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#include <bits/stdc++.h> std::vector<uint_fast64_t> get_primes_linear(uint_fast64_t limit) { std::vector<uint_fast64_t> lp(limit + 1); std::vector<uint_fast64_t> pr; for (uint_fast64_t i = 2; i <= limit; ++i) { if (lp[i] == 0) { lp[i] = i; pr.push_back(i); } for (uint_fast64_t j = 0; j < pr.size() && pr[j] <= lp[i] && i * pr[j] <= limit; ++j) lp[i * pr[j]] = pr[j]; } return pr; } uint_fast64_t binpow(uint_fast64_t a, uint_fast64_t n) { uint_fast64_t res = 1; while (n) { if (n & 1) res *= a; a *= a; n >>= 1; } return res; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); uint_fast64_t n, k, t; std::cin >> n >> k; std::vector<uint_fast64_t> a(n, 0); std::map<uint_fast64_t, uint_fast64_t> as; std::map<uint_fast64_t, uint_fast64_t> comp; for (uint_fast64_t i = 0; i < n; ++i) { std::cin >> a[i]; } auto ps = get_primes_linear(100000); for (auto num : a) { uint_fast64_t res = 1, comple = 1; for (auto &p : ps) { if (num < p) break; uint_fast64_t pow = 0; while (num % p == 0) { num /= p; ++pow; } pow %= k; res *= binpow(p, pow); comple *= binpow(p, (k - pow) % k); } as[res]++; comp[res] = comple; } uint_fast64_t tot = 0, tot2 = 0; for (auto &num : as) { if (comp[num.first] != num.first) tot += num.second * as[comp[num.first]]; else tot2 += num.second * (num.second - 1); } std::cout << tot / 2 + tot2 / 2 << std::endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int MAX = 1e5; int n, k, a, cnt[MAX + 1]; long long res; vector<pair<int, int> > extractPrimes(int x) { vector<pair<int, int> > res; for (int i = 2; i * i <= x; ++i) if (x % i == 0) { res.push_back(pair<int, int>(i, 0)); while (x % i == 0) { ++res.back().second; x /= i; } } if (x > 1) res.push_back(pair<int, int>(x, 1)); return res; } int main() { scanf("%d %d", &n, &k); while (n--) { scanf("%d", &a); vector<pair<int, int> > primes = extractPrimes(a); long long x = 1LL; for (pair<int, int>& prime : primes) { prime.second %= k; int need = k - prime.second; if (need == k) need = 0; for (int i = 0; i < need; ++i) if ((x *= prime.first) > MAX) { x = 0; break; } } if (x != 0) res += cnt[x]; x = 1LL; for (const pair<int, int>& prime : primes) for (int i = 0; i < prime.second; ++i) if ((x *= prime.first) > MAX) { x = 0; break; } if (x != 0) ++cnt[x]; } printf("%lld", res); return 0; }
#include <bits/stdc++.h> using namespace std; const int iinf = 1 << 29; const long long inf = 1ll << 60; const long long mod = 1e9 + 7; void GG() { cout << "No\n"; exit(0); } long long mpow(long long a, long long n, long long mo = mod) { long long re = 1; while (n > 0) { if (n & 1) re = re * a % mo; a = a * a % mo; n >>= 1; } return re; } long long inv(long long b, long long mo = mod) { if (b == 1) return b; return (mo - mo / b) * inv(mo % b) % mo; } const int maxn = 1e5 + 5; int main() { ios::sync_with_stdio(false), cin.tie(0), cout.tie(0); vector<int> ap(100005); vector<int> other(100005); int n; cin >> n; int k; cin >> k; bool tb = 0; if (k >= 33) tb = 1; k = min(k, 33); vector<int> a(n); vector<long long> out; vector<long long> pl; for (long long i = 2; i <= 10000000000; i++) { long long mo = pow(i, k); if (mo > 10000000000) break; out.push_back(mo); if (mo <= 100000) pl.push_back(mo); } for (int i = 0; i < (n); i++) { cin >> a[i]; for (int j = ((int)pl.size() - 1); j >= 0; j--) { if (a[i] % pl[j] == 0) a[i] /= pl[j]; } ap[a[i]]++; if (k == 3) { if (other[a[i]]) continue; other[a[i]] = 1; long long tmp = a[i]; for (int j = (2); j < (1 + sqrt(a[i])); j++) { int nat = 0; while (tmp % j == 0) tmp /= j, nat++; if (nat == 1) other[a[i]] *= (long long)j * j; if (nat == 2) other[a[i]] *= j; } if (tmp) other[a[i]] *= tmp * tmp; } } long long re = 0; for (int i = (1); i < (100005); i++) { if (ap[i] == 0) continue; if (i == 1) { re += (long long)ap[i] * (ap[i] - 1) / 2; continue; } if (tb) break; if (k > 3) { for (int j = 0; j < ((int)out.size()); j++) { if (out[j] % i == 0) { long long oth = out[j] / i; if (oth < i) re += (long long)ap[oth] * ap[i]; if (oth == i) re += (long long)ap[i] * (ap[i] - 1) / 2; break; } } } else if (k == 2) { re += (long long)ap[i] * (ap[i] - 1) / 2; } else { long long oth = other[i]; if (oth < i) re += (long long)ap[oth] * ap[i]; if (oth == i) re += (long long)ap[i] * (ap[i] - 1) / 2; } } cout << re << endl; }
