結果

問題 No.1214 Market
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-08-30 18:52:08
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 215 ms / 2,000 ms
コード長 5,999 bytes
コンパイル時間 1,660 ms
コンパイル使用メモリ 159,296 KB
実行使用メモリ 8,308 KB
最終ジャッジ日時 2023-09-04 09:44:47
合計ジャッジ時間 5,816 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge14
このコードへのチャレンジ
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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 1 ms
4,380 KB
testcase_01 AC 1 ms
4,376 KB
testcase_02 AC 1 ms
4,376 KB
testcase_03 AC 2 ms
4,376 KB
testcase_04 AC 3 ms
4,376 KB
testcase_05 AC 3 ms
4,376 KB
testcase_06 AC 4 ms
4,376 KB
testcase_07 AC 2 ms
4,376 KB
testcase_08 AC 189 ms
8,264 KB
testcase_09 AC 182 ms
8,304 KB
testcase_10 AC 193 ms
8,232 KB
testcase_11 AC 201 ms
8,240 KB
testcase_12 AC 215 ms
8,208 KB
testcase_13 AC 200 ms
8,236 KB
testcase_14 AC 207 ms
8,240 KB
testcase_15 AC 190 ms
8,224 KB
testcase_16 AC 208 ms
8,288 KB
testcase_17 AC 203 ms
8,308 KB
testcase_18 AC 4 ms
4,376 KB
testcase_19 AC 5 ms
4,380 KB
testcase_20 AC 27 ms
4,380 KB
testcase_21 AC 6 ms
4,376 KB
testcase_22 AC 2 ms
4,376 KB
testcase_23 AC 138 ms
8,240 KB
testcase_24 AC 12 ms
4,380 KB
testcase_25 AC 10 ms
4,376 KB
testcase_26 AC 53 ms
8,240 KB
testcase_27 AC 19 ms
4,384 KB
testcase_28 AC 113 ms
8,252 KB
testcase_29 AC 11 ms
4,376 KB
testcase_30 AC 23 ms
4,380 KB
testcase_31 AC 6 ms
4,376 KB
testcase_32 AC 1 ms
4,376 KB
testcase_33 AC 67 ms
8,236 KB
testcase_34 AC 2 ms
4,376 KB
testcase_35 AC 11 ms
4,380 KB
testcase_36 AC 36 ms
4,380 KB
testcase_37 AC 75 ms
8,204 KB
testcase_38 AC 2 ms
4,384 KB
testcase_39 AC 2 ms
4,376 KB
testcase_40 AC 2 ms
4,380 KB
testcase_41 AC 3 ms
4,380 KB
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(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 = 10^^9 + 7;
alias Mint = ModInt!MO;

enum LIM = 110;
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 (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);
  }
}


void main() {
  prepare;
  
  try {
    for (; ; ) {
      const N = readInt();
      const M = readInt();
      const K = readInt();
      auto A = new long[M];
      auto B = new long[M];
      foreach (i; 0 .. M) {
        A[i] = readLong();
        B[i] = readLong();
      }
      
      auto as = A.dup;
      as ~= 0;
      as ~= K + 1;
      as.sort;
      as = as.uniq.array;
      const asLen = cast(int)(as.length) - 1;
      auto bss = new long[][asLen];
      foreach (i; 0 .. M) {
        const e = as.upperBound(A[i]) - 1;
        bss[e] ~= B[i];
      }
      debug {
        writeln("as = ", as);
        writeln("bss = ", bss);
      }
      
      auto coef = new Mint[][](asLen, N + 1);
      auto coefGoal = new Mint[][](asLen, N + 1);
      foreach (e; 0 .. asLen) {
        foreach (dj; 0 .. N + 1) {
          coef[e][dj] = invFac[dj] * Mint(as[e + 1] - as[e])^^dj;
          coefGoal[e][dj] = invFac[dj] * Mint(K + 1 - as[e + 1])^^dj;
        }
      }
      
      Mint ans;
      foreach (b0; B) {
        debug {
          writeln("b0 = ", b0);
        }
        const numLarge = cast(int)(B.count!(b => (b > b0)));
        // processed poss, # of customers, stock (+, 0)
        auto dp = new Mint[2][][][](asLen + 1, N + 1, numLarge + 1);
        dp[0][0][0][0] = 1;
        foreach (e; 0 .. asLen) {
          int dx, dy;
          foreach (b; bss[e]) {
            if (b > b0) ++dx;
            if (b == b0) ++dy;
          }
          foreach (j; 0 .. N + 1) {
            foreach (x; 0 .. numLarge + 1) foreach (y; 0 .. 2) {
              if (dp[e][j][x][y]) {
                int xx = x + dx, yy = y + dy;
                foreach (dj; 0 .. N - j + 1) {
                  // dp[e + 1][j + dj][xx][yy][zz] += dp[e][j][x][y][z] * coef[e][dj];
                  if (y + dy > 0 && yy == 0) {
                    // goal
                    dp[asLen][N][0][0] += dp[e][j][x][y] * coef[e][dj] * coefGoal[e][N - (j + dj)];
                  } else {
                    dp[e + 1][j + dj][xx][yy] += dp[e][j][x][y] * coef[e][dj];
                  }
                  (xx > 0) ? --xx : (yy > 0) ? --yy : 0;
                }
              }
            }
          }
        }
        Mint sum;
        foreach (x; 0 .. numLarge + 1) {
          sum += dp[asLen][N][x][0];
        }
        sum *= fac[N];
        debug {
          writeln("  sum = ", sum);
          stdout.flush;
        }
        ans += sum * b0;
      }
      ans /= Mint(K + 1)^^N;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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