結果
| 問題 | No.1533 Don't be Negative! |
| ユーザー |
 uwi
|
| 提出日時 | 2021-06-04 22:34:53 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 339 ms / 8,000 ms |
| コード長 | 16,608 bytes |
| コンパイル時間 | 5,031 ms |
| コンパイル使用メモリ | 85,492 KB |
| 実行使用メモリ | 57,328 KB |
| 最終ジャッジ日時 | 2023-08-12 15:36:59 |
| 合計ジャッジ時間 | 22,688 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge9 |
（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 | 172 ms
56,232 KB |
| testcase_01 | AC | 212 ms
56,808 KB |
| testcase_02 | AC | 222 ms
56,640 KB |
| testcase_03 | AC | 235 ms
56,584 KB |
| testcase_04 | AC | 172 ms
56,352 KB |
| testcase_05 | AC | 201 ms
56,684 KB |
| testcase_06 | AC | 216 ms
56,856 KB |
| testcase_07 | AC | 177 ms
56,468 KB |
| testcase_08 | AC | 170 ms
56,580 KB |
| testcase_09 | AC | 222 ms
56,396 KB |
| testcase_10 | AC | 202 ms
56,332 KB |
| testcase_11 | AC | 275 ms
56,452 KB |
| testcase_12 | AC | 249 ms
56,196 KB |
| testcase_13 | AC | 217 ms
56,348 KB |
| testcase_14 | AC | 201 ms
56,384 KB |
| testcase_15 | AC | 243 ms
56,472 KB |
| testcase_16 | AC | 276 ms
56,736 KB |
| testcase_17 | AC | 192 ms
56,300 KB |
| testcase_18 | AC | 268 ms
56,584 KB |
| testcase_19 | AC | 255 ms
56,384 KB |
| testcase_20 | AC | 240 ms
56,536 KB |
| testcase_21 | AC | 254 ms
56,776 KB |
| testcase_22 | AC | 229 ms
56,548 KB |
| testcase_23 | AC | 151 ms
55,792 KB |
| testcase_24 | AC | 234 ms
56,256 KB |
| testcase_25 | AC | 271 ms
56,736 KB |
| testcase_26 | AC | 243 ms
57,328 KB |
| testcase_27 | AC | 217 ms
56,680 KB |
| testcase_28 | AC | 270 ms
56,448 KB |
| testcase_29 | AC | 291 ms
56,680 KB |
| testcase_30 | AC | 338 ms
56,988 KB |
| testcase_31 | AC | 231 ms
56,544 KB |
| testcase_32 | AC | 252 ms
56,864 KB |
| testcase_33 | AC | 297 ms
56,076 KB |
| testcase_34 | AC | 180 ms
56,480 KB |
| testcase_35 | AC | 150 ms
56,128 KB |
| testcase_36 | AC | 322 ms
56,416 KB |
| testcase_37 | AC | 265 ms
56,416 KB |
| testcase_38 | AC | 311 ms
56,700 KB |
| testcase_39 | AC | 265 ms
56,576 KB |
| testcase_40 | AC | 307 ms
56,472 KB |
| testcase_41 | AC | 271 ms
56,824 KB |
| testcase_42 | AC | 298 ms
56,600 KB |
| testcase_43 | AC | 267 ms
56,692 KB |
| testcase_44 | AC | 262 ms
56,640 KB |
| testcase_45 | AC | 298 ms
56,680 KB |
| testcase_46 | AC | 283 ms
56,652 KB |
| testcase_47 | AC | 309 ms
56,560 KB |
| testcase_48 | AC | 305 ms
56,620 KB |
| testcase_49 | AC | 262 ms
56,272 KB |
| testcase_50 | AC | 331 ms
56,472 KB |
| testcase_51 | AC | 335 ms
56,700 KB |
| testcase_52 | AC | 310 ms
56,560 KB |
| testcase_53 | AC | 325 ms
56,456 KB |
| testcase_54 | AC | 324 ms
56,576 KB |
| testcase_55 | AC | 339 ms
56,540 KB |
| testcase_56 | AC | 300 ms
57,088 KB |
ソースコード
package contest210604;
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 G {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
int n = ni(), M = ni(), K = ni();
final int mod = 998244353;
long[] dp = new long[2000];
int o = 1000;
dp[o] = 1;
long[] a = new long[200];
for(int i = 1;i <= 199;i++){
long[] ndp = new long[2000];
for(int j = 0;j < 2000;j++){
if(dp[j] == 0)continue;
for(int l = -M;l <= M;l++){
if(l == -K || l == K)continue;
ndp[j+l] += dp[j];
}
}
for(int j = 0;j < 2000;j++){
ndp[j] %= mod;
}
for(int j = 0;j < o;j++){
a[i] += ndp[j];
}
a[i] %= mod;
dp = ndp;
}
long[] hey = interpolate(n+1, mod, a);
long ans = 0;
int kk = 2*M+1 - (K == 0 ? 1 : 2);
for(int len = 1;len <= n;len++){
ans += hey[len] * (n-len+1) % mod * pow(kk, n-len, mod);
ans %= mod;
}
out.println(ans);
}
public 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;
