結果
問題 | No.1303 Inconvenient Kingdom |
ユーザー |
👑 |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 34 |
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;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 Hessenbergforeach (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 countsans = fs[1] / N * (1 - (N - 1)) + fs[2];}writeln(cost);writeln(ans);}} catch (EOFException e) {}}