結果
問題 | No.1138 No Bingo! |
ユーザー | uwi |
提出日時 | 2020-07-30 06:17:16 |
言語 | Java21 (openjdk 21) |
結果 |
AC
|
実行時間 | 945 ms / 3,000 ms |
コード長 | 16,124 bytes |
コンパイル時間 | 5,093 ms |
コンパイル使用メモリ | 89,944 KB |
実行使用メモリ | 63,108 KB |
最終ジャッジ日時 | 2024-07-02 08:47:59 |
合計ジャッジ時間 | 18,813 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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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 | 71 ms
39,344 KB |
testcase_01 | AC | 69 ms
39,212 KB |
testcase_02 | AC | 71 ms
39,676 KB |
testcase_03 | AC | 378 ms
51,164 KB |
testcase_04 | AC | 533 ms
60,648 KB |
testcase_05 | AC | 68 ms
39,036 KB |
testcase_06 | AC | 68 ms
39,252 KB |
testcase_07 | AC | 72 ms
39,252 KB |
testcase_08 | AC | 73 ms
39,620 KB |
testcase_09 | AC | 430 ms
54,760 KB |
testcase_10 | AC | 544 ms
60,404 KB |
testcase_11 | AC | 869 ms
60,872 KB |
testcase_12 | AC | 285 ms
49,112 KB |
testcase_13 | AC | 224 ms
46,736 KB |
testcase_14 | AC | 718 ms
61,196 KB |
testcase_15 | AC | 451 ms
54,052 KB |
testcase_16 | AC | 714 ms
60,576 KB |
testcase_17 | AC | 858 ms
63,108 KB |
testcase_18 | AC | 875 ms
62,852 KB |
testcase_19 | AC | 468 ms
54,504 KB |
testcase_20 | AC | 945 ms
61,684 KB |
testcase_21 | AC | 632 ms
60,940 KB |
testcase_22 | AC | 616 ms
61,168 KB |
testcase_23 | AC | 147 ms
42,628 KB |
testcase_24 | AC | 458 ms
54,404 KB |
testcase_25 | AC | 444 ms
53,544 KB |
testcase_26 | AC | 319 ms
50,916 KB |
testcase_27 | AC | 333 ms
50,928 KB |
testcase_28 | AC | 254 ms
48,796 KB |
testcase_29 | AC | 288 ms
49,336 KB |
ソースコード
package no1xxx; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class No1138 { InputStream is; PrintWriter out; String INPUT = ""; long[] pow(long[] a, int K) { long[] ret = {1}; for(int d = 31-Integer.numberOfLeadingZeros(K);d >= 0;d--) { ret = mul(ret, ret); if(K<<~d<0) { ret = mul(ret, a); } } return ret; } void solve() { int n = ni(); int[][] fif = enumFIF(200001, mod); int mod = 998244353; long[] a2 = {2, mod-4, 1}; long[] a1 = {mod-1, 1}; long[] a = mul(pow(a2, n/2), pow(a1, n%2)); long T = 0; for(int i = 0;i < a.length;i++) { T += fif[0][i] * a[i]; T %= mod; } long M = 0; long[] b = pow(a1, n); for(int i = 0;i < b.length;i++) { M += fif[0][i] * b[i]; M %= mod; } long A = fif[0][n]; out.println((A-2*M+T+2*mod)%mod); } // F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x) // if want p-destructive, comment out flipping p just before returning. public static long[] inv(long[] p) { int n = p.length; long[] f = {invl(p[0], mod)}; for(int i = 0;i < p.length;i++){ if(p[i] == 0)continue; p[i] = mod-p[i]; } for(int i = 1;i < 2*n;i*=2){ long[] f2 = mul(f, f, Math.min(n, 2*i)); long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i)); for(int j = 0;j < f.length;j++){ f2p[j] += 2L*f[j]; if(f2p[j] >= mod)f2p[j] -= mod; if(f2p[j] >= mod)f2p[j] -= mod; } f = f2p; } for(int i = 0;i < p.length;i++){ if(p[i] == 0)continue; p[i] = mod-p[i]; } return f; } // differentiate public static long[] d(long[] p) { long[] q = new long[p.length]; for(int i = 0;i < p.length-1;i++){ q[i] = p[i+1] * (i+1) % mod; } return q; } // integrate public static long[] i(long[] p) { long[] q = new long[p.length]; for(int i = 0;i < p.length-1;i++){ q[i+1] = p[i] * invl(i+1, mod) % mod; } return q; } static long[] exp(long[] a) { return exp(a, a.length); } /** * https://cs.uwaterloo.ca/~eschost/publications/BoSc09-final.pdf * @verified https://judge.yosupo.jp/problem/exp_of_formal_power_series * @param a * @param lim * @return */ static long[] exp(long[] a, int lim) { long[] F = {1L}; long[] G = {1L}; long[] da = d(a); for(int m = 1;;m *= 2) { long[] G2 = mul(G, G, m); G = sub(mul_(G, 2), mul(F, G2, m)); long[] Q = Arrays.copyOf(da, m-1); long[] W = add(Q, mul(G, sub(d(F), mul(F, Q, m), m-1))); F = mul(F, add(new long[] {1}, sub(Arrays.copyOf(a, m), i(W))), m); if(m >= lim)break; } return Arrays.copyOf(F, lim); } public static long[] add(long[] a, long[] b) { long[] c = new long[Math.max(a.length, b.length)]; for(int i = 0;i < a.length;i++)c[i] += a[i]; for(int i = 0;i < b.length;i++)c[i] += b[i]; for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod; return c; } public static long[] add(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i]; for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i]; for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod; return c; } public static long[] mul_(long[] a, long k) { for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod; return a; } public static long[] sub(long[] a, long[] b) { long[] c = new long[Math.max(a.length, b.length)]; for(int i = 0;i < a.length;i++)c[i] += a[i]; for(int i = 0;i < b.length;i++)c[i] -= b[i]; for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod; return c; } public static long[] sub(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i]; for(int i = 0;i < b.length && i < lim;i++)c[i] -= b[i]; for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod; return c; } // // // F_{t+1}(x) = F_t(x)-(ln F_t(x) - P(x)) * F_t(x) // public static long[] exp(long[] p) // { // int n = p.length; // long[] f = {p[0]}; // for(int i = 1;i < 2*n;i*=2){ // long[] ii = ln(f); // long[] sub = sub(ii, p, Math.min(n, 2*i)); // if(--sub[0] < 0)sub[0] += mod; // for(int j = 0;j < 2*i && j < n;j++){ // sub[j] = mod-sub[j]; // if(sub[j] == mod)sub[j] = 0; // } // f = mul(sub, f, Math.min(n, 2*i)); //// f = sub(f, mul(sub(ii, p, 2*i), f, 2*i)); // } // return f; // } // \int f'(x)/f(x) dx public static long[] ln(long[] f) { long[] ret = i(mul(d(f), inv(f))); // ret[0] = f[0]; return ret; } // ln F(x) - k ln P(x) = 0 // public static long[] pow(long[] p, int K) // { // long t = p[0]; // long it = invl(t, mod); // for(int i = 0;i < p.length;i++) { // p[i] = p[i] * it % mod; // } // // tr("BASE", p); // int n = p.length; // long[] lnp = ln(p); // lnp[0] = 0; // tr(lnp); // for(int i = 0;i < lnp.length;i++)lnp[i] = lnp[i] * K % mod; // long[] ret = exp(lnp);//Arrays.copyOf(lnp, n)); // tr("retsttt", ret); // // tr("lnp", lnp, K); // long m = pow(t, K, mod); // for(int i = 0;i < p.length;i++) { // ret[i] = ret[i] * m % mod; // } // tr("rets", ret); // return ret; // } public static int[][] enumFIF(int n, int mod) { int[] f = new int[n + 1]; int[] invf = new int[n + 1]; f[0] = 1; for (int i = 1; i <= n; i++) { f[i] = (int) ((long) f[i - 1] * i % mod); } long a = f[n]; long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } invf[n] = (int) (p < 0 ? p + mod : p); for (int i = n - 1; i >= 0; i--) { invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod); } return new int[][] { f, invf }; } public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681}; public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17}; // public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033}; // public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5}; public static long[] convoluteSimply(long[] a, long[] b, int P, int g) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2); long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for(int i = 0;i < m;i++){ fa[i] = fa[i]*fb[i]%P; } return nttmb(fa, m, true, P, g); } public static long[] convolute(long[] a, long[] b) { int USE = 2; int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2); long[][] fs = new long[USE][]; for(int k = 0;k < USE;k++){ int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for(int i = 0;i < m;i++){ fa[i] = fa[i]*fb[i]%P; } fs[k] = nttmb(fa, m, true, P, g); } int[] mods = Arrays.copyOf(NTTPrimes, USE); long[] gammas = garnerPrepare(mods); int[] buf = new int[USE]; for(int i = 0;i < fs[0].length;i++){ for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i]; long[] res = garnerBatch(buf, mods, gammas); long ret = 0; for(int j = res.length-1;j >= 0;j--)ret = ret * mods[j] + res[j]; fs[0][i] = ret; } return fs[0]; } public static long[] convolute(long[] a, long[] b, int USE, int mod) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2); long[][] fs = new long[USE][]; for(int k = 0;k < USE;k++){ int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for(int i = 0;i < m;i++){ fa[i] = fa[i]*fb[i]%P; } fs[k] = nttmb(fa, m, true, P, g); } int[] mods = Arrays.copyOf(NTTPrimes, USE); long[] gammas = garnerPrepare(mods); int[] buf = new int[USE]; for(int i = 0;i < fs[0].length;i++){ for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i]; long[] res = garnerBatch(buf, mods, gammas); long ret = 0; for(int j = res.length-1;j >= 0;j--)ret = (ret * mods[j] + res[j]) % mod; fs[0][i] = ret; } return fs[0]; } // static int[] wws = new int[270000]; // outer faster // Modifed Montgomery + Barrett private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; int[] wws = new int[1<<h-1]; long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P); long w = (1L<<32)%P; for(int k = 0;k < 1<<h-1;k++){ wws[k] = (int)w; w = modh(w*dw, M, H, P); } long J = invl(P, 1L<<32); for(int i = 0;i < h;i++){ for(int j = 0;j < 1<<i;j++){ for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){ long u = (dst[s] - dst[t] + 2*P)*wws[k]; dst[s] += dst[t]; if(dst[s] >= 2*P)dst[s] -= 2*P; // long Q = (u&(1L<<32)-1)*J&(1L<<32)-1; long Q = (u<<32)*J>>>32; dst[t] = (u>>>32)-(Q*P>>>32)+P; } } if(i < h-1){ for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2]; } } for(int i = 0;i < n;i++){ if(dst[i] >= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long in = invl(n, P); for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P); } return dst; } // Modified Shoup + Barrett private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P); long[] wws = new long[1<<h-1]; long[] ws = new long[1<<h-1]; long w = 1; for(int k = 0;k < 1<<h-1;k++){ wws[k] = (w<<32)/P; ws[k] = w; w = modh(w*dw, M, H, P); } for(int i = 0;i < h;i++){ for(int j = 0;j < 1<<i;j++){ for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){ long ndsts = dst[s] + dst[t]; if(ndsts >= 2*P)ndsts -= 2*P; long T = dst[s] - dst[t] + 2*P; long Q = wws[k]*T>>>32; dst[s] = ndsts; dst[t] = ws[k]*T-Q*P&(1L<<32)-1; } } // dw = dw * dw % P; if(i < h-1){ for(int k = 0;k < 1<<h-i-2;k++){ wws[k] = wws[k*2]; ws[k] = ws[k*2]; } } } for(int i = 0;i < n;i++){ if(dst[i] >= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long in = invl(n, P); for(int i = 0;i < n;i++){ dst[i] = modh(dst[i] * in, M, H, P); } } return dst; } static final long mask = (1L<<31)-1; public static long modh(long a, long M, int h, int mod) { long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod; return r < mod ? r : r-mod; } private static long[] garnerPrepare(int[] m) { int n = m.length; assert n == m.length; if(n == 0)return new long[0]; long[] gamma = new long[n]; for(int k = 1;k < n;k++){ long prod = 1; for(int i = 0;i < k;i++){ prod = prod * m[i] % m[k]; } gamma[k] = invl(prod, m[k]); } return gamma; } private static long[] garnerBatch(int[] u, int[] m, long[] gamma) { int n = u.length; assert n == m.length; long[] v = new long[n]; v[0] = u[0]; for(int k = 1;k < n;k++){ long temp = v[k-1]; for(int j = k-2;j >= 0;j--){ temp = (temp * m[j] + v[j]) % m[k]; } v[k] = (u[k] - temp) * gamma[k] % m[k]; if(v[k] < 0)v[k] += m[k]; } return v; } private static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } private static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static int mod = 998244353; public static long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod; public static int G = 3; public static long[] mul(long[] a, long[] b) { return Arrays.copyOf(convoluteSimply(a, b, mod, G), a.length+b.length-1); } public static long[] mul(long[] a, long[] b, int lim) { return Arrays.copyOf(convoluteSimply(a, b, mod, G), lim); } public static long[] mulnaive(long[] a, long[] b) { long[] c = new long[a.length+b.length-1]; for(int i = 0;i < a.length;i++){ for(int j = 0;j < b.length;j++){ c[i+j] += a[i]*b[j]; if(c[i+j] >= big)c[i+j] -= big; } } for(int i = 0;i < c.length;i++)c[i] %= mod; return c; } public static long[] mulnaive(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length;i++){ for(int j = 0;j < b.length && i+j < lim;j++){ c[i+j] += a[i]*b[j]; if(c[i+j] >= big)c[i+j] -= big; } } for(int i = 0;i < c.length;i++)c[i] %= mod; return c; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new No1138().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }