#543412 (D) No.1204 お菓子配り-FINAL

提出ソース

結果

問題	No.1204 お菓子配り-FINAL
ユーザー	👑 hos.lyric
提出日時	2020-08-30 04:09:24
言語	D (dmd 2.107.1)
結果	AC
実行時間	3 ms / 8,000 ms
コード長	9,116 bytes
コンパイル時間	1,730 ms
コンパイル使用メモリ	158,480 KB
実行使用メモリ	4,384 KB
最終ジャッジ日時	2023-09-04 09:34:49
合計ジャッジ時間	5,442 ms
ジャッジサーバーID （参考情報）	judge11 / judge12

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	2 ms 4,380 KB
testcase_01	AC	2 ms 4,376 KB
testcase_02	AC	2 ms 4,376 KB
testcase_03	AC	1 ms 4,380 KB
testcase_04	AC	1 ms 4,380 KB
testcase_05	AC	2 ms 4,380 KB
testcase_06	AC	1 ms 4,380 KB
testcase_07	AC	2 ms 4,380 KB
testcase_08	AC	2 ms 4,376 KB
testcase_09	AC	2 ms 4,376 KB
testcase_10	AC	1 ms 4,384 KB
testcase_11	AC	2 ms 4,376 KB
testcase_12	AC	1 ms 4,380 KB
testcase_13	AC	2 ms 4,380 KB
testcase_14	AC	1 ms 4,376 KB
testcase_15	AC	1 ms 4,380 KB
testcase_16	AC	1 ms 4,380 KB
testcase_17	AC	1 ms 4,376 KB
testcase_18	AC	1 ms 4,376 KB
testcase_19	AC	1 ms 4,376 KB
testcase_20	AC	1 ms 4,384 KB
testcase_21	AC	1 ms 4,380 KB
testcase_22	AC	2 ms 4,380 KB
testcase_23	AC	2 ms 4,380 KB
testcase_24	AC	2 ms 4,380 KB
testcase_25	AC	1 ms 4,384 KB
testcase_26	AC	2 ms 4,380 KB
testcase_27	AC	2 ms 4,376 KB
testcase_28	AC	1 ms 4,376 KB
testcase_29	AC	2 ms 4,376 KB
testcase_30	AC	1 ms 4,384 KB
testcase_31	AC	2 ms 4,380 KB
testcase_32	AC	2 ms 4,380 KB
testcase_33	AC	1 ms 4,380 KB
testcase_34	AC	1 ms 4,376 KB
testcase_35	AC	2 ms 4,380 KB
testcase_36	AC	1 ms 4,380 KB
testcase_37	AC	2 ms 4,380 KB
testcase_38	AC	2 ms 4,376 KB
testcase_39	AC	2 ms 4,380 KB
testcase_40	AC	2 ms 4,380 KB
testcase_41	AC	2 ms 4,380 KB
testcase_42	AC	1 ms 4,376 KB
testcase_43	AC	1 ms 4,384 KB
testcase_44	AC	1 ms 4,376 KB
testcase_45	AC	1 ms 4,376 KB
testcase_46	AC	1 ms 4,380 KB
testcase_47	AC	1 ms 4,376 KB
testcase_48	AC	2 ms 4,384 KB
testcase_49	AC	2 ms 4,380 KB
testcase_50	AC	1 ms 4,380 KB
testcase_51	AC	2 ms 4,380 KB
testcase_52	AC	2 ms 4,380 KB
testcase_53	AC	2 ms 4,376 KB
testcase_54	AC	2 ms 4,380 KB
testcase_55	AC	1 ms 4,376 KB
testcase_56	AC	2 ms 4,380 KB
testcase_57	AC	2 ms 4,380 KB
testcase_58	AC	2 ms 4,380 KB
testcase_59	AC	2 ms 4,380 KB
testcase_60	AC	2 ms 4,376 KB
testcase_61	AC	1 ms 4,380 KB
testcase_62	AC	1 ms 4,380 KB
testcase_63	AC	1 ms 4,380 KB
testcase_64	AC	1 ms 4,380 KB
