#655254 (D) No.1500 Super Knight

提出ソース

結果

問題	No.1500 Super Knight
ユーザー	👑 hos.lyric
提出日時	2021-05-07 22:38:13
言語	D (dmd 2.106.1)
結果	AC
実行時間	15 ms / 2,000 ms
コード長	5,442 bytes
コンパイル時間	1,408 ms
コンパイル使用メモリ	160,276 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-22 11:17:06
合計ジャッジ時間	2,742 ms
ジャッジサーバーID （参考情報）	judge4 / judge1

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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	12 ms 6,812 KB
testcase_01	AC	14 ms 6,940 KB
testcase_02	AC	14 ms 6,944 KB
testcase_03	AC	13 ms 6,940 KB
testcase_04	AC	14 ms 6,940 KB
testcase_05	AC	14 ms 6,940 KB
testcase_06	AC	15 ms 6,940 KB
testcase_07	AC	15 ms 6,940 KB
testcase_08	AC	14 ms 6,944 KB
testcase_09	AC	14 ms 6,944 KB
testcase_10	AC	14 ms 6,940 KB
testcase_11	AC	14 ms 6,944 KB
testcase_12	AC	14 ms 6,940 KB
testcase_13	AC	13 ms 6,940 KB
testcase_14	AC	13 ms 6,944 KB
testcase_15	AC	14 ms 6,940 KB
testcase_16	AC	13 ms 6,944 KB
testcase_17	AC	13 ms 6,940 KB
testcase_18	AC	13 ms 6,940 KB
testcase_19	AC	14 ms 6,940 KB
testcase_20	AC	14 ms 6,940 KB
testcase_21	AC	14 ms 6,940 KB
testcase_22	AC	14 ms 6,940 KB
testcase_23	AC	14 ms 6,944 KB
testcase_24	AC	14 ms 6,940 KB
testcase_25	AC	14 ms 6,940 KB
testcase_26	AC	14 ms 6,940 KB
testcase_27	AC	13 ms 6,944 KB
testcase_28	AC	13 ms 6,940 KB
testcase_29	AC	14 ms 6,944 KB
testcase_30	AC	13 ms 6,940 KB
testcase_31	AC	13 ms 6,940 KB
testcase_32	AC	14 ms 6,940 KB
testcase_33	AC	14 ms 6,940 KB
testcase_34	AC	13 ms 6,944 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 = 10^^9 + 7;
alias Mint = ModInt!MO;


// Pretty print (smaller abs)
int[] pretty(int M)(ModInt!M[] as) {
  import std.algorithm : map;
  import std.array : array;
  return as.map!(a => (a.x < M - a.x) ? a.x : -(M - a.x)).array;
}

// Berlekamp-Massey
//   F: field
//   \sum_{j=1}^0 cs[j] as[i - j] = 0 (d <= i < |as|), cs[0] = 1
//   M must be prime
F[] findLinearRecurrence(F)(F[] as) {
  import std.algorithm : min;
  const n = cast(int)(as.length);
  int d, m;
  auto cs = new F[n + 1], bs = new F[n + 1];
  cs[0] = bs[0] = 1;
  F invBef = 1;
  foreach (i; 0 .. n) {
    ++m;
    F dif = as[i];
    foreach (j; 1 .. d + 1) dif += cs[j] * as[i - j];
    if (dif.x != 0) {
      auto csDup = cs.dup;
      const r = dif * invBef;
      foreach (j; m .. n) cs[j] -= r * bs[j - m];
      if (2 * d <= i) {
        d = i + 1 - d;
        m = 0;
        bs = csDup;
        invBef = dif.inv;
      }
    }
  }
  return cs[0 .. d + 1];
}

ModInt!M[] findLinearRecurrence(int M)(long[] as) {
  import std.algorithm : map;
  import std.array : array;
  return findLinearRecurrence(as.map!(a => ModInt!M(a)).array);
}


void main() {
  enum LIM_N = 30;
  enum LIM = 200;
  auto dp = new bool[][][](LIM_N + 1, LIM, LIM);
  dp[0][LIM / 2][LIM / 2] = true;
  foreach (i; 0 .. LIM_N) {
    foreach (x; 0 .. LIM) foreach (y; 0 .. LIM) {
      if (dp[i][x][y]) {
        foreach (const dx; [-3, -2, 0, +2, +3]) foreach (const dy; [-3, -2, 0, +2, +3]) {
          if ((dx + dy) % 2 != 0) {
            const xx = x + dx;
            const yy = y + dy;
            if (0 <= xx && xx < LIM && 0 <= yy && yy < LIM) {
              dp[i + 1][xx][yy] = true;
            }
          }
        }
      }
    }
  }
  auto as = new Mint[LIM_N + 1];
  foreach (i; 0 .. LIM_N + 1) {
    foreach (x; 0 .. LIM) foreach (y; 0 .. LIM) {
      if (dp[i][x][y]) {
        as[i] += 1;
      }
    }
  }
  const cs = findLinearRecurrence(as);
  stderr.writeln("as = ", as);
  stderr.writeln("cs = ", cs);
  /*
[1, 12, 65, 172, 297, 456, 649, 876, 1137, 1432, 1761, 2124, 2521, 2952, 3417, 3916, 4449, 5016, 5617, 6252, 6921, 7624, 8361, 9132, 9937, 10776, 11649, 12556, 13497, 14472, 15481]
[1, 1000000004, 3, 1000000006, 0, 0, 0]
    
    172 297 456
    125 159
    34
  */
  
  try {
    for (; ; ) {
      const N = readLong();
      
      Mint ans;
      if (N < 3) {
        ans = [1, 12, 65][cast(int)(N)];
      } else {
        // 
        const Mint n = N - 3;
        ans += 172;
        ans += 125 * n;
        ans += 17 * n * (n - 1);
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}

yukicoder

結果

テストケース

ソースコード