結果

問題 No.2689 Populous
ユーザー 👑 hos.lyrichos.lyric
提出日時 2024-03-20 22:11:00
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 80 ms / 2,000 ms
コード長 8,122 bytes
コンパイル時間 2,816 ms
コンパイル使用メモリ 153,344 KB
実行使用メモリ 34,560 KB
最終ジャッジ日時 2024-09-30 08:05:13
合計ジャッジ時間 5,585 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 57 ms
26,368 KB
testcase_01 AC 57 ms
26,368 KB
testcase_02 AC 57 ms
26,240 KB
testcase_03 AC 57 ms
26,368 KB
testcase_04 AC 57 ms
26,240 KB
testcase_05 AC 56 ms
26,368 KB
testcase_06 AC 58 ms
26,368 KB
testcase_07 AC 55 ms
26,368 KB
testcase_08 AC 56 ms
26,240 KB
testcase_09 AC 58 ms
26,240 KB
testcase_10 AC 56 ms
26,368 KB
testcase_11 AC 54 ms
26,240 KB
testcase_12 AC 52 ms
26,240 KB
testcase_13 AC 52 ms
26,368 KB
testcase_14 AC 51 ms
26,240 KB
testcase_15 AC 52 ms
26,240 KB
testcase_16 AC 52 ms
26,368 KB
testcase_17 AC 52 ms
26,240 KB
testcase_18 AC 51 ms
26,240 KB
testcase_19 AC 52 ms
26,368 KB
testcase_20 AC 57 ms
30,464 KB
testcase_21 AC 56 ms
30,464 KB
testcase_22 AC 55 ms
30,464 KB
testcase_23 AC 58 ms
31,360 KB
testcase_24 AC 77 ms
34,048 KB
testcase_25 AC 76 ms
33,920 KB
testcase_26 AC 60 ms
31,488 KB
testcase_27 AC 71 ms
33,664 KB
testcase_28 AC 80 ms
34,560 KB
testcase_29 AC 78 ms
34,432 KB
testcase_30 AC 80 ms
34,560 KB
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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; }

string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; }

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 = cast(uint)(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 = 998244353;
alias Mint = ModInt!MO;

enum LIM_INV = 2 * 10^^6 + 10;
Mint[] inv, fac, invFac;
void prepare() {
  inv = new Mint[LIM_INV];
  fac = new Mint[LIM_INV];
  invFac = new Mint[LIM_INV];
  inv[1] = 1;
  foreach (i; 2 .. LIM_INV) {
    inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]);
  }
  fac[0] = invFac[0] = 1;
  foreach (i; 1 .. LIM_INV) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(long n, long k) {
  if (n < 0) {
    if (k >= 0) {
      return (-1)^^(k & 1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (-1)^^((n - k) & 1) * binom(-k - 1, n - k);
    } else {
      return Mint(0);
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
    } else {
      return Mint(0);
    }
  }
}


Mint solve(const(int[]) A, const(int[]) B, const(int) N) {
  debug {
    writefln("[solve] %s %s %s", A, B, N);
  }
  const M = cast(int)(A.length);
  auto dp = new Mint[N];
  dp[1 .. N-1] = Mint(1);
  foreach (x; 1 .. M) {
    auto dpSum = new Mint[N + 1];
    foreach (y; 0 .. N) dpSum[y + 1] = dpSum[y] + dp[y];
    dp[] = Mint(0);
    // [y0, y1]
    Mint get(int y0, int y1) {
      chmax(y0, 0);
      chmin(y1, N - 1);
      return (y0 <= y1) ? (dpSum[y1 + 1] - dpSum[y0]) : Mint(0);
    }
    const f = (abs(A[x - 1] - B[x    ]) > N);
    const g = (abs(A[x    ] - B[x - 1]) > N);
    foreach (y; 1 .. N-1) {
      dp[y] = get(g ? (y - 1) : 0, f ? (y + 1) : (N-1));
    }
    debug {
      writefln("f = %s, g = %s, dp = %s", f, g, dp);
    }
  }
  const ret = dp.sum;
  return ret;
}

void main() {
  prepare;
  