testcase_65	AC	2 ms 4,384 KB
testcase_66	AC	2 ms 4,376 KB
testcase_67	AC	2 ms 4,376 KB
testcase_68	AC	1 ms 4,376 KB
testcase_69	AC	1 ms 4,376 KB
testcase_70	AC	2 ms 4,376 KB
testcase_71	AC	1 ms 4,380 KB
testcase_72	AC	2 ms 4,380 KB
testcase_73	AC	1 ms 4,380 KB
testcase_74	AC	2 ms 4,376 KB
testcase_75	AC	1 ms 4,380 KB
testcase_76	AC	1 ms 4,380 KB
testcase_77	AC	2 ms 4,380 KB
testcase_78	AC	2 ms 4,380 KB
testcase_79	AC	1 ms 4,380 KB
testcase_80	AC	1 ms 4,380 KB
testcase_81	AC	2 ms 4,376 KB
testcase_82	AC	1 ms 4,380 KB
testcase_83	AC	2 ms 4,380 KB
testcase_84	AC	2 ms 4,380 KB
testcase_85	AC	2 ms 4,376 KB
testcase_86	AC	1 ms 4,376 KB
testcase_87	AC	2 ms 4,384 KB
testcase_88	AC	1 ms 4,380 KB
testcase_89	AC	1 ms 4,384 KB
testcase_90	AC	2 ms 4,380 KB
testcase_91	AC	3 ms 4,376 KB
testcase_92	AC	2 ms 4,376 KB
testcase_93	AC	2 ms 4,380 KB
testcase_94	AC	2 ms 4,380 KB
testcase_95	AC	2 ms 4,380 KB
testcase_96	AC	2 ms 4,380 KB
testcase_97	AC	2 ms 4,380 KB
testcase_98	AC	2 ms 4,380 KB
testcase_99	AC	2 ms 4,380 KB
testcase_100	AC	1 ms 4,380 KB
testcase_101	AC	2 ms 4,380 KB
testcase_102	AC	2 ms 4,380 KB
testcase_103	AC	2 ms 4,380 KB
testcase_104	AC	2 ms 4,380 KB
testcase_105	AC	2 ms 4,380 KB
testcase_106	AC	2 ms 4,380 KB
testcase_107	AC	2 ms 4,384 KB
testcase_108	AC	2 ms 4,380 KB
testcase_109	AC	2 ms 4,380 KB
testcase_110	AC	1 ms 4,376 KB
testcase_111	AC	1 ms 4,376 KB
testcase_112	AC	1 ms 4,376 KB
testcase_113	AC	2 ms 4,376 KB
testcase_114	AC	2 ms 4,380 KB
testcase_115	AC	2 ms 4,380 KB
testcase_116	AC	2 ms 4,376 KB
testcase_117	AC	2 ms 4,380 KB
testcase_118	AC	2 ms 4,380 KB
testcase_119	AC	2 ms 4,380 KB
testcase_120	AC	2 ms 4,380 KB
testcase_121	AC	2 ms 4,380 KB
testcase_122	AC	1 ms 4,380 KB
testcase_123	AC	1 ms 4,380 KB
testcase_124	AC	1 ms 4,380 KB
testcase_125	AC	2 ms 4,384 KB
testcase_126	AC	1 ms 4,384 KB
testcase_127	AC	1 ms 4,380 KB
testcase_128	AC	2 ms 4,380 KB
testcase_129	AC	2 ms 4,380 KB

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ソースコード

raw source code

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 = 1000000007;
alias Mint = ModInt!MO;


// inv[i] = 1 / i, fac[i] = i!, invFac[i] = 1 / i!
Mint[] inv, fac, invFac;
void prepareFac(int lim) {
  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];
  }
}

