結果
| 問題 | No.1907 DETERMINATION |
| ユーザー |
 uwi
|
| 提出日時 | 2023-10-14 17:34:55 |
| 言語 | Java21 (openjdk 21) |
| 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 |
（要ログイン）
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 | 70 ms
51,368 KB |
| testcase_01 | AC | 69 ms
50,672 KB |
| testcase_02 | AC | 69 ms
51,196 KB |
| testcase_03 | AC | 71 ms
50,768 KB |
| testcase_04 | AC | 72 ms
51,084 KB |
| testcase_05 | AC | 72 ms
50,944 KB |
| testcase_06 | AC | 71 ms
50,852 KB |
| testcase_07 | AC | 935 ms
59,876 KB |
| testcase_08 | AC | 668 ms
57,920 KB |
| testcase_09 | AC | 873 ms
60,616 KB |
| testcase_10 | AC | 1,980 ms
63,888 KB |
| testcase_11 | AC | 673 ms
60,720 KB |
| testcase_12 | AC | 1,943 ms
63,980 KB |
| testcase_13 | AC | 1,787 ms
63,292 KB |
| testcase_14 | AC | 1,694 ms
63,408 KB |
| testcase_15 | AC | 768 ms
57,620 KB |
| testcase_16 | AC | 523 ms
57,508 KB |
| testcase_17 | AC | 1,737 ms
63,916 KB |
| testcase_18 | AC | 1,473 ms
61,356 KB |
| testcase_19 | AC | 273 ms
57,604 KB |
| testcase_20 | AC | 1,643 ms
63,936 KB |
| testcase_21 | AC | 606 ms
57,640 KB |
| testcase_22 | AC | 904 ms
60,896 KB |
| testcase_23 | AC | 1,987 ms
63,636 KB |
| testcase_24 | AC | 1,039 ms
61,328 KB |
| testcase_25 | AC | 73 ms
51,088 KB |
| testcase_26 | AC | 1,822 ms
62,688 KB |
| testcase_27 | AC | 2,249 ms
64,092 KB |
| testcase_28 | AC | 2,251 ms
63,996 KB |
| testcase_29 | AC | 2,234 ms
64,040 KB |
| testcase_30 | AC | 73 ms
50,704 KB |
| testcase_31 | AC | 1,944 ms
63,804 KB |
| testcase_32 | AC | 1,915 ms
63,180 KB |
| testcase_33 | AC | 1,781 ms
62,408 KB |
| testcase_34 | AC | 1,838 ms
62,512 KB |
| testcase_35 | AC | 74 ms
51,128 KB |
| testcase_36 | AC | 73 ms
51,048 KB |
| testcase_37 | AC | 75 ms
50,952 KB |
| testcase_38 | AC | 1,799 ms
62,480 KB |
| testcase_39 | AC | 1,866 ms
63,360 KB |
| testcase_40 | AC | 2,530 ms
63,840 KB |
| testcase_41 | AC | 1,878 ms
63,160 KB |
| testcase_42 | AC | 2,509 ms
63,864 KB |
| testcase_43 | AC | 2,443 ms
63,792 KB |
| testcase_44 | AC | 2,180 ms
63,876 KB |
| testcase_45 | AC | 2,190 ms
63,892 KB |
| testcase_46 | AC | 1,898 ms
63,680 KB |
| testcase_47 | AC | 1,839 ms
62,692 KB |
| testcase_48 | AC | 1,857 ms
63,136 KB |
| testcase_49 | AC | 1,949 ms
64,024 KB |
| testcase_50 | AC | 1,879 ms
63,076 KB |
| testcase_51 | AC | 1,818 ms
63,164 KB |
| testcase_52 | AC | 70 ms
51,096 KB |
| testcase_53 | AC | 1,124 ms
60,740 KB |
| testcase_54 | AC | 1,119 ms
61,000 KB |
| testcase_55 | AC | 70 ms
50,912 KB |
| testcase_56 | AC | 1,090 ms
60,928 KB |
| testcase_57 | AC | 1,120 ms
60,952 KB |
| testcase_58 | AC | 1,286 ms
64,104 KB |
| testcase_59 | AC | 1,121 ms
63,448 KB |
| testcase_60 | AC | 1,005 ms
62,396 KB |
| testcase_61 | AC | 1,501 ms
64,048 KB |
| testcase_62 | AC | 1,093 ms
63,160 KB |
| testcase_63 | AC | 1,881 ms
63,168 KB |
| testcase_64 | AC | 72 ms
51,028 KB |
| testcase_65 | AC | 70 ms
50,688 KB |
| testcase_66 | AC | 70 ms
50,932 KB |
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 pivot
while(true){
int pivot = -1;
for(int j = i;j < n;j++){
if(M1[j][i] != 0){
pivot = j;
break;
}
}
if(pivot == -1) {
// multiply x
for(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;
}
// swap
if (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 1
public 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)); }
}