結果

問題 No.1504 ヌメロニム
コンテスト
ユーザー 👑 ygussany
提出日時 2021-05-07 23:31:29
言語 C
(gcc 13.3.0)
結果
AC  
実行時間 535 ms / 2,000 ms
コード長 3,599 bytes
コンパイル時間 463 ms
コンパイル使用メモリ 34,432 KB
実行使用メモリ 64,184 KB
最終ジャッジ日時 2024-09-15 11:37:18
合計ジャッジ時間 12,760 ms
ジャッジサーバーID
（参考情報） 		judge6 / judge2
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ファイルパターン 結果
other AC * 61
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], tmpp;
	long long tmp;
	static int *b[21] = {}, *c[21] = {}, *x[21] = {}, *y[21] = {};
	if (b[k] == NULL) {
		b[k] = (int*)malloc(sizeof(int) * d);
		c[k] = (int*)malloc(sizeof(int) * d);
		x[k] = (int*)malloc(sizeof(int) * d);
		y[k] = (int*)malloc(sizeof(int) * d);
	}
	for (i = 0; i < d; i++) {
		b[k][i] = a[i*2];
		c[k][i] = a[i*2+1];
	}
	NTT(k - 1, b[k], x[k]);
	NTT(k - 1, c[k], y[k]);
	for (i = 0, tmp = 1; i < d; i++, tmp = tmp * root[k] % Mod) {
		tmpp = tmp * y[k][i] % Mod;
		z[i] = x[k][i] + tmpp;
		if (z[i] >= Mod) z[i] -= Mod;
		z[i+d] = x[k][i] - tmpp;
		if (z[i+d] < 0) z[i+d] += Mod;
	}
}

void NTT_reverse(int k, int z[], int a[])
{
	if (k == 0) {
		a[0] = z[0];
		return;
	}
	
	int i, d = bit[k-1], tmpp;
	long long tmp;
	static int *b[21] = {}, *c[21] = {}, *x[21] = {}, *y[21] = {};
	if (b[k] == NULL) {
		b[k] = (int*)malloc(sizeof(int) * d);
		c[k] = (int*)malloc(sizeof(int) * d);
		x[k] = (int*)malloc(sizeof(int) * d);
		y[k] = (int*)malloc(sizeof(int) * d);
	}
	for (i = 0; i < d; i++) {
		x[k][i] = z[i*2];
		y[k][i] = z[i*2+1];
	}
	NTT_reverse(k - 1, x[k], b[k]);
	NTT_reverse(k - 1, y[k], c[k]);
	for (i = 0, tmp = 1; i < d; i++, tmp = tmp * root_inv[k] % Mod) {
		tmpp = tmp * c[k][i] % Mod;
		a[i] = b[k][i] + tmpp;
		if (a[i] >= Mod) a[i] -= Mod;
		a[i+d] = b[k][i] - tmpp;
		if (a[i+d] < 0) a[i+d] += Mod;
	}
}

void prod_poly_NTT(int da, int db, int a[], int b[], int c[])
{
	int i, k;
	for (k = 0, bit[0] = 1; bit[k] < da + db - 1; 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;
	}
	
	int *x = (int*)malloc(sizeof(int) * bit[k]), *y = (int*)malloc(sizeof(int) * bit[k]), *z = (int*)malloc(sizeof(int) * bit[k]);
	NTT(k, a, x);
	NTT(k, b, y);
	for (i = 0; i < bit[k]; i++) z[i] = (long long)x[i] * y[i] % Mod;
	NTT_reverse(k, z, c);
	for (i = 0; i < da + db - 1; i++) c[i] = (long long)c[i] * bit_inv[k] % Mod;
	
	free(x);
	free(y);
	free(z);
}

int main()
{
	int i, N;
	char S[300001];
	scanf("%d", &N);
	scanf("%s", S);
	
	int a[1048576] = {}, b[1048576] = {}, c[1048576] = {};
	for (i = 0; i < N; i++) {
		if (S[i] == 'i') a[N-i-1] = 1;
		else b[i] = 1;
	}
	prod_poly_NTT(N, N, a, b, c);
	
	long long ans = 0, fact[300001], fact_inv[300001];
	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 (i = N; i < N * 2 - 1; i++) a[i-N] = c[i] * fact[i-N] % Mod;
	for (i = N - 1; i < 1048576; i++) a[i] = 0;
	for (i = 0; i < N - 1; i++) b[i] = fact_inv[N-2-i];
	for (i = N - 1; i < 1048576; i++) b[i] = 0;
	prod_poly_NTT(N - 1, N - 1, a, b, c);
	for (i = 0; i < N - 1; i++) ans ^= c[i+N-2] * fact_inv[i] % Mod;
	printf("%lld\n", ans);
	fflush(stdout);
	return 0;
}
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