結果
問題 | No.1907 DETERMINATION |
ユーザー |
|
提出日時 | 2023-10-14 17:34:55 |
言語 | Java (openjdk 23) |
結果 |
AC
|
実行時間 | 2,530 ms / 4,000 ms |
コード長 | 16,893 bytes |
コンパイル時間 | 4,769 ms |
コンパイル使用メモリ | 93,356 KB |
実行使用メモリ | 64,104 KB |
最終ジャッジ日時 | 2024-09-16 11:49:45 |
合計ジャッジ時間 | 88,644 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge6 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 63 |
ソースコード
package no1xxx;import java.io.*;import java.util.ArrayDeque;import java.util.Arrays;import java.util.InputMismatchException;import java.util.Queue;import java.util.function.IntUnaryOperator;import java.util.function.LongUnaryOperator;public class No1907 {InputStream is;FastWriter out;String INPUT = "";public void solve(){final int mod = 998244353;int n = ni();long[][] M0 = nml(n, n);long[][] M1 = nml(n, n);long[] res = detLinear(M0, M1);for(int i = 0;i <= n;i++){out.println(res[i]);}}static final int mod = 998244353;// det(M0+M1x) = 1/(det A*det B) * det(A(M0+M1x)B)// = 1/(det A*det B) * det(xI_N+AM_0B)long[] detLinear(long[][] M0, long[][] M1){int n = M0.length;assert M0[0].length == n;assert M1.length == n;assert M1[0].length == n;long con = 1;int promote = 0;// 行基本変形for(int i = 0;i < n;i++){// tr(i);// for(long[] row : M0){// tr(row);// }// for(long[] row : M1){// tr(row);// }// find pivotwhile(true){int pivot = -1;for(int j = i;j < n;j++){if(M1[j][i] != 0){pivot = j;break;}}if(pivot == -1) {// multiply xfor(int j = i-1;j >= 0;j--){long linv = mod - M1[j][i];for(int k = 0;k < n;k++){M1[k][i] = (M1[k][i] + M1[k][j] * linv) % mod;M0[k][i] = (M0[k][i] + M0[k][j] * linv) % mod;}}for(int j = 0;j < n;j++){assert M1[j][i] == 0;M1[j][i] = M0[j][i];M0[j][i] = 0;}if (++promote > n)return new long[n + 1];continue;}// swapif (pivot != i) {long[] tmp = M1[i];M1[i] = M1[pivot];M1[pivot] = tmp;tmp = M0[i];M0[i] = M0[pivot];M0[pivot] = tmp;con = mod - con;}break;}// (0 0) (1 5)// (-2/4 -3/4) (0 1)assert M1[i][i] != 0;long inv = invl(M1[i][i], mod);con = con * M1[i][i] % mod;for(int j = i;j < n;j++){M1[i][j] = M1[i][j] * inv % mod;}for(int j = 0;j < n;j++){M0[i][j] = M0[i][j] * inv % mod;}for (int j = i + 1; j < n; j++) {long mul = mod - M1[j][i];M1[j][i] = 0;for (int k = i + 1; k < n; k++) {M1[j][k] = (M1[j][k] + M1[i][k] * mul) % mod;}for (int k = 0; k < n; k++) {M0[j][k] = (M0[j][k] + M0[i][k] * mul) % mod;}}}for(int i = 0;i < n;i++){for(int j = i+1;j < n;j++){long mul = mod - M1[i][j];M1[i][j] = 0;for(int k = 0;k < n;k++){M0[k][j] = (M0[k][j] + M0[k][i] * mul) % mod;}}}for(int i = 0;i < n;i++){for(int j = 0;j < n;j++){M0[i][j] = mod - M0[i][j];}}long[] res = calculateCharacteristicPolynomial(reduceToHessenbergMatrix(M0, mod), mod);long[] ret = new long[res.length];for(int i = promote;i < res.length;i++){ret[i-promote] = res[i] * con % mod;}return ret;}public static long[][] reduceToHessenbergMatrix(long[][] a, int mod){int n = a.length;if(n == 0)return new long[0][];assert n == a[0].length;for(int i = 0;i < n-1;i++){for(int j = i+1;j < n;j++){if(a[j][i] != 0){long[] d = a[j]; a[j] = a[i+1]; a[i+1] = d;for(int k = 0;k < n;k++){long t = a[k][j]; a[k][j] = a[k][i+1]; a[k][i+1] = t;}long inv = invl(a[i+1][i], mod);for(int k = i+2;k < n;k++){if(a[k][i] == 0)continue;long invq = a[k][i] * inv % mod;a[k][i] = 0;for(int l = i+1;l < n;l++){a[k][l] -= invq * a[i+1][l];a[k][l] %= mod;if(a[k][l] < 0)a[k][l] += mod;}for(int l = 0;l < n;l++){a[l][i+1] += invq * a[l][k];a[l][i+1] %= mod;}}break;}}}return a;}/*** Hessenberg行列hから特性多項式を求める。* reduceToHessenbergMatrixとあわせると任意の行列に対して行える。** seeのAlgorithm 2のindex=nを忠実に実装。* @see https://ipsen.math.ncsu.edu/ps/charpoly3.pdf* @param h* @param mod* @return モニックな特性多項式* @verified https://judge.yosupo.jp/problem/characteristic_polynomial*/public static long[] calculateCharacteristicPolynomial(long[][] h, int mod){int n = h.length;if(n == 0)return new long[]{1L};assert h[0].length == n;for(int i = 0;i < n;i++){for(int j = i+2;j < n;j++){assert h[j][i] == 0;}}long[][] c = new long[n][n];c[0][0] = mod - h[0][0];if(c[0][0] == mod)c[0][0] = 0;if(n == 1)return new long[]{c[0][0], 1};c[1][0] = c[0][0] - h[1][1];if(c[1][0] < 0)c[1][0] += mod;c[1][1] = (h[0][0] * h[1][1] - h[0][1] * h[1][0]) % mod;if(c[1][1] < 0)c[1][1] += mod;final long big = (Long.MAX_VALUE / mod / mod - 1) *mod*mod;for(int i = 2;i < n;i++){c[i][0] = c[i-1][0] - h[i][i];if(c[i][0] < 0)c[i][0] += mod;for(int j = 1;j <= i;j++){c[i][j] = c[i-1][j] - h[i][i] * c[i-1][j-1];long q = 1;for(int k = 1;k <= j;k++){q = q * h[i-k+1][i-k] % mod;c[i][j] -= h[i-k][i] * q % mod * (k == j ? 