結果
| 問題 | No.2747 Permutation Adjacent Sum |
| ユーザー |
 Yu_212
|
| 提出日時 | 2024-04-20 16:18:31 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 14,646 bytes |
| コンパイル時間 | 3,905 ms |
| コンパイル使用メモリ | 103,532 KB |
| 実行使用メモリ | 271,904 KB |
| 最終ジャッジ日時 | 2024-10-12 12:05:53 |
| 合計ジャッジ時間 | 12,476 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / 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 | TLE | - |
| testcase_01 | -- | - |
| testcase_02 | -- | - |
| testcase_03 | -- | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
ソースコード
import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import static java.lang.Math.min;
public class Main {
static In in = new In();
static Out out = new Out(false, false);
static final long inf = 0x1fffffffffffffffL;
static final int iinf = 0x3fffffff;
static final double eps = 1e-9;
static long mod = 998244353;
void solve() {
long n = in.nextLong();
int k = in.nextInt();
long a1 = f(n - 1, k);
long a2 = f(n - 1, k + 1);
long temp = (n * a1 + mod - a2) % mod;
long fact = 1;
for (long i = 2; i < n; i++) {
fact = fact * i % mod;
}
out.println(fact * 2 * temp % mod);
}
long f(long n, int k) {
long[] y = new long[k + 2];
for (int i = 1; i < k + 2; i++) {
y[i] = (y[i - 1] + Comb.pow(i, k)) % mod;
}
return lagrange(y, n);
}
public long lagrange(long[] y, long t) {
int n = y.length - 1;
if (t <= n) {
return y[(int)t];
}
long ret = 0;
long[] dp = new long[n + 1];
long[] pd = new long[n + 1];
dp[0] = 1;
pd[n] = 1;
for (int i = 0; i < n; i++) {
dp[i + 1] = dp[i] * ((t - i) % mod) % mod;
}
for (int i = n; i > 0; i--) {
pd[i - 1] = pd[i] * ((t - i) % mod) % mod;
}
for (int i = 0; i <= n; i++) {
long temp = y[i] * dp[i] % mod * pd[i] % mod * Comb.invFact(i) % mod * Comb.invFact(n - i) % mod;
if (((n - i) & 1) == 1) {
ret = (ret + mod - temp) % mod;
} else {
ret = (ret + temp) % mod;
}
}
return ret;
}
public static void main(String... args) {
new Main().solve();
out.flush();
}
}
class Comb {
private static final int MEMO_THRESHOLD = 1000000;
static long mod = Main.mod;
private static final List<Long> inv = new ArrayList<>();
private static final List<Long> fact = new ArrayList<>();
private static final List<Long> invFact = new ArrayList<>();
private static final Map<Long, List<Long>> pow = new HashMap<>();
private static void buildInvTable(int n) {
if (inv.isEmpty()) {
inv.add(null);
inv.add(1L);
}
for (int i = inv.size(); i <= n; i++) {
inv.add(mod - inv.get((int)(mod % i)) * (mod / i) % mod);
}
}
private static void buildFactTable(int n) {
if (fact.isEmpty()) {
fact.add(1L);
invFact.add(1L);
}
for (int i = fact.size(); i <= n; i++) {
fact.add(fact.get(i - 1) * i % mod);
invFact.add(inv(fact.get(i)));
}
}
public static void setupPowTable(long a) {
pow.put(a, new ArrayList<>(Collections.singleton(1L)));
}
private static void rangeCheck(long n, long r) {
if (n < r) {
throw new IllegalArgumentException("n < r");
}
if (n < 0) {
throw new IllegalArgumentException("n < 0");
}
if (r < 0) {
throw new IllegalArgumentException("r < 0");
}
}
static long fact(int n) {
buildFactTable(n);
return fact.get(n);
}
static long invFact(int n) {
buildFactTable(n);
return invFact.get(n);
}
private static long comb0(int n, int r) {
rangeCheck(n, r);
return fact(n) * invFact(r) % mod * invFact(n - r) % mod;
}
static long comb(long n, long r) {
rangeCheck(n, r);
if (n < MEMO_THRESHOLD) {
return comb0((int)n, (int)r);
}
r = min(r, n - r);
long x = 1, y = 1;
for (long i = 1; i <= r; i++) {
x = x * (n - r + i) % mod;
y = y * i % mod;
}
return x * inv(y) % mod;
}
private static long perm0(int n, int r) {
rangeCheck(n, r);
return fact(n) * invFact(n - r) % mod;
}
static long perm(long n, long r) {
rangeCheck(n, r);
