結果

問題 No.2083 OR Subset
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-09-25 21:33:37
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 831 ms / 3,000 ms
コード長 5,483 bytes
コンパイル時間 1,439 ms
コンパイル使用メモリ 155,940 KB
実行使用メモリ 104,736 KB
最終ジャッジ日時 2024-06-22 16:17:38
合計ジャッジ時間 11,581 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 17
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)); }
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 = cast(uint)(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_INV = 5010;
Mint[] inv, fac, invFac;
void prepare() {
inv = new Mint[LIM_INV];
fac = new Mint[LIM_INV];
invFac = new Mint[LIM_INV];
inv[1] = 1;
foreach (i; 2 .. LIM_INV) {
inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]);
}
fac[0] = invFac[0] = 1;
foreach (i; 1 .. LIM_INV) {
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_INV);
return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
} else {
return Mint(0);
}
}
}
void main() {
prepare;
auto S2 = new Mint[][](LIM_INV, LIM_INV);
foreach (n; 0 .. LIM_INV) {
S2[n][0] = 0;
S2[n][n] = 1;
foreach (k; 1 .. n) {
S2[n][k] = S2[n - 1][k - 1] + k * S2[n - 1][k];
}
}
debug {
foreach (n; 0 .. 4 + 1) {
auto freq = new int[1 << n];
foreach (p; 0 .. 1 << (1 << n)) if (popcnt(p) <= 4) {
int[] xs;
foreach (x; 0 .. 1 << n) if (p >> x & 1) {
xs ~= x;
}
const xsLen = cast(int)(xs.length);
auto xsOr = new int[1 << xsLen];
foreach (i; 0 .. xsLen) foreach (q; 0 .. 1 << i) {
xsOr[q | 1 << i] = xsOr[q] | xs[i];
}
xsOr.sort;
bool ok = true;
foreach (q; 1 .. 1 << xsLen) {
ok = ok && (xsOr[q - 1] != xsOr[q]);
}
if (ok) {
++freq[xs.length];
if (n == 3) {
writeln(" ", xs);
}
}
}
writeln(n, ": ", freq);
}
}
try {
for (; ; ) {
const N = readInt;
Mint ans;
foreach (m; 0 .. N + 1) {
Mint sum;
const two = Mint(2)^^m;
Mint pw = 1;
foreach_reverse (l; m .. N + 1) {
Mint num = 1;
num *= S2[l][m];
num *= binom(N, l);
num *= pw;
pw *= (two - m);
sum += num;
}
debug {
if (N <= 10) {
writeln(N, " ", m, ": ", sum);
}
}
ans += sum;
}
writeln(ans);
}
} catch (EOFException e) {
}
}
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