結果
| 問題 | No.1760 Setwise Coprime |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2021-11-20 15:02:49 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
AC
|
| 実行時間 | 50 ms / 2,000 ms |
| コード長 | 5,730 bytes |
| コンパイル時間 | 1,826 ms |
| コンパイル使用メモリ | 159,652 KB |
| 実行使用メモリ | 13,240 KB |
| 最終ジャッジ日時 | 2024-06-22 13:23:11 |
| 合計ジャッジ時間 | 4,124 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 * 36 |
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 = 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 = 4 * 10^^5 + 10;Mint[] inv, fac, invFac;void prepare() {inv = new Mint[LIM];fac = new Mint[LIM];invFac = new Mint[LIM];inv[1] = 1;foreach (i; 2 .. LIM) {inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]);}fac[0] = invFac[0] = 1;foreach (i; 1 .. LIM) {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);return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];} else {return Mint(0);}}}void main() {prepare;auto lpf = iota(LIM).array;auto moe = new int[LIM];moe[1] = 1;foreach (p; 2 .. LIM) if (lpf[p] == p) {for (int n = p; n < LIM; n += p) {chmin(lpf[n], p);moe[n] = (n / p % p == 0) ? 0 : -moe[n / p];}}try {for (; ; ) {const N = readInt();Mint ans;auto gs = new Mint[N + 1];foreach (d; 1 .. N + 1) {gs[d] = moe[d] * Mint(2)^^(N / d);}const sumGs = gs.sum;debug {if (N <= 10) {writeln(gs);}}foreach (p; 2 .. N + 1) if (lpf[p] == p) {foreach (n; 1 .. N / p + 1) {gs[p * n] += gs[n];}}foreach (n; 1 .. N + 1) {gs[n] = gs[n] * gs[n];}foreach (p; 2 .. N + 1) if (lpf[p] == p) {foreach_reverse (n; 1 .. N / p + 1) {gs[p * n] -= gs[n];}}const sumGs2 = gs.sum;debug {if (N <= 10) {writeln(gs);}}foreach (f; 1 .. N + 1) {ans += gs[f] * (Mint(3) / Mint(4))^^(N / f);}ans += (sumGs^^2 - sumGs2);const sumMoe = Mint(moe[1 .. N + 1].sum);ans -= 2 * sumMoe * sumGs;ans += sumMoe^^2;writeln(ans);debug {Mint[4] brt;foreach (d; 1 .. N + 1) foreach (e; 1 .. N + 1) {const f = d / gcd(d, e) * e;brt[0] += moe[d] * moe[e] * Mint(2)^^(N / d - N / f) * Mint(2)^^(N / e - N / f) * Mint(3)^^(N / f);brt[1] += moe[d] * moe[e] * Mint(2)^^(N / e);brt[2] += moe[d] * moe[e] * Mint(2)^^(N / d);brt[3] += moe[d] * moe[e] * 1;}writeln(brt, " ", brt[0] - brt[1] - brt[2] + brt[3]);}}} catch (EOFException e) {}}