結果
問題 | No.1116 Cycles of Dense Graph |
ユーザー |
👑 |
提出日時 | 2020-07-17 22:04:31 |
言語 | D (dmd 2.109.1) |
結果 |
AC
|
実行時間 | 159 ms / 2,000 ms |
コード長 | 6,524 bytes |
コンパイル時間 | 1,961 ms |
コンパイル使用メモリ | 163,868 KB |
実行使用メモリ | 13,612 KB |
最終ジャッジ日時 | 2024-06-22 07:41:33 |
合計ジャッジ時間 | 3,799 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 38 |
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(int M_) {import std.conv : to;alias M = M_;int x;this(ModInt a) { x = a.x; }this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }ref ModInt opAssign(long a) { return (this = ModInt(a)); }ref ModInt opOpAssign(string op)(ModInt a) {static if (op == "+") { x += a.x; if (x >= M) x -= M; }else static if (op == "-") { x -= a.x; if (x < 0) x += M; }else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }else static if (op == "/") { this *= a.inv(); }else static assert(false);return this;}ref ModInt opOpAssign(string op)(long a) {static if (op == "^^") {if (a < 0) return (this = inv()^^(-a));ModInt t2 = this, te = ModInt(1);for (long e = a; e > 0; e >>= 1) {if (e & 1) te *= t2;t2 *= t2;}x = cast(int)(te.x);return this;} else return mixin("this " ~ op ~ "= ModInt(a)");}ModInt inv() const {int a = x, b = M, y = 1, z = 0, t;for (; ; ) {t = a / b; a -= t * b;if (a == 0) {assert(b == 1 || b == -1);return ModInt(b * z);}y -= t * z;t = b / a; b -= t * a;if (b == 0) {assert(a == 1 || a == -1);return ModInt(a * y);}z -= t * y;}}ModInt opUnary(string op: "-")() const { return ModInt(-x); }ModInt opBinary(string op, T)(T a) const {return mixin("ModInt(this) " ~ op ~ "= a");}ModInt opBinaryRight(string op)(long a) const {return mixin("ModInt(a) " ~ op ~ "= this");}bool opCast(T: bool)() const { return (x != 0); }string toString() const { return x.to!string; }}enum MO = 998244353;alias Mint = ModInt!MO;enum LIM = 2 * 10^^5 + 100;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 (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);}}int root(int[] uf, int u) {return (uf[u] < 0) ? u : (uf[u] = uf.root(uf[u]));}bool connect(int[] uf, int u, int v) {u = uf.root(u);v = uf.root(v);if (u == v) return false;if (uf[u] > uf[v]) swap(u, v);uf[u] += uf[v];uf[v] = u;return true;}void main() {prepare;auto two = new Mint[LIM];two[0] = 1;foreach (i; 1 .. LIM) {two[i] = two[i - 1] * 2;}try {for (; ; ) {const N = readInt();const M = readInt();auto A = new int[M];auto B = new int[M];foreach (i; 0 .. M) {A[i] = readInt() - 1;B[i] = readInt() - 1;}int[] us = A.dup ~ B.dup;us = us.sort.uniq.array;const usLen = cast(int)(us.length);foreach (i; 0 .. M) {A[i] = us.lowerBound(A[i]);B[i] = us.lowerBound(B[i]);}Mint ans;// 0foreach (k; 3 .. N + 1) {ans += binom(N, k) * fac[k - 1] * inv[2];}// 1foreach (j; 1 .. (N - 2) + 1) {ans -= M * (binom(N - 2, j) * fac[j]);debug {writeln(j, ": ", binom(N - 2, j) * fac[j]);}}auto mem = new bool[][](2 * M + 1, 2 * M + 1);auto cache = new Mint[][](2 * M + 1, 2 * M + 1);Mint calc(int x, int y) {Mint ret;if (!mem[x][y]) {foreach (j; 0 .. (N - y) + 1) {ret += binom(N - y, j) * two[x - 1] * fac[x + j - 1];}debug {writefln("calc %s %s = %s", x, y, ret);}mem[x][y] = true;cache[x][y] = ret;} else {ret = cache[x][y];}return ret;}foreach (p; 0 .. 1 << M) {if (popcnt(p) >= 2) {auto uf = new int[usLen];uf[] = -1;auto deg = new int[usLen];foreach (i; 0 .. M) {if (p & 1 << i) {uf.connect(A[i], B[i]);++deg[A[i]];++deg[B[i]];}}auto uss = new int[][usLen];foreach (u; 0 .. usLen) {uss[uf.root(u)] ~= u;}int numComps, numVertices;int numCycles;foreach (r; 0 .. usLen) {if (uss[r].length >= 2) {numComps += 1;numVertices += uss[r].length;if (uss[r].any!(u => (deg[u] >= 3))) {goto failed;}if (uss[r].all!(u => (deg[u] == 2))) {++numCycles;}}}{Mint num;switch (numCycles) {case 0: {num = calc(numComps, numVertices);} break;case 1: {num = (numComps == 1) ? 1 : 0;} break;default: {}}ans += (-1)^^(popcnt(p) & 1) * num;}failed:}}writeln(ans);}} catch (EOFException e) {}}