1 : c[i-k-1][j-k-1]);if(c[i][j] < -big)c[i][j] += big;}c[i][j] %= mod;if(c[i][j] < 0)c[i][j] += mod;}}long[] ret = new long[n+1];for(int i = 0;i < n;i++)ret[i] = c[n-1][n-1-i];ret[n] = 1;return ret;}public 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 void main(String[] args) {new No1907().run();}public void run(){long S = System.currentTimeMillis();is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());out = new FastWriter(System.out);solve();out.flush();long G = System.currentTimeMillis();tr(G-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();}private boolean eof(){if(lenbuf == -1)return true;int lptr = ptrbuf;while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;try {is.mark(1000);while(true){int b = is.read();if(b == -1){is.reset();return true;}else if(!isSpaceChar(b)){is.reset();return false;}}} catch (IOException e) {return true;}}private final 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 boolean isSpaceChar(int c) { return !(c >= 32 && 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))){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 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 long[][] nml(int n, int m){long[][] map = new long[n][];for(int i = 0;i < n;i++)map[i] = nal(m);return map;}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 int ni(){int num = 0, 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 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();}}public static class FastWriter{private static final int BUF_SIZE = 1<<13;private final byte[] buf = new byte[BUF_SIZE];private final OutputStream out;private int ptr = 0;private FastWriter(){out = null;}public FastWriter(OutputStream os){this.out = os;}public FastWriter(String path){try {this.out = new FileOutputStream(path);} catch (FileNotFoundException e) {throw new RuntimeException("FastWriter");}}public FastWriter write(byte b){buf[ptr++] = b;if(ptr == BUF_SIZE)innerflush();return this;}public FastWriter write(char c){return write((byte)c);}public FastWriter write(char[] s){for(char c : s){buf[ptr++] = (byte)c;if(ptr == BUF_SIZE)innerflush();}return this;}public FastWriter write(String s){s.chars().forEach(c -> {buf[ptr++] = (byte)c;if(ptr == BUF_SIZE)innerflush();});return this;}private static int countDigits(int l) {if (l >= 1000000000) return 10;if (l >= 100000000) return 9;if (l >= 10000000) return 8;if (l >= 1000000) return 7;if (l >= 100000) return 6;if (l >= 10000) return 5;if (l >= 1000) return 4;if (l >= 100) return 3;if (l >= 10) return 2;return 1;}public FastWriter write(int x){if(x == Integer.MIN_VALUE){return write((long)x);}if(ptr + 12 >= BUF_SIZE)innerflush();if(x < 0){write((byte)'-');x = -x;}int d = countDigits(x);for(int i = ptr + d - 1;i >= ptr;i--){buf[i] = (byte)('0'+x%10);x /= 10;}ptr += d;return this;}private static int countDigits(long l) {if (l >= 1000000000000000000L) return 19;if (l >= 100000000000000000L) return 18;if (l >= 10000000000000000L) return 17;if (l >= 1000000000000000L) return 16;if (l >= 100000000000000L) return 15;if (l >= 10000000000000L) return 14;if (l >= 1000000000000L) return 13;if (l >= 100000000000L) return 12;if (l >= 10000000000L) return 11;if (l >= 1000000000L) return 10;if (l >= 100000000L) return 9;if (l >= 10000000L) return 8;if (l >= 1000000L) return 7;if (l >= 100000L) return 6;if (l >= 10000L) return 5;if (l >= 1000L) return 4;if (l >= 100L) return 3;if (l >= 10L) return 2;return 1;}public FastWriter write(long x){if(x == Long.MIN_VALUE){return write("" + x);}if(ptr + 21 >= BUF_SIZE)innerflush();if(x < 0){write((byte)'-');x = -x;}int d = countDigits(x);for(int i = ptr + d - 1;i >= ptr;i--){buf[i] = (byte)('0'+x%10);x /= 10;}ptr += d;return this;}public FastWriter write(double