結果

問題 No.1963 Subset Mex
ユーザー 👑 hos.lyric
提出日時 2025-01-14 11:18:28
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 44 ms / 4,000 ms
コード長 5,640 bytes
コンパイル時間 6,848 ms
コンパイル使用メモリ 140,160 KB
実行使用メモリ 19,456 KB
最終ジャッジ日時 2025-01-14 11:18:37
合計ジャッジ時間 3,900 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 26
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 # 

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; }

string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; }

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;



void main() {
  try {
    for (; ; ) {
      const SLen = readInt;
      auto S = new int[SLen];
      foreach (i; 0 .. SLen) {
        S[i] = readInt;
      }
      
      // [0, N]
      const N = max(SLen, S.maxElement);
      auto A = new int[N + 1];
      foreach (x; S) ++A[max(x, 1)];
      
      /*
        dp[x][s][p][q]
          x: submultiset?
            x=2: submultiset: consider last op., min element chosen
          p: need
          q: zero
      */
      auto dp = new Mint[][][][](N + 2, 3, N + 1, N + 1);
      dp[N + 1][1][0][0] += 1;
      foreach_reverse (x; 2 .. N + 1) {
        foreach (s; 0 .. 3) foreach (p; 0 .. N/(x+1) + 1) foreach (q; 0 .. N + 1) {
          const f = dp[x + 1][s][p][q];
          if (!f) continue;
          if (s == 0 || s == 1) {
            // amaru
            foreach (b; 0 .. A[x] + 1) {
              const a = A[x] - b;
              const t = min(p, a);
              const pp = 2 * p - t;
              if (pp <= N) dp[x][s][pp][q + a - t] += f;
            }
            // tarinai
            foreach (b; A[x] + 1 .. N + 1) {
              const pp = 2 * p + (b - A[x]);
              if (pp <= N) dp[x][0][pp][q] += f;
            }
          } else {
            const a = A[x];
            const t = min(p, a);
            const pp = 2 * p - t;
            if (pp <= N) dp[x][2][pp][q + a - t] += f;
          }
          // submultiset, min = x
          if (s == 1) {
            assert(p == 0);
            foreach (b; 1 .. A[x] + 1) {
              const a = A[x] - (b - 1);
              dp[x][2][1][q + a] += f;
            }
          }
        }
      }
      
      auto anss = new Mint[3];
      foreach (s; 0 .. 3) foreach (p; 0 .. N + 1) foreach (q; 0 .. N + 1) {
        const f = dp[2][s][p][q];
        if (!f) continue;
        if (s == 0 || s == 1) {
          // not submultiset
          foreach (b; 0 .. N + 1) if (!(s == 1 && A[1] >= b)) {
            if (2 * p + b <= q + A[1]) anss[0] += f * (b + 1);
          }
        } else {
          // submultiset, min > 1
          if (2 * p <= q + A[1]) anss[2] += f;
        }
        // submultiset, min = 1
        if (s == 1) {
          assert(p == 0);
          foreach (b; 1 .. A[1] + 1) {
            if (b <= q + A[1]) anss[2] += f * (b + 1);
          }
        }
      }
      
      // equal && should not operate
      if (!A[1]) anss[1] += 1;
      
      debug writeln("anss = ", anss);
      const ans = anss.sum;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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