#864728 (C) No.2303 Frog on Grid

提出ソース

結果

問題	No.2303 Frog on Grid
ユーザー	👑 ygussany
提出日時	2023-04-29 17:04:10
言語	C (gcc 12.3.0)
結果	AC
実行時間	43 ms / 2,000 ms
コード長	4,769 bytes
コンパイル時間	307 ms
コンパイル使用メモリ	33,920 KB
実行使用メモリ	20,096 KB
最終ジャッジ日時	2024-04-29 09:24:15
合計ジャッジ時間	1,843 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
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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	1 ms 5,248 KB
testcase_01	AC	1 ms 5,376 KB
testcase_02	AC	36 ms 18,048 KB
testcase_03	AC	20 ms 9,856 KB
testcase_04	AC	40 ms 17,792 KB
testcase_05	AC	42 ms 19,072 KB
testcase_06	AC	20 ms 10,368 KB
testcase_07	AC	40 ms 17,536 KB
testcase_08	AC	38 ms 17,664 KB
testcase_09	AC	11 ms 6,016 KB
testcase_10	AC	20 ms 9,600 KB
testcase_11	AC	11 ms 6,016 KB
testcase_12	AC	22 ms 11,136 KB
testcase_13	AC	1 ms 5,376 KB
testcase_14	AC	1 ms 5,376 KB
testcase_15	AC	1 ms 5,376 KB
testcase_16	AC	1 ms 5,376 KB
testcase_17	AC	1 ms 5,376 KB
testcase_18	AC	35 ms 19,968 KB
testcase_19	AC	40 ms 19,968 KB
testcase_20	AC	43 ms 19,968 KB
testcase_21	AC	39 ms 19,840 KB
testcase_22	AC	40 ms 20,096 KB

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ソースコード

raw source code

#include <stdio.h>

const int Mod = 998244353,
	bit[22] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152},
	bit_inv[22] = {1, 499122177, 748683265, 873463809, 935854081, 967049217, 982646785, 990445569, 994344961, 996294657, 997269505, 997756929, 998000641, 998122497, 998183425, 998213889, 998229121, 998236737, 998240545, 998242449, 998243401, 998243877},
	root[22] = {1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936, 584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129, 733596141},
	root_inv[22] = {1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368, 335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366, 428961804};

void NTT_inline(int kk, int a[], int x[])
{
	int h, hh, i, ii, j, jj, k, l, r = bit[kk], d = bit[kk-1], tmpp, cur, prev;
	int *pi, *pii, *pj, *pjj;
	static int y[2][2097152];
	long long tmp;
	for (i = 0; i < r; i++) y[0][i] = a[i];
	for (k = 1, kk--, cur = 1, prev = 0; kk >= 0; k++, kk--, cur ^= 1, prev ^= 1) {
		for (h = 0, tmp = 1; h << (kk + 1) < r; h++, tmp = tmp * root[k] % Mod) {
			for (hh = 0, pi = &(y[cur][h<<kk]), pii = pi + d, pj = &(y[prev][h<<(kk+1)]), pjj = pj + bit[kk]; hh < bit[kk]; hh++, pi++, pii++, pj++, pjj++) {
				tmpp = tmp * (*pjj) % Mod;
				*pi = *pj + tmpp;
				if (*pi >= Mod) *pi -= Mod;
				*pii = *pj - tmpp;
				if (*pii < 0) *pii += Mod;
			}
		}
	}
	for (i = 0; i < r; i++) x[i] = y[prev][i];
}

void NTT_reverse_inline(int kk, int a[], int x[])
{
	int h, hh, i, ii, j, jj, k, l, r = bit[kk], d = bit[kk-1], tmpp, cur, prev;
	int *pi, *pii, *pj, *pjj;
	static int y[2][2097152];
	long long tmp;
	for (i = 0; i < r; i++) y[0][i] = a[i];
	for (k = 1, kk--, cur = 1, prev = 0; kk >= 0; k++, kk--, cur ^= 1, prev ^= 1) {
		for (h = 0, tmp = 1; h << (kk + 1) < r; h++, tmp = tmp * root_inv[k] % Mod) {
			for (hh = 0, pi = &(y[cur][h<<kk]), pii = pi + d, pj = &(y[prev][h<<(kk+1)]), pjj = pj + bit[kk]; hh < bit[kk]; hh++, pi++, pii++, pj++, pjj++) {
				tmpp = tmp * (*pjj) % Mod;
				*pi = *pj + tmpp;
				if (*pi >= Mod) *pi -= Mod;
				*pii = *pj - tmpp;
				if (*pii < 0) *pii += Mod;
			}
		}
	}
	for (i = 0; i < r; i++) x[i] = y[prev][i];
}

// Compute the product of two polynomials a[0-da] and b[0-db] using NTT in O(d * log d) time
void prod_poly_NTT(int da, int db, int a[], int b[], int c[])
{
	int i, k;
	static int aa[2097152], bb[2097152], cc[2097152];
	for (k = 0; bit[k] <= da + db; k++);
	for (i = 0; i <= da; i++) aa[i] = a[i];
	for (i = da + 1; i < bit[k]; i++) aa[i] = 0;
	for (i = 0; i <= db; i++) bb[i] = b[i];
	for (i = db + 1; i < bit[k]; i++) bb[i] = 0;
	
	static int x[2097152], y[2097152], z[2097152];
	NTT_inline(k, aa, x);
	if (db == da) {
		for (i = 0; i <= da; i++) if (a[i] != b[i]) break;
		if (i <= da) NTT_inline(k, bb, y);
		else for (i = 0; i < bit[k]; i++) y[i] = x[i];
	} else NTT_inline(k, bb, y);
	for (i = 0; i < bit[k]; i++) z[i] = (long long)x[i] * y[i] % Mod;
	NTT_reverse_inline(k, z, cc);
	for (i = 0; i <= da + db; i++) c[i] = (long long)cc[i] * bit_inv[k] % Mod;
}

// Compute the product of two polynomials a[0-da] and b[0-db] naively in O(da * db) time
void prod_poly_naive(int da, int db, int a[], int b[], int c[])
{
	int i, j;
	static long long tmp[2097152];
	for (i = 0; i <= da + db; i++) tmp[i] = 0;
	for (i = 0; i <= da; i++) for (j = 0; j <= db; j++) tmp[i+j] += (long long)a[i] * b[j] % Mod;
	for (i = 0; i <= da + db; i++) c[i] = tmp[i] % Mod;
}

// Compute the product of two polynomials a[0-da] and b[0-db] in an appropriate way
void prod_polynomial(int da, int db, int a[], int b[], int c[])
{
	if (da <= 70 || db <= 70) prod_poly_naive(da, db, a, b, c);
	else prod_poly_NTT(da, db, a, b, c);
}

long long fact[400001], fact_inv[400001];

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;
}

int main()
{
	int H, W;
	scanf("%d %d", &H, &W);
	
	int i, N = H + W;
	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;
	
	int a[400001], b[400001], c[400001];
	for (i = 0; i * 2 <= H; i++) a[i] = fact_inv[i] * fact_inv[H-i*2] % Mod;
	for (i = 0; i * 2 <= W; i++) b[i] = fact_inv[i] * fact_inv[W-i*2] % Mod;
	prod_polynomial(H / 2, W / 2, a, b, c);
	
	long long ans = 0;
	for (i = 0; i <= H / 2 + W / 2; i++) ans += c[i] * fact[H+W-i] % Mod;
	printf("%lld\n", ans % Mod);
	fflush(stdout);
	return 0;
}

yukicoder

結果

テストケース

ソースコード