[1][1] - a[0][1] * a[1][0], P);
const t = modInv(det, P);
auto b = [[a[1][1], -a[0][1]], [-a[1][0], a[0][0]]];
foreach (i; 0 .. 2) foreach (j; 0 .. 2) {
b[i][j] = mod(t * b[i][j], P);
}
return b;
}
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 solveBBGS() {
assert(detA != 0);
const m = cast(int)(floorKthRoot(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;
auto invA = inv(A);
auto invAm = inv(al);
long[][] amk = B;
amk = mul(amk, invA);
foreach (k; 0 .. m) {
const pos = als.lowerBound(tuple(amk, 0));
if (pos < m && als[pos][0] == amk) {
return 1 + k * cast(long)(m) + als[pos][1];
}
amk = mul(amk, invAm);
}
return -1;
}
/*
c^-1 A c = [[r, u], [0, s]]
a00 c00 + a01 c10 = c00 r
a10 c00 + a11 c10 = c10 r
a00 c01 + a01 c11 = c01 s + c00 u
a10 c01 + a11 c11 = c11 s + c10 u
*/
long[][] getTr(long[] ts) {
auto c = new long[][](2, 2);
// tasukete
return null;
}
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();
}
detA = mod(A[0][0] * A[1][1] - A[0][1] * A[1][0], P);
// (A[0][0] - T) (A[1][1] - T) - A[0][1] * A[1][0]
auto ts = modRoots2(detA, mod(-(A[0][0] + A[1][1]), P), P);
debug {
writeln("ts = ", ts);
}
long ans;
if (ts.length == 2) {
if (ts[0] == ts[1]) {
// yabai
auto c = getTr(ts);
auto invC = inv(c);
auto a = mul(mul(invC, A), c);
auto b = mul(mul(invC, B), c);
debug {
writeln("a = ", a);
writeln("b = ", b);
}
import core.stdc.stdlib;
exit(1);
} else {
if (ts[0] == 0 && ts[1] == 0) {
// zero
if (B[0][0] == 0 && B[0][1] == 0 && B[1][0] == 0 && B[1][1] == 0) {
ans = 1;
} else {
ans = -1;
}
} else if (ts[0] == 0) {
// ?
import core.stdc.stdlib;
exit(1);
} else {
ans = solveBBGS();
}
}
} else {
import core.stdc.stdlib;
exit(1);
ans = solveBBGS();
}
writeln(ans);
}
} catch (EOFException e) {
}
}