}
public static long[] interpolate(int n, int mod, long... base)
{
int m = base.length;
long[][] res = guessLeaned(mod, base);
return interpolate(res, Arrays.copyOf(base, n+1), m, n+1, mod);
}
public static long[][] guessLeaned(int mod, long... a)
{
int n = a.length;
// #formula >= #variable
// n-r+2 >= r(r+1)/2
for(int r = n;r >= 1;r--){
if(n-r+2 < r*(r+1)/2)continue;
int[][] M = new int[n-r+2][r*(r+1)/2];
for(int i = 0;i < n-r+1;i++){
int p = 0;
for(int j = 0;j < r;j++){
long prod = 1;
for(int k = 0;k <= r-j-1;k++){
M[i][p++] = (int)(prod*a[i+j]%mod);
prod = prod * i % mod;
}
}
}
M[n-r+1][0] = 1;
int[] v = new int[n-r+2];
v[n-r+1] = 1;
Result res = gaussElimination(M, v, mod);
if(res.exists){
long[][] ret = new long[r][];
int p = 0;
for(int i = 0;i < r;i++){
ret[i] = new long[r-i];
for(int j = 0;j < r-i;j++){
ret[i][j] = res.sol[p++];
}
}
// reformat
int ilast = r;
for(int i = r-1;i >= 0;i--){
int last = ret[i].length;
while(last > 0 && ret[i][last-1] == 0)last--;
ret[i] = Arrays.copyOf(ret[i], last);
if(last == 0 && i+1 == ilast){
ilast--;
}
}
ret = Arrays.copyOf(ret, ilast);
return ret;
}
}
return null;
}
public static Result gaussElimination(int[][] M, int[] v, int mod)
{
int n = M.length, m = M[0].length;
int[] head = new int[n];
// if not needed, comment out.
for(int[] row : M){
for(int i = 0;i < row.length;i++){
row[i] %= mod;
if(row[i] < 0)row[i] += mod;
}
}
// Forward Elimination
int row = 0;
for(int col = 0;col < m;col++){
// select pivot
boolean pivotFound = false;
out:
for(int prow = row;prow < n;prow++){
if(M[prow][col] != 0){
// pivot found
if(prow != row){
// swap rows
for(int k = 0;k < m;k++){
int u = M[prow][k]; M[prow][k] = M[row][k]; M[row][k] = u;
}
int dum = v[prow]; v[prow] = v[row]; v[row] = dum;
}
pivotFound = true;
break out;
}
}
if(!pivotFound)continue;
head[row] = col;
// diag to 1
long imul = invl(M[row][col], mod);
for(int k = 0;k < m;k++){
M[row][k] = (int)(M[row][k] * imul % mod);
}
v[row] = (int)(v[row] * imul % mod);
for(int j = row+1;j < n;j++){
if(M[j][col] != 0){
long mul = mod-M[j][col];
for(int k = col;k < m;k++){
M[j][k] = (int)((M[j][k] + M[row][k] * mul) % mod);
}
v[j] = (int)((v[j] + v[row] * mul) % mod);
}
}
row++;
}
Result ret = new Result();
ret.mat = M;
for(int i = row;i < n;i++){
if(v[i] != 0){
ret.rank = row;
ret.exists = false;
return ret;
}
}
for(int i = row-1;i >= 0;i--){
for(int j = i-1;j >= 0;j--){
if(M[j][head[i]] != 0){
long mul = mod-M[j][head[i]];
for(int k = head[i];k < m;k++){
M[j][k] = (int)((M[j][k] + M[i][k] * mul) % mod);
}
v[j] = (int)((v[j] + v[i] * mul) % mod);
}
}
}
int[] retv = new int[m];
for(int i = 0;i < row;i++){
retv[head[i]] = v[i];
}
ret.sol = retv;
ret.rank = row;
ret.exists = true;
return ret;
}
public static class Result
{
public int[][] mat;
public int[] sol;
public int rank;
public boolean exists;
}
/**
* vals[0,x-1]の情報を利用してvals[x]を埋める
* @param ged
* @param vals
* @param x
* @param mod
*/
public static long[] interpolate(long[][] ged, long[] vals, int l, int r, int mod)
{
int n = ged.length;
for(int x = l, xx = x-(n-1);x < r;x++, xx++){
int pos = x;
long s = 0;
long tar = 0;
for(int i = 0;i < n;i++){
long co = 0;
for(int j = ged[i].length-1;j >= 0;j--){
co = (co * xx + ged[i][j]) % mod;
}
if(i < n-1){
s += co * vals[i+xx];
s %= mod;
}else{
tar = co;
}
}
long ret = (mod-invl(tar, mod)) * s % mod;
vals[pos] = ret;
}
return vals;
}
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 G().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)); }
}