結果
問題 | No.2503 Typical Path Counting Problem on a Grid |
ユーザー |
👑 |
提出日時 | 2023-10-13 22:31:33 |
言語 | D (dmd 2.109.1) |
結果 |
WA
|
実行時間 | - |
コード長 | 5,329 bytes |
コンパイル時間 | 1,673 ms |
コンパイル使用メモリ | 152,492 KB |
実行使用メモリ | 45,848 KB |
最終ジャッジ日時 | 2024-09-15 18:16:33 |
合計ジャッジ時間 | 11,279 ms |
ジャッジサーバーID (参考情報) |
judge6 / judge1 |
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ファイルパターン | 結果 |
---|---|
other | AC * 8 WA * 2 |
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;// x^e mod rev(cs)Mint[] powerRev(const(Mint[]) cs, long e) {assert(!cs.empty);assert(cs[0].x == 1);const d = cast(int)(cs.length) - 1;if (d == 0) {return [];} else if (d == 1) {return [(-cs[1])^^e];}Mint[] mul(const(Mint[]) fs, const(Mint[]) gs) {auto hs = new Mint[d + d - 1];foreach (i; 0 .. d) foreach (j; 0 .. d) {hs[i + j] += fs[i] * gs[j];}foreach_reverse (i; d .. d + d - 1) {foreach (j; 1 .. d + 1) {hs[i - j] -= cs[j] * hs[i];}}hs.length = d;return hs;}auto xs = new Mint[d];auto ys = new Mint[d];xs[1] = 1;ys[0] = 1;for (; ; xs = mul(xs, xs)) {if (e & 1) ys = mul(ys, xs);if (!(e >>= 1)) break;}return ys;}Mint linearRecurrenceAt(const(Mint[]) as, const(Mint[]) cs, long e) {assert(!cs.empty);assert(cs[0].x == 1);const d = cast(int)(cs.length) - 1;assert(as.length >= d);const fs = powerRev(cs, e);Mint ans;foreach (i; 0 .. d) {ans += fs[i] * as[i];}return ans;}void main() {enum LIM = 10^^7 + 5;auto dp = new Mint[LIM];dp[0] = 1;foreach (n; 0 .. LIM) {if (n + 1 < LIM) dp[n + 1] += dp[n] * (n + 1);if (n + 1 < LIM) dp[n + 1] += dp[n] * (n + 1);if (n + 2 < LIM) dp[n + 2] += dp[n] * (n + 1);}debug {writeln(dp[0 .. 100]);}try {for (; ; ) {const numCases = readInt;foreach (caseId; 0 .. numCases) {long M = readLong;long N = readLong;if (M > N) {swap(M, N);}// 1 / (1 - p x - q x^2)const Mint p = 2 * M + 1;const Mint q = M;const as = [Mint(1), p, p * p + q];const cs = [Mint(1), -p, -q];const f = dp[M];const g = M ? (dp[M - 1] * M) : Mint(0);Mint ans;if (N - M == 0) {ans += g * g * N;}if (N - M >= 0) ans += f * f * linearRecurrenceAt(as, cs, N - M);if (N - M >= 1) ans += 2 * f * g * linearRecurrenceAt(as, cs, N - M - 1);if (N - M >= 2) ans += g * g * linearRecurrenceAt(as, cs, N - M - 2);writeln(ans);}}} catch (EOFException e) {}}