#740129 (D) No.1847 Good Sequence

提出ソース

結果

問題	No.1847 Good Sequence
ユーザー	👑 hos.lyric
提出日時	2022-02-18 21:36:18
言語	D (dmd 2.106.1)
結果	AC
実行時間	341 ms / 3,000 ms
コード長	5,435 bytes
コンパイル時間	1,627 ms
コンパイル使用メモリ	155,976 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-22 14:18:41
合計ジャッジ時間	4,829 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

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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 6,816 KB
testcase_01	AC	1 ms 6,940 KB
testcase_02	AC	120 ms 6,940 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	1 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	3 ms 6,944 KB
testcase_10	AC	1 ms 6,944 KB
testcase_11	AC	1 ms 6,940 KB
testcase_12	AC	1 ms 6,940 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	3 ms 6,940 KB
testcase_15	AC	4 ms 6,944 KB
testcase_16	AC	8 ms 6,940 KB
testcase_17	AC	17 ms 6,940 KB
testcase_18	AC	28 ms 6,944 KB
testcase_19	AC	47 ms 6,944 KB
testcase_20	AC	2 ms 6,940 KB
testcase_21	AC	283 ms 6,944 KB
testcase_22	AC	46 ms 6,940 KB
testcase_23	AC	2 ms 6,944 KB
testcase_24	AC	2 ms 6,944 KB
testcase_25	AC	88 ms 6,940 KB
testcase_26	AC	1 ms 6,940 KB
testcase_27	AC	10 ms 6,940 KB
testcase_28	AC	91 ms 6,944 KB
testcase_29	AC	2 ms 6,944 KB
testcase_30	AC	10 ms 6,940 KB
testcase_31	AC	167 ms 6,940 KB
testcase_32	AC	48 ms 6,940 KB
testcase_33	AC	171 ms 6,944 KB
testcase_34	AC	1 ms 6,940 KB
testcase_35	AC	1 ms 6,940 KB
testcase_36	AC	293 ms 6,940 KB
testcase_37	AC	96 ms 6,940 KB
testcase_38	AC	1 ms 6,944 KB
testcase_39	AC	1 ms 6,944 KB
testcase_40	AC	341 ms 6,940 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(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;


// square matrices
Mint[][] mul(Mint[][] a, Mint[][] b) {
  const size = cast(int)(a.length);
  auto c = new Mint[][](size, size);
  foreach (i; 0 .. size) foreach (k; 0 .. size) foreach (j; 0 .. size) {
    c[i][j] += a[i][k] * b[k][j];
  }
  return c;
}
Mint[] mul(Mint[][] a, Mint[] x) {
  const size = cast(int)(a.length);
  auto y = new Mint[size];
  foreach (i; 0 .. size) foreach (j; 0 .. size) {
    y[i] += a[i][j] * x[j];
  }
  return y;
}
Mint[][] power(Mint[][] a, long e) {
  const size = cast(int)(a.length);
  auto b = new Mint[][](size, size), c = new Mint[][](size, size);
  foreach (i; 0 .. size) foreach (j; 0 .. size) b[i][j] = a[i][j];
  foreach (i; 0 .. size) foreach (j; 0 .. size) c[i][j] = (i == j) ? 1 : 0;
  for (; e; e >>= 1) {
    if (e & 1) c = mul(c, b);
    b = mul(b, b);
  }
  return c;
}


void main() {
  try {
    for (; ; ) {
      const L = readLong;
      const N = readInt;
      const M = readInt;
      auto K = new int[M];
      foreach (m; 0 .. M) {
        K[m] = readInt;
      }
      
      int V;
      auto ids = new int[][](N + 1, N + 2);
      foreach (x; 0 .. N + 1) {
        ids[x][] = -1;
      }
      int[] xs, ys;
      foreach (x; 1 .. N + 1) {
        foreach (y; 1 .. (x + 1) + 1) {
          ids[x][y] = V++;
          xs ~= x;
          ys ~= y;
        }
      }
      debug {
        writeln("ids = ", ids);
        writeln("xs = ", xs);
        writeln("ys = ", ys);
      }
      auto good = new bool[V];
      foreach (k; K) {
        good[ids[k][k]] = true;
      }
      
      auto a = new Mint[][](V + 1, V + 1);
      foreach (u; 0 .. V) {
        foreach (xx; 1 .. N + 1) {
          const yy = (xs[u] == xx) ? min(ys[u] + 1, xx + 1) : 1;
          const v = (good[u] && xs[u] != xx) ? V : ids[xx][yy];
          debug {
            if (N <= 3) {
              writeln(u, " ", xx, ": ", v);
            }
          }
          a[u][v] += 1;
        }
      }
      a[V][V] += N;
      debug {
        if (N <= 3) {
          writeln("a = ", a);
        }
      }
      
      const aa = a.power(L - 1);
      Mint ans;
      foreach (x; 1 .. N + 1) {
        const u = ids[x][1];
        foreach (v; 0 .. V + 1) {
          if (v == V || good[v]) {
            ans += aa[u][v];
          }
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}

yukicoder

結果

テストケース

ソースコード