// Find f(n) for the polynomial f s.t. fs = [f(0), f(1), ...] and deg f < |fs|
Mint interpolateIota(const(Mint[]) fs, long n) {
  const fsLen = cast(int)(fs.length);
  auto prodR = new Mint[fsLen + 1];
  prodR[fsLen] = 1;
  foreach_reverse (i; 0 .. fsLen) prodR[i] = (n - i) * prodR[i + 1];
  Mint ans;
  Mint prodL = 1;
  for (int i = 0; i < fsLen; ++i) {
    // (i - 0) ... (i - (i - 1)) (i - (i + 1)) ... (i - (fsLen - 1))
    ans += invFac[i] * (((fsLen - 1 - i) & 1) ? -1 : +1) *
           invFac[fsLen - 1 - i] * fs[i] * prodL * prodR[i + 1];
    prodL *= (n - i);
  }
  return ans;
}

// pws[i] = i^d (0 <= i < n)
Mint[] getMonomials(long d, int n) {
  auto lpf = new int[n];
  foreach (i; 0 .. n) lpf[i] = i;
  foreach (p; 2 .. n) if (lpf[p] == p) {
    for (int i = 2 * p; i < n; i += p) if (lpf[i] > p) lpf[i] = p;
  }
  auto pws = new Mint[n];
  foreach (i; 0 .. n) {
    pws[i] = (lpf[i] == i) ? Mint(i)^^d : (pws[lpf[i]] * pws[i / lpf[i]]);
  }
  return pws;
}

// \sum_{i=0}^{\infty} r^i f(i) (deg f <= d)
Mint sumPowerPolyLimit(Mint r, int d, const(Mint[]) fs) {
  assert(r.x != 1, "sumPowerPolyLimit: r != 1 must hold");
  assert(d + 1 < inv.length, "sumPowerPolyLimit: inv[d + 1] must be prepared");
  assert(d + 1 <= fs.length, "sumPowerPolyLimit: d + 1 < |fs| must hold");
  auto rr = new Mint[d + 1];
  rr[0] = 1;
  foreach (i; 1 .. d + 1) rr[i] = rr[i - 1] * r;
  Mint ans, sumRF;
  foreach (i; 0 .. d + 1) {
    sumRF += rr[i] * fs[i];
    ans += invFac[d - i] * invFac[i + 1] * (((d - i) & 1) ? -1 : +1) *
           rr[d - i] * sumRF;
  }
  ans *= (1 - r)^^(-(d + 1)) * fac[d + 1];
  return ans;
}

// \sum_{i=0}^{\infty} r^i i^d
Mint sumPowerPolyLimit(Mint r, int d) {
  return sumPowerPolyLimit(r, d, getMonomials(d, d + 1));
}

// \sum_{i=0}^{n-1} r^i f(i) (deg f <= d)
Mint sumPowerPoly(Mint r, int d, const(Mint[]) fs, long n) {
  assert(d + 1 < inv.length, "sumPowerPoly: inv[d + 1] must be prepared");
  assert(d + 1 <= fs.length, "sumPowerPoly: d + 1 < |fs| must hold");
  assert(n >= 0, "sumPowerPoly: n >= 0 must hold.");
  if (r.x == 0) return (0 < n) ? fs[0] : Mint(0);
  auto gs = new Mint[d + 2];
  Mint rr = 1;
  gs[0] = 0;
  foreach (i; 0 .. d + 1) {
    gs[i + 1] = gs[i] + rr * fs[i];
    rr *= r;
  }
  if (r.x == 1) return interpolateIota(gs, n);
  const c = sumPowerPolyLimit(r, d, fs);
  const rInv = r.inv();
  Mint rrInv = 1;
  foreach (i; 0 .. d + 2) {
    gs[i] = rrInv * (gs[i] - c);
    rrInv *= rInv;
  }
  return c + r^^n * interpolateIota(gs, n);
}

// \sum_{i=0}^{n-1} r^i i^d
Mint sumPowerPoly(Mint r, int d, long n) {
  return sumPowerPoly(r, d, getMonomials(d, d + 1), n);
}


enum LIM = 205;

