結果
| 問題 | No.1516 simple 門松列 problem Re:MASTER |
| ユーザー |
 uwi
|
| 提出日時 | 2021-05-21 22:00:35 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 162 ms / 6,000 ms |
| コード長 | 18,091 bytes |
| コンパイル時間 | 4,825 ms |
| コンパイル使用メモリ | 96,704 KB |
| 実行使用メモリ | 56,248 KB |
| 最終ジャッジ日時 | 2024-10-10 08:40:54 |
| 合計ジャッジ時間 | 8,181 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（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 | 86 ms
51,012 KB |
| testcase_01 | AC | 159 ms
56,140 KB |
| testcase_02 | AC | 162 ms
56,104 KB |
| testcase_03 | AC | 91 ms
51,296 KB |
| testcase_04 | AC | 84 ms
51,064 KB |
| testcase_05 | AC | 87 ms
50,636 KB |
| testcase_06 | AC | 100 ms
51,728 KB |
| testcase_07 | AC | 145 ms
55,796 KB |
| testcase_08 | AC | 112 ms
53,712 KB |
| testcase_09 | AC | 85 ms
51,244 KB |
| testcase_10 | AC | 123 ms
56,084 KB |
| testcase_11 | AC | 96 ms
51,704 KB |
| testcase_12 | AC | 89 ms
51,036 KB |
| testcase_13 | AC | 86 ms
50,760 KB |
| testcase_14 | AC | 157 ms
56,148 KB |
| testcase_15 | AC | 112 ms
53,636 KB |
| testcase_16 | AC | 112 ms
54,128 KB |
| testcase_17 | AC | 102 ms
51,908 KB |
| testcase_18 | AC | 99 ms
51,892 KB |
| testcase_19 | AC | 88 ms
51,064 KB |
| testcase_20 | AC | 157 ms
56,248 KB |
| testcase_21 | AC | 156 ms
56,204 KB |
ソースコード
package contest210521;
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 F {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
int n = ni(), K = ni();
final int mod = 998244353;
long[][] dp = new long[K][K];
long[][] ep = new long[K][K];
for(int i = 0;i < K;i++){
Arrays.fill(dp[i], 1L);
for(int j = 0;j < K;j++){
ep[i][j] = i + j;
}
}
long[] dpss = new long[1000];
long[] epss = new long[1000];
for(int i = 2;i < 1002;i++){
long[][] ndp = new long[K][K];
long[][] nep = new long[K][K];
for(int k = 0;k < K;k++){
long dps = 0;
long eps = 0;
for(int l = 0;l < k;l++) {
dps += dp[l][k];
eps += ep[l][k] + l * dp[l][k];
eps %= mod;
}
dps %= mod;
for(int j = 0;j < k;j++){
ndp[k][j] = dps - dp[j][k];
if(ndp[k][j] < 0)ndp[k][j] += mod;
nep[k][j] = eps - ep[j][k] - j * dp[j][k];
nep[k][j] %= mod;
if(nep[k][j] < 0)nep[k][j] += mod;
}
long dpu = 0;
long epu = 0;
for(int l = k+1;l < K;l++){
dpu += dp[l][k];
epu += ep[l][k] + l * dp[l][k];
epu %= mod;
}
dpu %= mod;
for(int j = k+1;j < K;j++){
ndp[k][j] = dpu - dp[j][k];
if(ndp[k][j] < 0)ndp[k][j] += mod;
nep[k][j] = epu - ep[j][k] - j * dp[j][k];
nep[k][j] %= mod;
if(nep[k][j] < 0)nep[k][j] += mod;
}
}
dp = ndp;
ep = nep;
long ans = 0;
for(int k = 0;k <K;k++){
for(int j = 0;j < K;j++){
ans += dp[k][j];
}
}
dpss[i-2] = ans % mod;
long sum = 0;
for(int k = 0;k < K;k++){
for(int j = 0;j < K;j++){
sum += ep[k][j];
}
}
epss[i-2] = sum % mod;
}
out.print(guess(dpss, mod, n-3) + " ");
out.println(guess(epss, mod, n-3));
}
public static long guess(long[] a, int mod, long n)
{
if(a.length % 2 == 1)a = Arrays.copyOf(a, a.length/2*2); // strip to even length
long[] q = modifiedBerlekampMassey(a, mod);
long[] r = new long[q.length-1];
for(int i = 0;i < q.length-1;i++)r[i] = (mod-q[i]) % mod;
// return dot(LinearRecurrence2.powCompanionMatrixes(r, n, mod)[0], all, mod);
return lr(Arrays.copyOf(a, r.length), r, n, mod);
}
public static long lr(long[] a, long[] co, long n, long mod)
{
int m = a.length;
if(m == 1){
long ret = a[0];
long mul = co[0];
for(;n > 0;n >>>= 1){
if((n&1)==1){
ret = (ret * mul) % mod;
}
mul = (mul * mul) % mod;
}
return ret;
}
