結果

問題 No.1214 Market
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-08-30 13:38:32
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 1,484 ms / 2,000 ms
コード長 6,295 bytes
コンパイル時間 1,937 ms
コンパイル使用メモリ 162,464 KB
実行使用メモリ 56,524 KB
最終ジャッジ日時 2024-06-22 08:41:42
合計ジャッジ時間 20,291 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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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
6,812 KB
testcase_01 AC 2 ms
6,812 KB
testcase_02 AC 1 ms
6,940 KB
testcase_03 AC 10 ms
6,940 KB
testcase_04 AC 27 ms
7,744 KB
testcase_05 AC 33 ms
7,728 KB
testcase_06 AC 34 ms
7,808 KB
testcase_07 AC 10 ms
6,940 KB
testcase_08 AC 1,334 ms
39,508 KB
testcase_09 AC 1,484 ms
56,524 KB
testcase_10 AC 1,442 ms
39,500 KB
testcase_11 AC 1,332 ms
39,496 KB
testcase_12 AC 1,156 ms
56,448 KB
testcase_13 AC 1,372 ms
39,444 KB
testcase_14 AC 1,399 ms
39,532 KB
testcase_15 AC 1,361 ms
39,464 KB
testcase_16 AC 1,198 ms
39,488 KB
testcase_17 AC 1,264 ms
39,536 KB
testcase_18 AC 37 ms
7,760 KB
testcase_19 AC 44 ms
7,720 KB
testcase_20 AC 247 ms
25,748 KB
testcase_21 AC 32 ms
7,752 KB
testcase_22 AC 3 ms
6,944 KB
testcase_23 AC 934 ms
39,504 KB
testcase_24 AC 80 ms
15,136 KB
testcase_25 AC 46 ms
7,724 KB
testcase_26 AC 397 ms
25,772 KB
testcase_27 AC 126 ms
15,132 KB
testcase_28 AC 712 ms
25,700 KB
testcase_29 AC 98 ms
15,144 KB
testcase_30 AC 132 ms
15,164 KB
testcase_31 AC 27 ms
7,696 KB
testcase_32 AC 1 ms
6,944 KB
testcase_33 AC 401 ms
25,848 KB
testcase_34 AC 7 ms
6,940 KB
testcase_35 AC 85 ms
15,104 KB
testcase_36 AC 226 ms
15,244 KB
testcase_37 AC 561 ms
25,756 KB
testcase_38 AC 6 ms
6,944 KB
testcase_39 AC 1 ms
6,944 KB
testcase_40 AC 1 ms
6,940 KB
testcase_41 AC 5 ms
6,944 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 {
long counter;
          writeln("b0 = ", b0);
        }
        const numLarge = cast(int)(B.count!(b => (b > b0)));
        const numSmall = cast(int)(B.count!(b => (b < b0)));
        // processed poss, # of customers, stock (+, 0, -)
        auto dp = new Mint[][][][][](asLen + 1, N + 1, numLarge + 1, 2, numSmall + 1);
        dp[0][0][0][0][0] = 1;
        foreach (e; 0 .. asLen) {
          int dx, dy, dz;
          foreach (b; bss[e]) {
            if (b > b0) ++dx;
            if (b == b0) ++dy;
            if (b < b0) ++dz;
          }
          foreach (j; 0 .. N + 1) {
            foreach (x; 0 .. numLarge + 1) foreach (y; 0 .. 2) foreach (z; 0 .. numSmall + 1) {
              if (dp[e][j][x][y][z]) {
                int xx = x + dx, yy = y + dy, zz = z + dz;
                foreach (dj; 0 .. N - j + 1) {
debug{
++counter;
}
                  // 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][0] += dp[e][j][x][y][z] * coef[e][dj] * coefGoal[e][N - (j + dj)];
                  } else {
                    dp[e + 1][j + dj][xx][yy][zz] += dp[e][j][x][y][z] * coef[e][dj];
                  }
                  (xx > 0) ? --xx : (yy > 0) ? --yy : (zz > 0) ? --zz : 0;
                }
              }
            }
          }
        }
        Mint sum;
        foreach (x; 0 .. numLarge + 1) foreach (z; 0 .. numSmall + 1) {
          sum += dp[asLen][N][x][0][z];
        }
        sum *= fac[N];
        debug {
writeln("counter = ",counter);
          writeln("  sum = ", sum);
          stdout.flush;
        }
        ans += sum * b0;
      }
      ans /= Mint(K + 1)^^N;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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