結果

問題 No.1303 Inconvenient Kingdom
ユーザー 👑 hos.lyric
提出日時 2020-11-28 20:33:56
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 19 ms / 3,000 ms
コード長 6,173 bytes
コンパイル時間 1,603 ms
コンパイル使用メモリ 161,992 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-06-22 10:08:23
合計ジャッジ時間 2,858 ms
ジャッジサーバーID
(参考情報)
judge4 / judge2
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 34
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(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;
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;
}
// 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];
}
void main() {
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;
}
auto uf = new int[N];
uf[] = -1;
foreach (i; 0 .. M) {
uf.connect(A[i], B[i]);
}
int[] szs;
foreach (r; 0 .. N) {
if (uf[r] < 0) {
szs ~= -uf[r];
}
}
szs.sort.reverse;
debug {
writeln("szs = ", szs);
}
int cost = N * (N - 1) / 2;
foreach (s; szs) {
cost -= s * (s - 1) / 2;
}
if (szs.length >= 2) {
cost -= szs[0] * szs[1];
}
cost *= 2;
int id;
auto ids = new int[N];
foreach (r; 0 .. N) {
if (uf[r] < 0) {
foreach (u; 0 .. N) {
if (uf.root(u) == r) {
ids[u] = id++;
}
}
}
}
auto lap = new Mint[][](N, N);
foreach (i; 0 .. M) {
const x = ids[A[i]];
const y = ids[B[i]];
lap[x][x] += 1;
lap[x][y] -= 1;
lap[y][x] -= 1;
lap[y][y] += 1;
}
const fs = charPoly(lap);
debug {
writeln("fs = ", fs);
}
Mint ans;
if (szs.length >= 2) {
int cnt;
foreach (x; 0 .. szs.length) foreach (y; x + 1 .. szs.length) {
if (szs[0] * szs[1] == szs[x] * szs[y]) {
++cnt;
}
}
ans = fs[szs.length];
foreach (sz; szs) {
ans /= sz;
}
ans *= cnt;
ans *= szs[0] * szs[1];
} else {
// (N - 1) double counts
ans = fs[1] / N * (1 - (N - 1)) + fs[2];
}
writeln(cost);
writeln(ans);
}
} catch (EOFException e) {
}
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0