結果
問題 | No.2083 OR Subset |
ユーザー |
👑 |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 17 |
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 = 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) {}}