結果
| 問題 | No.1873 Bracket Swapping |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2022-03-17 02:18:13 |
| 言語 | D (dmd 2.106.1) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 7,407 bytes |
| コンパイル時間 | 2,023 ms |
| コンパイル使用メモリ | 159,488 KB |
| 実行使用メモリ | 20,520 KB |
| 最終ジャッジ日時 | 2024-06-22 14:37:23 |
| 合計ジャッジ時間 | 13,944 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
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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 | AC | 1 ms
6,812 KB |
| testcase_01 | AC | 1 ms
6,940 KB |
| testcase_02 | AC | 2 ms
6,940 KB |
| testcase_03 | AC | 118 ms
6,944 KB |
| testcase_04 | AC | 47 ms
6,940 KB |
| testcase_05 | AC | 44 ms
6,944 KB |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | AC | 960 ms
18,364 KB |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | AC | 6 ms
6,940 KB |
| testcase_12 | AC | 396 ms
10,588 KB |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | AC | 202 ms
7,036 KB |
| testcase_16 | WA | - |
| testcase_17 | AC | 465 ms
10,896 KB |
| testcase_18 | WA | - |
| testcase_19 | AC | 31 ms
6,944 KB |
| testcase_20 | AC | 785 ms
16,068 KB |
| testcase_21 | AC | 6 ms
6,944 KB |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | WA | - |
| testcase_26 | AC | 493 ms
10,848 KB |
| testcase_27 | WA | - |
| testcase_28 | AC | 36 ms
14,112 KB |
| testcase_29 | AC | 1 ms
6,940 KB |
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)); }
struct ModInt(uint M_) {
import std.conv : to;
alias M = M_;
uint x;
this(ModInt a) { x = a.x; }
this(uint x_) { x = x_ % M; }
this(ulong x_) { x = x_ % M; }
this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; }
this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); }
ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); }
ref ModInt opOpAssign(string op, T)(T a) {
static if (is(T == ModInt)) {
static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; }
else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; }
else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); }
else static if (op == "/") { this *= a.inv(); }
else static assert(false);
return this;
} else static if (op == "^^") {
if (a < 0) return this = inv()^^(-a);
ModInt b = this, c = 1U;
for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; }
return this = c;
} else {
return mixin("this " ~ op ~ "= ModInt(a)");
}
}
ModInt inv() const {
uint a = M, b = x; int y = 0, z = 1;
for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; }
assert(a == 1); return ModInt(y);
}
ModInt opUnary(string op)() const {
static if (op == "+") { return this; }
else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; }
else static assert(false);
}
ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
bool opCast(T: bool)() const { return (x != 0U); }
string toString() const { return x.to!string; }
}
enum MO = 998244353;
alias Mint = ModInt!MO;
enum LIM = 410;
Mint[] inv, fac, invFac;
void prepare() {
inv = new Mint[LIM];
fac = new Mint[LIM];
invFac = new Mint[LIM];
inv[1] = 1;
foreach (i; 2 .. LIM) {
inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]);
}
fac[0] = invFac[0] = 1;
foreach (i; 1 .. LIM) {
fac[i] = fac[i - 1] * i;
invFac[i] = invFac[i - 1] * inv[i];