// (n - k + 1) (n + 1)^(k-1)
void main() {
  prepareFac(LIM);
  
  auto small = new Mint[LIM];
  foreach (n; 0 .. LIM) {
    small[n] = Mint(n + 1)^^(n - 1) * invFac[n];
  }
  
  try {
    for (; ; ) {
      const N = readLong();
      const M = readInt();
      const S = readToken();
      
      int[] ones;
      if (S[0] == 'o') {
        ones ~= 0;
      }
      for (int i = 0, j; i < M; i = j) {
        for (j = i; j < M && S[i] == S[j]; ++j) {}
        if (S[i] == '-') {
          ones ~= (j - i);
        }
      }
      if (S[M - 1] == 'o') {
        ones ~= 0;
      }
      const onesLen = cast(int)(ones.length);
      debug {
        writeln("ones = ", ones);
      }
      
      int innerSum;
      Mint innerNum = 1;
      alias Query = Tuple!(int[], "as", int, "coef");
      auto qss = new Query[][M + 1];
      if (onesLen == 1) {
        qss[0] ~= Query([0], 1);
        qss[1] ~= Query([0], -M);
        foreach (m; 2 .. M + 1) {
          qss[m] ~= Query([m - 2], M - m + 1);
        }
      } else {
        foreach (a; ones[1 .. onesLen - 1]) {
          innerSum += a;
          innerNum *= small[a];
        }
        foreach (a; 0 .. ones[0] + 1) foreach (b; 0 .. ones[onesLen - 1] + 1) {
          qss[M - (ones[0] - a) - (ones[onesLen - 1] - b)] ~=
              Query([max(a - 1, 0), max(b - 1, 0)], ((a == 0) ? +1 : -1) * ((b == 0) ? +1 : -1));
        }
      }
      debug {
        foreach (m; 0 .. M + 1) {
          writefln("qss[%s] = %s", m, qss[m]);
        }
        void pie(string s, int sig) {
          if (s.length >= 1 && s[0] == '-') {
            pie(s[1 .. $], sig);
            pie('o' ~ s[1 .. $], -sig);
          } else if (s.length >= 1 && s[$ - 1] == '-') {
            pie(s[0 .. $ - 1], sig);
            pie(s[0 .. $ - 1] ~ 'o', -sig);
          } else {
            // writeln("query ", s.length, " ", s, " ", sig);
          }
        }
        pie(S, +1);
      }
      
      Mint ans;
      
      // m = 0
      if (onesLen == 1) {
        ans += Mint(N)^^N * Mint(N + 1);
      }
      
      foreach (m; 1 .. M + 1) {
        auto nums = new Mint[m + 1];
        foreach (ref q; qss[m]) {
          int sum = innerSum;
          Mint num = innerNum;
          foreach (a; q.as) {
            sum += a;
            num *= small[a];
          }
          nums[sum] += q.coef * num;
        }
        debug {
          writefln("m = %s, nums = %s", m, nums);
        }
        
        /*
          0 <= k <= N - m
          (N - m - k + 1) (N - m + 1)^(k-1) / k! * (k + l)! * N^(N - (k + l))
          = (N^(N - l) / (N - m + 1)) * (N - m - k + 1) ((k + l)! / k!) * ((N - m + 1) / N)^k
        */
        foreach (l; 0 .. m + 1) {
          if (nums[l]) {
            auto fs = new Mint[l + 2];
            foreach (k; 0 .. l + 2) {
              fs[k] = (N - m - k + 1) * fac[k + l] * invFac[k];
            }
            const res = sumPowerPoly(Mint(N - m + 1) / Mint(N), l + 1, fs, N - m + 1);
            ans += nums[l] * Mint(N)^^(N - l) / Mint(N - m + 1) * res;
          }
        }
      }
      
      ans *= (N - M + 1);
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}

yukicoder

結果

テストケース

ソースコード