結果
| 問題 |
No.2149 Vanitas Vanitatum
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2022-12-06 00:43:02 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
AC
|
| 実行時間 | 109 ms / 2,000 ms |
| コード長 | 6,474 bytes |
| コンパイル時間 | 1,881 ms |
| コンパイル使用メモリ | 164,904 KB |
| 実行使用メモリ | 52,680 KB |
| 最終ジャッジ日時 | 2024-06-22 16:59:59 |
| 合計ジャッジ時間 | 5,529 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 24 |
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; }
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 = 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 = 4 * 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);
}
}
}
/*
http://www.math.aoyama.ac.jp/~kyo/sotsuken/2008/konishi.pdf
Th. 2.2.1
*/
alias Result = Tuple!(int, "area", Mint, "way");
Result solve(int[] seq) {
const m = cast(int)(seq.count(0));
const n = cast(int)(seq.count(1));
auto as = new int[m];
auto bs = new int[n];
{
int x = 0, y = n;
foreach (s; seq) {
if (s == 0) {
as[x++] = y;
} else {
bs[--y] = x;
}
}
assert(x == m);
assert(y == 0);
}
debug {
if (m <= 10 && n <= 10) {
writeln("seq = ", seq);
writeln("as = ", as);
writeln("bs = ", bs);
}
}
int area;
Mint way = 1;
foreach (x; 0 .. m) {
foreach (y; 0 .. as[x]) {
++area;
way *= inv[(as[x] - y) + (bs[y] - x) - 1];
}
}
return Result(area, way);
}
void main() {
prepare;
try {
for (; ; ) {
const M = readInt;
auto A = new int[M];
foreach (x; 0 .. M) {
A[x] = readInt;
}
A.sort.reverse;
A ~= 0;
bool special;
if (A.sum % 2 != 0) {
writeln(0);
} else {
int[] seq;
foreach (x; 0 .. M) {
seq ~= 0;
foreach_reverse (y; A[x + 1] .. A[x]) {
seq ~= 1;
}
}
debug {
if (M <= 10 && A[0] <= 10) {
writeln("A = ", A);
writeln("seq = ", seq);
}
}
/*
bool check() {
int[] stack;
foreach (s; seq) {
if (!stack.empty && stack.back == s) {
stack.popBack;
} else {
stack ~= s;
}
}
foreach (i; 0 .. cast(int)(stack.length) - 1) {
if (stack[i] == 0 && stack[i + 1] == 1) {
return false;
}
}
return true;
}
*/
// if (!check) {
// writeln(0);
// } else {
int[][2] seqs;
foreach (i; 0 .. cast(int)(seq.length)) {
seqs[i & 1] ~= seq[i];
}
const res0 = solve(seqs[0]);
const res1 = solve(seqs[1]);
debug {
writeln("res0 = ", res0);
writeln("res1 = ", res1);
}
if (A.sum / 2 != res0.area + res1.area) {
writeln(0);
} else {
Mint ans = fac[res0.area + res1.area];
ans *= res0.way;
ans *= res1.way;
writeln(ans);
}
// }
}
}
} catch (EOFException e) {
}
}