結果

問題 No.1116 Cycles of Dense Graph
ユーザー 👑 hos.lyric
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
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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(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;
// 0
foreach (k; 3 .. N + 1) {
ans += binom(N, k) * fac[k - 1] * inv[2];
}
// 1
foreach (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) {
}
}
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