}
}
Mint binom(long n, long k) {
if (n < 0) {
if (k >= 0) {
return (-1)^^(k & 1) * binom(-n + k - 1, k);
} else if (n - k >= 0) {
return (-1)^^((n - k) & 1) * binom(-k - 1, n - k);
} else {
return Mint(0);
}
} else {
if (0 <= k && k <= n) {
assert(n < LIM);
return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
} else {
return Mint(0);
}
}
}
// det(x I + a)
// O(n^3)
T[] charPoly(T)(const(T[][]) a) {
import std.algorithm.mutation : swap;
const n = cast(int)(a.length);
auto b = new T[][](n, n);
foreach (i; 0 .. n) b[i][] = a[i][];
// upper Hessenberg
foreach (j; 0 .. n - 2) {
foreach (i; j + 1 .. n) {
if (b[i][j]) {
swap(b[j + 1], b[i]);
foreach (ii; 0 .. n) swap(b[ii][j + 1], b[ii][i]);
break;
}
}
if (b[j + 1][j]) {
const r = 1 / b[j + 1][j];
foreach (i; j + 2 .. n) {
const s = r * b[i][j];
foreach (jj; j .. n) b[i][jj] -= s * b[j + 1][jj];
foreach (ii; 0 .. n) b[ii][j + 1] += s * b[ii][i];
}
}
}
// fss[i] := det(x I_i + b[0..i][0..i])
auto fss = new T[][n + 1];
fss[0] = [T(1)];
foreach (i; 0 .. n) {
fss[i + 1] = new T[i + 2];
foreach (k; 0 .. i + 1) fss[i + 1][k + 1] = fss[i][k];
foreach (k; 0 .. i + 1) fss[i + 1][k] += b[i][i] * fss[i][k];
T prod = 1;
foreach_reverse (j; 0 .. i) {
prod *= -b[j + 1][j];
const s = prod * b[j][i];
foreach (k; 0 .. j + 1) fss[i + 1][k] += s * fss[j][k];
}
}
return fss[n];
}
Mint solve(Mint[] as, Mint[] cs, long N) {
const d = cast(int)(cs.length) - 1;
Mint[] mul(Mint[] fs, Mint[] gs) {
auto hs = new Mint[d + d - 1];
foreach (i; 0 .. d) foreach (j; 0 .. d) {
hs[i + j] += fs[i] * gs[j];
}
foreach_reverse (i; d .. d + d - 1) {
foreach (j; 1 .. d + 1) {
hs[i - j] -= cs[j] * hs[i];
}
}
hs.length = d;
return hs;
}
auto xs = new Mint[d];
auto ys = new Mint[d];
xs[1] = 1;
ys[0] = 1;
for (long e = N; e; e >>= 1) {
if (e & 1) ys = mul(ys, xs);
xs = mul(xs, xs);
}
Mint ans;
foreach (i; 0 .. d) {
ans += as[i] * ys[i];
}
return ans;
}
void main() {
prepare;
try {
for (; ; ) {
const S = readToken;
const K = readLong;
const N = cast(int)(S.length) / 2;
// pos, depth, state
auto dp = new Mint[][][](2 * N + 1, N + 2, N + 2);
dp[0][0][0] = 1;
foreach (i; 0 .. 2 * N) {
foreach (j; 0 .. N + 1) foreach (u; 0 .. N + 1) {
dp[i + 1][j + 1][u] += dp[i][j][u];
if (j > 0) {
dp[i + 1][j - 1][u + ((S[i] == '(') ? 1 : 0)] += dp[i][j][u];
}
}
}
debug {
writeln("dp[2 N][0] = ", dp[2 * N][0]);
}
// initial state, final state
auto mat = new Mint[][](N + 1, N + 1);
foreach (u; 0 .. N + 1) {
mat[u][u] += ((2 * N) * (2 * N - 1) / 2 - (N - u)^^2 - u^^2);
if (u < N) mat[u][u + 1] += (N - u)^^2;
if (u > 0) mat[u][u - 1] += u^^2;
}
auto cs = charPoly(mat);
cs.reverse;
for (int i = 1; i <= N; i += 2) {
cs[i] *= -1;
}
debug {
writeln("mat = ", mat);
writeln("cs = ", cs);
}
// # of ops, state
auto DP = new Mint[][](N + 1, N + 1);
DP[0][0] = 1;
foreach (k; 0 .. N) {
foreach (u; 0 .. N + 1) foreach (v; 0 .. N + 1) {
DP[k + 1][v] += DP[k][u] * mat[u][v];
}
}
auto gs = new Mint[N + 1];
foreach (u; 0 .. N + 1) {
auto as = iota(N + 1).map!(k => DP[k][u]).array;
gs[u] = solve(as, cs, K);
gs[u] /= binom(N, u)^^2;
}
Mint ans;
foreach (u; 0 .. N + 1) {
ans += dp[2 * N][0][u] * gs[u];
}
writeln(ans);
}
} catch (EOFException e) {
}
}