#655398 (C) No.1504 ヌメロニム

提出ソース

結果

問題	No.1504 ヌメロニム
ユーザー	ygussany
提出日時	2021-05-07 23:31:29
言語	C (gcc 12.3.0)
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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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	11 ms 14,080 KB
testcase_01	AC	11 ms 14,208 KB
testcase_02	AC	11 ms 14,080 KB
testcase_03	AC	11 ms 14,080 KB
testcase_04	AC	11 ms 14,080 KB
testcase_05	AC	11 ms 14,080 KB
testcase_06	AC	11 ms 14,080 KB
testcase_07	AC	11 ms 14,080 KB
testcase_08	AC	11 ms 14,080 KB
testcase_09	AC	11 ms 14,208 KB
testcase_10	AC	11 ms 13,952 KB
testcase_11	AC	11 ms 14,080 KB
testcase_12	AC	11 ms 14,080 KB
testcase_13	AC	11 ms 13,952 KB
testcase_14	AC	11 ms 14,080 KB
testcase_15	AC	11 ms 14,208 KB
testcase_16	AC	11 ms 14,208 KB
testcase_17	AC	11 ms 14,080 KB
testcase_18	AC	10 ms 14,208 KB
testcase_19	AC	11 ms 14,080 KB
testcase_20	AC	14 ms 14,592 KB
testcase_21	AC	12 ms 14,208 KB
testcase_22	AC	13 ms 14,464 KB
testcase_23	AC	11 ms 14,208 KB
testcase_24	AC	514 ms 63,644 KB
testcase_25	AC	252 ms 40,000 KB
testcase_26	AC	517 ms 64,048 KB
testcase_27	AC	254 ms 40,676 KB
testcase_28	AC	255 ms 40,808 KB
testcase_29	AC	535 ms 63,912 KB
testcase_30	AC	518 ms 63,916 KB
testcase_31	AC	255 ms 40,396 KB
testcase_32	AC	257 ms 40,672 KB
testcase_33	AC	524 ms 63,912 KB
testcase_34	AC	68 ms 20,456 KB
testcase_35	AC	67 ms 20,188 KB
testcase_36	AC	252 ms 39,032 KB
testcase_37	AC	38 ms 17,060 KB
testcase_38	AC	525 ms 64,056 KB
testcase_39	AC	521 ms 64,180 KB
testcase_40	AC	515 ms 64,056 KB
testcase_41	AC	519 ms 64,052 KB
testcase_42	AC	516 ms 64,180 KB
testcase_43	AC	518 ms 64,184 KB
testcase_44	AC	518 ms 64,060 KB
testcase_45	AC	516 ms 64,056 KB
testcase_46	AC	522 ms 64,056 KB
testcase_47	AC	522 ms 64,180 KB
testcase_48	AC	257 ms 40,396 KB
testcase_49	AC	255 ms 39,996 KB
testcase_50	AC	13 ms 14,592 KB
testcase_51	AC	12 ms 14,336 KB
testcase_52	AC	10 ms 14,080 KB
testcase_53	AC	13 ms 14,336 KB
testcase_54	AC	11 ms 14,208 KB
testcase_55	AC	66 ms 20,180 KB
testcase_56	AC	11 ms 14,080 KB
testcase_57	AC	11 ms 14,080 KB
testcase_58	AC	11 ms 14,208 KB
testcase_59	AC	11 ms 14,080 KB
testcase_60	AC	11 ms 14,208 KB

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ソースコード

raw source code

#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;
}

yukicoder

結果

テストケース

ソースコード