  /*
  debug {{
    // 1 wall in each row
    enum INF = 10^^9;
    foreach (m; 1 .. 5 + 1) foreach (n; 3 .. 7 + 1) {
      auto freq = new int[m * n];
      foreach (p; 0 .. (n - 2)^^m) {
        const ys = iota(m).map!(x => (1 + p / (n - 2)^^(m-1-x) % (n - 2))).array;
        auto wall = new bool[][](m, n);
        foreach (x; 0 .. m) wall[x][ys[x]] = true;
        const U = m * n;
        auto dist = new int[][](U, U);
        foreach (u; 0 .. U) {
          dist[u][] = INF;
          dist[u][u] = 0;
        }
        void ae(int x0, int y0, int x1, int y1) {
          const u = x0 * n + y0;
          const v = x1 * n + y1;
          chmin(dist[u][v], 1);
          chmin(dist[v][u], 1);
        }
        foreach (x; 0 .. m) foreach (y; 0 .. n) if (!wall[x][y]) {
          if (x + 1 < m && !wall[x + 1][y]) ae(x, y, x + 1, y);
          if (y + 1 < n && !wall[x][y + 1]) ae(x, y, x, y + 1);
        }
        foreach (w; 0 .. U) foreach (u; 0 .. U) foreach (v; 0 .. U) chmin(dist[u][v], dist[u][w] + dist[w][v]);
        int mn = INF;
        foreach (x0; 0 .. m) foreach (x1; 0 .. m) chmin(mn, dist[x0 * n + 0][x1 * n + (n - 1)]);
        if (mn < INF) {
          ++freq[mn];
          assert(mn == n);
        }
      }
      writeln(m, " ", n, ": ", freq);
    }
  }}
  //*/
  
  try {
    for (; ; ) {
      const M = readInt;
      const N = readInt;
      auto A = new int[][](M, N);
      foreach (y; 0 .. N) A[0  ][y] = readInt;
      foreach (x; 1 .. M-1) {
        A[x][0  ] = readInt;
        A[x][N-1] = readInt;
      }
      foreach (y; 0 .. N) A[M-1][y] = readInt;
      debug {
        writeln("A = ", A);
      }
      
      bool ok = true;
      foreach (y; 0 .. N - 1) ok = ok && (abs(A[0  ][y] - A[0  ][y + 1]) <= 1);
      foreach (y; 0 .. N - 1) ok = ok && (abs(A[M-1][y] - A[M-1][y + 1]) <= 1);
      foreach (x; 0 .. M - 1) ok = ok && (abs(A[x][0  ] - A[x + 1][0  ]) <= 1);
      foreach (x; 0 .. M - 1) ok = ok && (abs(A[x][N-1] - A[x + 1][N-1]) <= 1);
      
      if (ok) {
        int[] xs, ys;
        foreach (x; 0 .. M) if (abs(A[x][0] - A[x][N-1]) > N - 1) xs ~= x;
        foreach (y; 0 .. N) if (abs(A[0][y] - A[M-1][y]) > M - 1) ys ~= y;
        debug {
          writefln("M = %s, N = %s; xs = %s, ys = %s", M, N, xs, ys);
        }
        const xsLen = cast(int)(xs.length);
        const ysLen = cast(int)(ys.length);
        Mint ans = 1;
        if (xsLen) {
          if (ysLen) {
            assert(false);
          } else {
            for (int i = 0, j; i < xsLen; i = j) {
              for (; j < xsLen && xs[i] - i == xs[j] - j; ++j) {}
              int[] as, bs;
              foreach (k; i .. j) {
                as ~= A[xs[k]][0];
                bs ~= A[xs[k]][N-1];
              }
              ans *= solve(as, bs, N);
            }
          }
        } else {
          if (ysLen) {
            for (int i = 0, j; i < ysLen; i = j) {
              for (; j < ysLen && ys[i] - i == ys[j] - j; ++j) {}
              int[] as, bs;
              foreach (k; i .. j) {
                as ~= A[0][ys[k]];
                bs ~= A[M-1][ys[k]];
              }
              ans *= solve(as, bs, M);
            }
          } else {
            //
          }
        }
        writeln(ans);
      } else {
        writeln(-1);
      }
    }
  } catch (EOFException e) {
  }
}
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