結果
| 問題 |
No.2689 Populous
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2024-03-20 22:11:00 |
| 言語 | D (dmd 2.109.1) |
| 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 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 28 |
ソースコード
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) {
}
}