結果

問題 No.1302 Random Tree Score
コンテスト
ユーザー 👑 ygussany
提出日時 2020-12-01 14:34:44
言語 C
(gcc 13.3.0)
結果
AC  
実行時間 2,070 ms / 3,000 ms
コード長 3,188 bytes
コンパイル時間 517 ms
コンパイル使用メモリ 34,676 KB
実行使用メモリ 11,656 KB
最終ジャッジ日時 2024-09-13 02:58:59
合計ジャッジ時間 16,784 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <stdio.h>
#include <stdlib.h>

const int Mod = 998244353;
int bit[21], bit_inv[21], root[21], root_inv[21];

long long div_mod(long long x, long long y, long long z)
{
	if (x % y == 0) return x / y;
	else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}

long long pow_mod(int n, int k)
{
	long long N, ans = 1;
	for (N = n; k > 0; k >>= 1, N = N * N % Mod) if (k & 1) ans = ans * N % Mod;
	return ans;
}

void NTT(int k, int a[], int z[])
{
	if (k == 0) {
		z[0] = a[0];
		return;
	}
	
	int i, d = bit[k-1];
	long long tmp;
	int tmpp, *b = (int*)malloc(sizeof(int) * d), *c = (int*)malloc(sizeof(int) * d), *x = (int*)malloc(sizeof(int) * d), *y = (int*)malloc(sizeof(int) * d);
	for (i = 0; i < d; i++) {
		b[i] = a[i*2];
		c[i] = a[i*2+1];
	}
	NTT(k - 1, b, x);
	NTT(k - 1, c, y);
	for (i = 0, tmp = 1; i < d; i++, tmp = tmp * root[k] % Mod) {
		tmpp = tmp * y[i] % Mod;
		z[i] = x[i] + tmpp;
		if (z[i] >= Mod) z[i] -= Mod;
		z[i+d] = x[i] - tmpp;
		if (z[i+d] < 0) z[i+d] += Mod;
	}
	
	free(b);
	free(c);
	free(x);
	free(y);
}

void NTT_reverse(int k, int z[], int a[])
{
	if (k == 0) {
		a[0] = z[0];
		return;
	}
	
	int i, d = bit[k-1];
	long long tmp;
	int tmpp, *b = (int*)malloc(sizeof(int) * d), *c = (int*)malloc(sizeof(int) * d), *x = (int*)malloc(sizeof(int) * d), *y = (int*)malloc(sizeof(int) * d);
	for (i = 0; i < d; i++) {
		x[i] = z[i*2];
		y[i] = z[i*2+1];
	}
	NTT_reverse(k - 1, x, b);
	NTT_reverse(k - 1, y, c);
	for (i = 0, tmp = 1; i < d; i++, tmp = tmp * root_inv[k] % Mod) {
		tmpp = tmp * c[i] % Mod;
		a[i] = b[i] + tmpp;
		if (a[i] >= Mod) a[i] -= Mod;
		a[i+d] = b[i] - tmpp;
		if (a[i+d] < 0) a[i+d] += Mod;
	}
	
	free(b);
	free(c);
	free(x);
	free(y);
}

int main()
{
	int N;
	scanf("%d", &N);
	
	int i, j, k, a[262145], x[262145], y[262145], ans[262145] = {};
	long long fact[100001], fact_inv[100001];
	for (i = 1, fact[0] = 1; i <= N; i++) fact[i] = fact[i-1] * i % Mod;
	for (i = N - 1, fact_inv[N] = div_mod(1, fact[N], Mod); i >= 0; i--) fact_inv[i] = fact_inv[i+1] * (i + 1) % Mod;
	for (k = 0, bit[0] = 1; bit[k] < N * 2; k++) bit[k+1] = bit[k] * 2;
	for (i = k - 1, bit_inv[k] = div_mod(1, bit[k], Mod); i >= 0; i--) bit_inv[i] = bit_inv[i+1] * 2 % Mod;
	for (i = k - 1, root[k] = pow_mod(3, (Mod - 1) / bit[k]), root_inv[k] = pow_mod(3, Mod - 1 - (Mod - 1) / bit[k]); i >= 0; i--) {
		root[i] = (long long)root[i+1] * root[i+1] % Mod;
		root_inv[i] = (long long)root_inv[i+1] * root_inv[i+1] % Mod;
	}
	
	for (i = 0; i < N - 1; i++) a[i] = fact_inv[i] * (i + 1) % Mod;
	for (j = N, ans[0] = fact[N-2]; j > 0; j >>= 1) {
		for (i = N - 1; i < bit[k]; i++) a[i] = 0;
		NTT(k, a, x);
		if ((j & 1) == 1) {
			NTT(k, ans, y);
			for (i = 0; i < bit[k]; i++) y[i] = (long long)y[i] * x[i] % Mod;
			NTT_reverse(k, y, ans);
			for (i = 0; i < N - 1; i++) ans[i] = (long long)ans[i] * bit_inv[k] % Mod;
			for (; i < bit[k]; i++) ans[i] = 0;
		}
		if (j > 1) {
			for (i = 0; i < bit[k]; i++) x[i] = (long long)x[i] * x[i] % Mod;
			NTT_reverse(k, x, a);
			for (i = 0; i < N - 1; i++) a[i] = (long long)a[i] * bit_inv[k] % Mod;
		}
	}
	printf("%lld\n", div_mod(ans[N-2], pow_mod(N, N - 2), Mod));
	fflush(stdout);
	return 0;
}
0