結果

問題 No.1815 K色問題
ユーザー hos.lyric
提出日時 2022-02-26 12:40:24
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 1,278 ms / 2,000 ms
コード長 6,202 bytes
コンパイル時間 2,125 ms
コンパイル使用メモリ 155,592 KB
実行使用メモリ 14,004 KB
最終ジャッジ日時 2024-09-29 22:44:08
合計ジャッジ時間 6,515 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 13
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; }
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 = 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 = 10^^9 + 7;
alias Mint = ModInt!MO;

enum LIM = 2 * 10^^5 + 10;
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 (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);
      return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
    } else {
      return Mint(0);
    }
  }
}


Mint[2][2] mul(Mint[2][2] a, Mint[2][2] b) {
  Mint[2][2] c;
  static foreach (i; 0 .. 2) static foreach (k; 0 .. 2) static foreach (j; 0 .. 2) {
    c[i][j] += a[i][k] * b[k][j];
  }
  return c;
}
Mint[2][2] power(Mint[2][2] a, long e) {
  Mint[2][2] x = a, y;
  y[0][0] = y[1][1] = 1;
  for (; e; e >>= 1) {
    if (e & 1) y = mul(y, x);
    x = mul(x, x);
  }
  return y;
}

void main() {
  prepare;
  
  // 010, 012
  int[6 + 1][2][2] cnt;
  {
    int[3] bs;
    void dfs(int s, int pos, int k) {
      if (pos == 3) {
        const a2 = [0, 2][s];
        bool ok = true;
        ok = ok && (0 != bs[0]);
        ok = ok && (1 != bs[1]);
        ok = ok && (a2 != bs[2]);
        ok = ok && (bs[0] != bs[1]);
        ok = ok && (bs[1] != bs[2]);
        if (ok) {
          ++cnt[s][(bs[0] == bs[2]) ? 0 : 1][k];
        }
      } else {
        foreach (b; 0 .. k + 1) {
          bs[pos] = b;
          dfs(s, pos + 1, (b == k) ? (k + 1) : k);
        }
      }
    }
    dfs(0, 0, 2);
    dfs(1, 0, 3);
  }
  debug {
    writeln("cnt = ", cnt);
  }
  
  try {
    for (; ; ) {
      const N = readInt;
      const M = readLong;
      const K = readInt;
      
      Mint calc(Mint k) {
        Mint ret;
        final switch (N) {
          case 1: {
            ret = k * (k - 1)^^(M - 1);
          } break;
          case 2: {
            Mint num;
            // 01 -> 10
            num += 1;
            // 01 -> 12, 20
            num += 2 * (k - 2);
            // 01 -> 23
            num += (k - 2) * (k - 3);
            
            ret = k * (k - 1) * num^^(M - 1);
          } break;
          case 3: {
            Mint[2][2] a;
            foreach (i; 0 .. 2) foreach (j; 0 .. 2) {
              Mint num = 1;
              foreach (l; [2, 3][i] .. 6 + 1) {
                a[i][j] += cnt[i][j][l] * num;
                num *= (k - l);
              }
            }
            const aa = a.power(M - 1);
            ret += k * (k - 1) * (aa[0][0] + aa[0][1]);
            ret += k * (k - 1) * (k - 2) * (aa[1][0] + aa[1][1]);
          } break;
        }
        return ret;
      }
      
      Mint ans;
      foreach (k; 0 .. K + 1) {
        ans += (-1)^^(k & 1) * binom(K, k) * calc(Mint(K - k));
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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