if (n < MEMO_THRESHOLD) {
return perm0((int)n, (int)r);
}
long x = 1;
for (long i = 1; i <= r; i++) {
x = x * (n - r + i) % mod;
}
return x;
}
static long homo(long n, long r) {
return r == 0 ? 1 : comb(n + r - 1, r);
}
private static long inv0(int a) {
buildInvTable(a);
return inv.get(a);
}
static long inv(long a) {
if (a < MEMO_THRESHOLD) {
return inv0((int)a);
}
long b = mod;
long u = 1, v = 0;
while (b >= 1) {
long t = a / b;
a -= t * b;
u -= t * v;
if (a < 1) {
return (v %= mod) < 0 ? v + mod : v;
}
t = b / a;
b -= t * a;
v -= t * u;
}
return (u %= mod) < 0 ? u + mod : u;
}
static long pow(long a, long b) {
if (pow.containsKey(a) && b < MEMO_THRESHOLD) {
return powMemo(a, (int)b);
}
long x = 1;
while (b > 0) {
if (b % 2 == 1) {
x = x * a % mod;
}
a = a * a % mod;
b >>= 1;
}
return x;
}
static long powMemo(long a, int b) {
List<Long> powMemo = pow.get(a);
while (powMemo.size() <= b) {
powMemo.add(powMemo.get(powMemo.size() - 1) * a % mod);
}
return powMemo.get(b);
}
static long sqrt(long x) {
if (x < 2) {
return x;
}
long p = (mod - 1) / 2;
if (pow(x, p) != 1) {
return -1;
}
while (true) {
long a = ThreadLocalRandom.current().nextLong(mod);
long w = (a * a + mod - x) % mod;
if (pow(w, p) == 1) {
continue;
}
long n = p + 1;
long k = Long.highestOneBit(n);
long r = 1;
long i = 0;
while (k > 0) {
long nr = (r * r + i * i % mod * w) % mod;
long ni = r * i * 2 % mod;
r = nr;
i = ni;
if ((n & k) > 0) {
nr = (r * a + i * w) % mod;
ni = (i * a + r) % mod;
r = nr;
i = ni;
}
k >>= 1;
}
return min(r, mod - r);
}
}
}
class In {
private final BufferedInputStream reader = new BufferedInputStream(System.in);
private final byte[] buffer = new byte[0x10000];
private int i = 0;
private int length = 0;
public int read() {
if (i == length) {
i = 0;
try {
length = reader.read(buffer);
} catch (IOException ignored) {
}
if (length == -1) {
return 0;
}
}
if (length <= i) {
throw new RuntimeException();
}
return buffer[i++];
}
public String next() {
StringBuilder builder = new StringBuilder();
int b = read();
while (b < '!' || '~' < b) {
b = read();
}
while ('!' <= b && b <= '~') {
builder.appendCodePoint(b);
b = read();
}
return builder.toString();
}
public String nextLine() {
StringBuilder builder = new StringBuilder();
int b = read();
while (b != 0 && b != '\r' && b != '\n') {
builder.appendCodePoint(b);
b = read();
}
if (b == '\r') {
read();
}
return builder.toString();
}
public int nextInt() {
long val = nextLong();
if (val < Integer.MIN_VALUE || Integer.MAX_VALUE < val) {
throw new NumberFormatException();
}
return (int)val;
}
public long nextLong() {
int b = read();
while (b < '!' || '~' < b) {
b = read();
}
boolean neg = false;
if (b == '-') {
neg = true;
b = read();
}
long n = 0;
int c = 0;
while ('0' <= b && b <= '9') {
n = n * 10 + b - '0';
b = read();
c++;
}
if (c == 0 || c >= 2 && n == 0) {
throw new NumberFormatException();
}
return neg ? -n : n;
}
public double nextDouble() {
return Double.parseDouble(next());
}
public char[] nextCharArray() {
return next().toCharArray();
}
public String[] nextStringArray(int n) {
String[] s = new String[n];
for (int i = 0; i < n; i++) {
s[i] = next();
}
return s;
}
public char[][] nextCharMatrix(int n, int m) {
char[][] a = new char[n][m];
for (int i = 0; i < n; i++) {
a[i] = next().toCharArray();
}
return a;
}
public int[] nextIntArray(int n) {
int[] a = new int[n];
for (int i = 0; i < n; i++) {
a[i] = nextInt();
}
return a;
}
public int[] nextIntArray(int n, IntUnaryOperator op) {
int[] a = new int[n];
for (int i = 0; i < n; i++) {
a[i] = op.applyAsInt(nextInt());
}
return a;
}
public int[][] nextIntMatrix(int h, int w) {
int[][] a = new int[h][w];
for (int i = 0; i < h; i++) {
a[i] = nextIntArray(w);
}
return a;
}
public long[] nextLongArray(int n) {
long[] a = new long[n];
for (int i = 0; i < n; i++) {
a[i] = nextLong();
}
return a;
}
public long[] nextLongArray(int n, LongUnaryOperator op) {
long[] a = new long[n];
for (int i = 0; i < n; i++) {
a[i] = op.applyAsLong(nextLong());
}
return a;
}
public long[][] nextLongMatrix(int h, int w) {
long[][] a = new long[h][w];
for (int i = 0; i < h; i++) {
a[i] = nextLongArray(w);
}
return a;
}
public List<List<Integer>> nextGraph(int n, int m, boolean directed) {
List<List<Integer>> res = new ArrayList<>();
for (int i = 0; i < n; i++) {
res.add(new ArrayList<>());
}
for (int i = 0; i < m; i++) {
int u = nextInt() - 1;
int v = nextInt() - 1;
res.get(u).add(v);
if (!directed) {
res.get(v).add(u);
}
}
return res;
}
}
class Out {
private final PrintWriter out = new PrintWriter(System.out);
private final PrintWriter err = new PrintWriter(System.err);
public boolean autoFlush;
public boolean enableDebug;
public Out(boolean autoFlush, boolean enableDebug) {
this.autoFlush = autoFlush;
this.enableDebug = enableDebug;
}
public void debug(Object... args) {
if (!enableDebug) {
return;
}
if (args == null || args.getClass() != Object[].class) {
args = new Object[] {args};
}
err.println(Arrays.stream(args).map(obj -> format(obj, true)).collect(Collectors.joining(" ")));
err.flush();
}
private String format(Object obj, boolean canMultiline) {
if (obj == null) return "null";
Class<?> clazz = obj.getClass();
if (clazz == Double.class) return String.format("%.10f", obj);
if (clazz == int[].class) return Arrays.toString((int[])obj);
if (clazz == long[].class) return Arrays.toString((long[])obj);
if (clazz == char[].class) return String.valueOf((char[])obj);
if (clazz == boolean[].class) return IntStream.range(0, ((boolean[])obj).length).mapToObj(i -> ((boolean[])obj)[i] ? "1" : "0").collect(Collectors.joining());
if (clazz == double[].class) return Arrays.toString(Arrays.stream((double[])obj).mapToObj(a -> format(a, false)).toArray());
if (canMultiline && clazz.isArray() && clazz.componentType().isArray()) return Arrays.stream((Object[])obj).map(a -> format(a, false)).collect(Collectors.joining("\n"));
if (clazz == Object[].class) return Arrays.toString(Arrays.stream((Object[])obj).map(a -> format(a, false)).toArray());
if (clazz.isArray()) return Arrays.toString((Object[])obj);
return String.valueOf(obj);
}
public void println(Object... args) {
if (args == null || args.getClass() != Object[].class) {
args = new Object[] {args};
}
out.println(Arrays.stream(args)
.map(obj -> obj instanceof Double ? String.format("%.10f", obj) : String.valueOf(obj))
.collect(Collectors.joining(" ")));
if (autoFlush) {
out.flush();
}
}
public void println(char a) {
out.println(a);
if (autoFlush) {
out.flush();
}
}
public void println(int a) {
out.println(a);
if (autoFlush) {
out.flush();
}
}
public void println(long a) {
out.println(a);
if (autoFlush) {
out.flush();
}
}
public void println(double a) {
out.println(String.format("%.10f", a));
if (autoFlush) {
out.flush();
}
}
public void println(String s) {
out.println(s);
if (autoFlush) {
out.flush();
}
}
public void println(char[] s) {
out.println(String.valueOf(s));
if (autoFlush) {
out.flush();
}
}
public void println(int[] a) {
StringJoiner joiner = new StringJoiner(" ");
for (int i : a) {
joiner.add(Integer.toString(i));
}
out.println(joiner);
if (autoFlush) {
out.flush();
}
}
public void println(long[] a) {
StringJoiner joiner = new StringJoiner(" ");
for (long i : a) {
joiner.add(Long.toString(i));
}
out.println(joiner);
if (autoFlush) {
out.flush();
}
}
public void flush() {
err.flush();
out.flush();
}
}