x, int precision){if(x < 0){write('-');x = -x;}x += Math.pow(10, -precision)/2;// if(x < 0){ x = 0; }write((long)x).write(".");x -= (long)x;for(int i = 0;i < precision;i++){x *= 10;write((char)('0'+(int)x));x -= (int)x;}return this;}public FastWriter writeln(char c){ return write(c).writeln(); }public FastWriter writeln(int x){ return write(x).writeln(); }public FastWriter writeln(long x){ return write(x).writeln(); }public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); }public FastWriter write(int... xs){boolean first = true;for(int x : xs) {if (!first) write(' ');first = false;write(x);}return this;}public FastWriter write(long... xs){boolean first = true;for(long x : xs) {if (!first) write(' ');first = false;write(x);}return this;}public FastWriter write(IntUnaryOperator f, int... xs){boolean first = true;for(int x : xs) {if (!first) write(' ');first = false;write(f.applyAsInt(x));}return this;}public FastWriter write(LongUnaryOperator f, long... xs){boolean first = true;for(long x : xs) {if (!first) write(' ');first = false;write(f.applyAsLong(x));}return this;}public FastWriter writeln(){return write((byte)'\n');}public FastWriter writeln(int... xs) { return write(xs).writeln(); }public FastWriter writeln(long... xs) { return write(xs).writeln(); }public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); }public FastWriter writeln(char[] line) { return write(line).writeln(); }public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; }public FastWriter writeln(String s) { return write(s).writeln(); }private void innerflush(){try {out.write(buf, 0, ptr);ptr = 0;} catch (IOException e) {throw new RuntimeException("innerflush");}}public void flush(){innerflush();try {out.flush();} catch (IOException e) {throw new RuntimeException("flush");}}public FastWriter print(byte b) { return write(b); }public FastWriter print(char c) { return write(c); }public FastWriter print(char[] s) { return write(s); }public FastWriter print(String s) { return write(s); }public FastWriter print(int x) { return write(x); }public FastWriter print(long x) { return write(x); }public FastWriter print(double x, int precision) { return write(x, precision); }public FastWriter println(char c){ return writeln(c); }public FastWriter println(int x){ return writeln(x); }public FastWriter println(long x){ return writeln(x); }public FastWriter println(double x, int precision){ return writeln(x, precision); }public FastWriter print(int... xs) { return write(xs); }public FastWriter print(long... xs) { return write(xs); }public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); }public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }public FastWriter println(int... xs) { return writeln(xs); }public FastWriter println(long... xs) { return writeln(xs); }public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); }public FastWriter println(char[] line) { return writeln(line); }public FastWriter println(char[]... map) { return writeln(map); }public FastWriter println(String s) { return writeln(s); }public FastWriter println() { return writeln(); }}public static void trnz(int... o){for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");System.out.println();}// print ids which are 1public static void trt(long... o){Queue<Integer> stands = new ArrayDeque<>();for(int i = 0;i < o.length;i++){for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));}System.out.println(stands);}public static void tf(boolean... r){for(boolean x : r)System.out.print(x?'#':'.');System.out.println();}public static void tf(boolean[]... b){for(boolean[] r : b) {for(boolean x : r)System.out.print(x?'#':'.');System.out.println();}System.out.println();}public void tf(long[]... b){if(INPUT.length() != 0) {for (long[] r : b) {for (long x : r) {for (int i = 0; i < 64; i++) {System.out.print(x << ~i < 0 ? '#' : '.');}}System.out.println();}System.out.println();}}public void tf(long... b){if(INPUT.length() != 0) {for (long x : b) {for (int i = 0; i < 64; i++) {System.out.print(x << ~i < 0 ? '#' : '.');}}System.out.println();}}private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }}