結果

問題 No.2133 Take it easy!
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-11-25 22:42:24
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 13 ms / 2,000 ms
コード長 6,177 bytes
コンパイル時間 1,775 ms
コンパイル使用メモリ 166,260 KB
実行使用メモリ 8,312 KB
最終ジャッジ日時 2024-06-22 16:49:38
合計ジャッジ時間 3,013 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 11 ms
7,684 KB
testcase_01 AC 10 ms
7,400 KB
testcase_02 AC 10 ms
7,544 KB
testcase_03 AC 11 ms
7,832 KB
testcase_04 AC 12 ms
7,756 KB
testcase_05 AC 9 ms
8,040 KB
testcase_06 AC 10 ms
7,988 KB
testcase_07 AC 13 ms
7,756 KB
testcase_08 AC 12 ms
8,060 KB
testcase_09 AC 12 ms
7,852 KB
testcase_10 AC 12 ms
7,920 KB
testcase_11 AC 12 ms
7,708 KB
testcase_12 AC 12 ms
8,256 KB
testcase_13 AC 12 ms
7,872 KB
testcase_14 AC 12 ms
7,784 KB
testcase_15 AC 12 ms
7,780 KB
testcase_16 AC 12 ms
7,592 KB
testcase_17 AC 13 ms
8,312 KB
testcase_18 AC 13 ms
7,828 KB
testcase_19 AC 12 ms
7,796 KB
testcase_20 AC 12 ms
7,864 KB
testcase_21 AC 12 ms
7,780 KB
testcase_22 AC 12 ms
7,692 KB
testcase_23 AC 12 ms
7,872 KB
testcase_24 AC 13 ms
8,128 KB
testcase_25 AC 11 ms
7,992 KB
testcase_26 AC 9 ms
7,468 KB
testcase_27 AC 12 ms
7,932 KB
testcase_28 AC 12 ms
7,784 KB
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ソースコード

diff # 

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 = 4 * 10^^5 + 10;
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);
    }
  }
}

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;
  
  try {
    for (; ; ) {
      const N = readInt;
      const Q = readInt;
      auto L = new int[Q];
      auto R = new int[Q];
      foreach (q; 0 .. Q) {
        L[q] = readInt - 1;
        R[q] = readInt;
      }
      
      auto cat = new Mint[(N + 1) / 2 + 1];
      foreach (n; 0 .. (N + 1) / 2 + 1) {
        cat[n] = inv[n + 1] * binom(2 * n, n);
      }
      
      auto uf = new int[Q];
      uf[] = -1;
      foreach (q0; 0 .. Q) foreach (q1; 0 .. Q) {
        if (L[q0] <= L[q1] && L[q1] <= R[q0] && R[q0] <= R[q1]) {
          uf.connect(q0, q1);
        }
      }
      auto xss = new int[][Q];
      foreach (q; 0 .. Q) {
        const r = uf.root(q);
        xss[r] ~= L[q];
        xss[r] ~= R[q];
      }
      auto ls = new int[Q];
      int[] rs;
      foreach (r; 0 .. Q) if (uf[r] < 0) {
        xss[r] = xss[r].sort.uniq.array;
        ls[r] = xss[r][$ - 1] - xss[r][0];
        rs ~= r;
      }
      rs.sort!((r0, r1) => (ls[r0] < ls[r1]));
      debug {
        writeln("xss = ", xss);
        writeln("rs = ", rs);
      }
      
      Mint ans = 1;
      auto vis = new bool[Q];
      foreach (r; rs) {
        auto xs = xss[r];
        const xsLen = cast(int)(xs.length);
        foreach (i; 0 .. xsLen - 1) {
          int d = xs[i + 1] - xs[i];
          foreach (rr; rs) if (r != rr && !vis[rr] && xs[i] <= xss[rr][0] && xss[rr][$ - 1] <= xs[i + 1]) {
            vis[rr] = true;
            d -= ls[rr];
          }
          debug {
            writefln("[%s, %s): d = %s", xs[i], xs[i + 1], d);
          }
          if (d % 2 != 0) {
            ans = 0;
          } else {
            ans *= cat[d / 2];
          }
        }
      }
      {
        int d = N;
        foreach (r; rs) if (!vis[r]) {
          d -= ls[r];
        }
        ans *= cat[(d + 1) / 2];
      }
      
      ans *= fac[(N + 1) / 2];
      ans *= fac[N / 2];
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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