long[][] m2 = new long[m-1][m];
for(int j = 0;j < m;j++){
m2[0][j] = co[j];
}
for(int i = 1;i < m-1;i++){
for(int j = 0;j < m;j++){
long x = m2[i-1][m-1] * co[j];
if(j-1 >= 0)x += m2[i-1][j-1];
m2[i][j] = x % mod;
}
}
long[] ret = new long[m];
ret[0] = 1;
long[] temp = new long[2*m];
for(int l = 62;l >= 0;l--){
if(n<<~l<0){
for(int i = 0;i < m;i++)temp[i] = ret[m-1] * co[i];
for(int i = 1;i < m;i++)temp[i] += ret[i-1];
for(int i = 0;i < m;i++)ret[i] = temp[i] % mod;
}
if(l > 0){
Arrays.fill(temp, 0L);
for(int i = 0;i < m;i++){
for(int j = 0;j < m;j++){
temp[i+j] += ret[i] * ret[j] % mod;
}
}
for(int i = 0;i < 2*m-1;i++){
temp[i] %= mod;
}
for(int i = 0;i < m;i++){
long s = temp[i];
for(int j = m;j < 2*m-1;j++){
s += temp[j] * m2[j-m][i] % mod;
}
ret[i] = s % mod;
}
}
}
long s = 0;
for(int i = 0;i < m;i++){
s += ret[i] * a[i] % mod;
}
return s % mod;
}
public static long dot(long[] a, long[] b, int mod)
{
long s = 0;
for(int i = 0;i < a.length;i++){
s += a[i] * b[i];
s %= mod;
}
return s;
}
//////////
public static long[] modifiedBerlekampMassey(long[] a, int mod)
{
assert a.length % 2 == 0;
int n = a.length/2;
int m = 2*n-1;
long[] R0 = new long[2*n+1]; R0[2*n] = 1;
long[] R1 = new long[2*n];
for(int i = 0;i < 2*n;i++)R1[i] = a[m-i];
R1 = strip(R1);
long[] v0 = {0L};
long[] v1 = {1L};
while(n <= R1.length-1){
long[][] QR = divmod(R0, R1, mod);
long[] v = sub(v0, mul(QR[0], v1, mod), mod);
v0 = v1; v1 = v; R0 = R1; R1 = QR[1];
}
// normalize
long z = invl(v1[v1.length-1], mod);
for(int i = 0;i < v1.length;i++){
v1[i] = v1[i] * z % mod;
}
return strip(v1);
}
public static long[] mul(long[] a, long[] b, int mod)
{
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];
c[i+j] %= mod;
}
}
return strip(c);
}
public static long[] sub(long[] a, long[] b, int mod)
{
long[] c = Arrays.copyOf(a, Math.max(a.length, b.length));
for(int i = 0;i < c.length;i++){
c[i] -= b[i];
if(c[i] < 0)c[i] += mod;
}
return strip(c);
}
public static long[] strip(long[] a)
{
int i;
for(i = a.length-1;i > 0 && a[i] == 0;i--);
if(i + 1 == a.length)return a;
return Arrays.copyOf(a, i+1);
}
public static long[][] divmod(long[] A, long[] B, int mod)
{
assert B[B.length-1] != 0;
long[] R = Arrays.copyOf(A, A.length);
long[] Q = new long[Math.max(1, A.length-B.length+1)];
long ib = invl(B[B.length-1], mod);
for(int i = A.length-1, t = Q.length-1;i >= B.length-1;i--,t--){
long m = R[i] * ib % mod;
Q[t] = m;
for(int j = 0, k = i-B.length+1+j;j < B.length;j++,k++){
R[k] -= B[j] * m;
R[k] %= mod;
if(R[k] < 0)R[k] += mod;
}
assert R[i] == 0;
}
return new long[][]{Q, strip(R)};
}
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 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 long guessDirectly2(long mod, long x, int[][] fif, long... y)
{
int n = y.length;
if(0 <= x && x < n){
return y[(int)x];
}else{
x %= mod;
long s = 0;
long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod;
long[] left = new long[n+1];
left[0] = 1;
for(int i = 0;i < n;i++){
left[i+1] = left[i] * (x-i) % mod;
}
long right = 1;
for(int i = n-1;i >= 0;i--){
s += left[i] * right % mod * fif[1][i] % mod * fif[1][n-1-i] % mod * y[i];
if(s >= big)s -= big;
if(s <= -big)s += big;
right = right * -(x-i) % mod;
}
s %= mod;
if(s < 0)s += mod;
return s;
}
}
public static void main(String[] args) {
new F().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[] 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)); }
}