#975527 (Java) No.2747 Permutation Adjacent Sum

• 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: Java (openjdk 23)
• 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

ファイルパターン	結果
sample	-- * 2
other	TLE * 1 -- * 39

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();
    }
}