結果

問題 No.1873 Bracket Swapping
ユーザー heno239heno239
提出日時 2022-03-11 21:57:25
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 153 ms / 2,000 ms
コード長 5,644 bytes
コンパイル時間 2,183 ms
コンパイル使用メモリ 156,116 KB
実行使用メモリ 45,636 KB
最終ジャッジ日時 2023-10-14 07:04:41
合計ジャッジ時間 5,471 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge14
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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 34 ms
45,232 KB
testcase_01 AC 33 ms
45,268 KB
testcase_02 AC 33 ms
45,500 KB
testcase_03 AC 44 ms
45,264 KB
testcase_04 AC 37 ms
45,292 KB
testcase_05 AC 37 ms
45,244 KB
testcase_06 AC 81 ms
45,388 KB
testcase_07 AC 33 ms
45,460 KB
testcase_08 AC 122 ms
45,420 KB
testcase_09 AC 122 ms
45,412 KB
testcase_10 AC 102 ms
45,368 KB
testcase_11 AC 34 ms
45,264 KB
testcase_12 AC 69 ms
45,552 KB
testcase_13 AC 62 ms
45,312 KB
testcase_14 AC 121 ms
45,436 KB
testcase_15 AC 52 ms
45,316 KB
testcase_16 AC 33 ms
45,280 KB
testcase_17 AC 79 ms
45,392 KB
testcase_18 AC 34 ms
45,228 KB
testcase_19 AC 36 ms
45,292 KB
testcase_20 AC 109 ms
45,372 KB
testcase_21 AC 34 ms
45,488 KB
testcase_22 AC 38 ms
45,284 KB
testcase_23 AC 153 ms
45,428 KB
testcase_24 AC 113 ms
45,392 KB
testcase_25 AC 126 ms
45,576 KB
testcase_26 AC 78 ms
45,348 KB
testcase_27 AC 99 ms
45,568 KB
testcase_28 AC 36 ms
45,636 KB
testcase_29 AC 34 ms
45,228 KB
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 # 

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-8;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 100005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;


int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------
typedef vector<vector<modint>> mat;
typedef vector<modint> vec;
mat mtmul(mat& A, mat& B) {
	mat C(A.size(), vec(B[0].size()));
	rep(i, (int)A.size()) {
		rep(k, (int)B.size()) {
			rep(j, (int)B[0].size()) {
				C[i][j] += A[i][k] * B[k][j];
			}
		}
	}
	return C;
}
mat mtpow(mat A, ll n) {
	mat B(A.size(), vec(A.size()));
	rep(i, (int)A.size()) {
		B[i][i] = 1;
	}
	while (n > 0) {
		if (n & (ll)1)B = mtmul(B, A);
		A = mtmul(A, A);
		n >>= 1;
	}
	return B;
}

modint dp[205][205][205];
void solve() {
	string s; int k; cin >> s >> k;
	int n = s.size();
	dp[0][0][0] = 1;
	rep(i, n) {
		int c = 0;
		if (s[i] == ')')c = 1;
		rep(j, i+1) {
			rep(k, i + 1) {
				//(
				dp[i + 1][j + 1][k + c] += dp[i][j][k];
				//)
				if (j > 0) {
					dp[i + 1][j - 1][k + (c ^ 1)] += dp[i][j][k];
				}
			}
		}
	}
	mat A(n / 2+1, vec(n / 2+1));
	int d = n / 2;
	rep(i, n / 2+1) {
		int j = n / 2 - i;
		A[i][i] += d * (d - 1);
		A[i][i] += 2 * i * j;
		if (i > 0)A[i - 1][i] += i * i;
		if (i + 1 <= n / 2) {
			A[i + 1][i] += j * j;
		}
	}
	A = mtpow(A, k);
	modint ans = 0;
	rep(i, n / 2 + 1) {
		//cout << i << " " << dp[n][0][2 * i] << " " << A[0][i] << "\n";
		ans += dp[n][0][2 * i] * A[0][i];
	}
	cout << ans << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout << fixed << setprecision(10);
	//init_f();
	//init();
	//while(true)
	//useexpr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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