#include <bits/stdc++.h> using namespace std; long long k; long long trans(long long a) { for (long long i = 2; i * i <= a; ++i) { if ((a % i) == 0) { long long cnt = 0, val = 1; while ((a % i) == 0) { ++cnt; val *= i; if ((cnt % k) == 0) val = 1; a /= i; } a *= val; } } return a; } long long mp(long long a) { long long ans = 1; for (long long i = 2; i * i <= a; ++i) { if ((a % i) == 0) { long long cnt = 0, val = 1; while ((a % i) == 0) { ++cnt; val *= i; a /= i; } while (cnt < k) { ++cnt; ans *= i; } } } if (a > 1) { long long cnt = 1; while (cnt < k) { ++cnt; ans *= a; } } return ans; } void solve() { long long n; cin >> n >> k; long long a[n]; for (long long i = 0; i < n; ++i) cin >> a[i]; for (long long i = 0; i < n; ++i) a[i] = trans(a[i]); long long ans = 0; sort(a, a + n); for (long long i = 0; i < n; ++i) { long long l = -1, r = n; long long cnst = mp(a[i]); while (l < r - 1) { long long m = (l + r) / 2; if (a[m] <= cnst) l = m; else r = m; } long long id1 = l; l = -1; r = n; while (l < r - 1) { long long m = (l + r) / 2; if (a[m] >= cnst) r = m; else l = m; } if (a[i] == cnst) --ans; ans += abs(id1 - l); } cout << ans / 2; } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int nmax = 1e6 + 42; int n, k, inp[nmax]; map<vector<pair<int, int> >, int> seen; int main() { long long output = 0; scanf("%i%i", &n, &k); for (int i = 1; i <= n; i++) { scanf("%i", &inp[i]); vector<pair<int, int> > now = {}; for (int j = 2; j * j <= inp[i]; j++) if (inp[i] % j == 0) { int t = 0; while (inp[i] % j == 0) inp[i] = inp[i] / j, t++; t = t % k; if (t) now.push_back({j, t}); } if (inp[i] != 1) { now.push_back({inp[i], 1}); } vector<pair<int, int> > rev = {}; for (auto p : now) rev.push_back({p.first, k - p.second}); output = output + seen[rev]; seen[now]++; } printf("%lld\n", output); return 0; }
#include <bits/stdc++.h> using namespace std; const long long MOD = 1000000007; long long POW(long long a, long long b, long long MMM = MOD) { long long ret = 1; for (; b; b >>= 1, a = (a * a) % MMM) if (b & 1) ret = (ret * a) % MMM; return ret; } long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } long long lcm(long long a, long long b) { if (a == 0 || b == 0) return a + b; return a * (b / gcd(a, b)); } int dx[] = {0, 1, 0, -1, 1, 1, -1, -1}, dy[] = {1, 0, -1, 0, 1, -1, 1, -1}; int ddx[] = {2, 2, -2, -2, 1, 1, -1, -1}, ddy[] = {1, -1, 1, -1, 2, -2, 2, -2}; vector<int> t = {0}; map<vector<pair<int, int> >, int> M; int n, k; vector<pair<int, int> > op(vector<pair<int, int> > &v) { vector<pair<int, int> > p; for (auto P : v) p.push_back(make_pair(P.first, k - P.second)); return p; } int main() { scanf("%d%d", &n, &k); for (int i = 1;; i++) { long long c = 1; for (int(j) = (1); (j) <= (k); (j) += (1)) { c *= i; if (c > 100000) { c = -1; break; } } if (c == -1) break; t.push_back(c); } for (int(i) = (0); (i) <= (n - 1); (i) += (1)) { long long x; scanf("%lld", &x); for (int(k) = (2); (k) <= ((int)t.size() - 1); (k) += (1)) while (x % t[k] == 0) x /= t[k]; vector<pair<int, int> > vv; for (int k = 2; k * k <= x; k++) { if (x % k == 0) { int cc = 0; while (x % k == 0) { cc++; x /= k; } vv.push_back(make_pair(k, cc)); } } if (x != 1) vv.push_back(make_pair(x, 1)); M[vv]++; } long long ans = 0; for (auto it = M.begin(); it != M.end(); it++) { auto t = it->first; if (t.empty()) ans += 1LL * it->second * (it->second - 1); else { auto vp = op(t); if (it->first == vp) ans += 1LL * it->second * (it->second - 1); else ans += 1LL * it->second * M[vp]; } } printf("%lld", ans / 2); }
#include <bits/stdc++.h> using namespace std; signed main() { ios::sync_with_stdio(false); cin.tie(nullptr); long long n, k; cin >> n >> k; vector<long long> b(n); for (long long i = 0; i < n; ++i) { cin >> b[i]; } map<vector<long long>, vector<vector<long long>>> nb; for (long long i = 0; i < n; ++i) { vector<long long> cur, push; for (long long j = 2; j * j <= b[i]; ++j) { if (b[i] % j == 0) { cur.push_back(j); push.push_back(0); while (b[i] % j == 0) { push.back()++, b[i] /= j; } push.back() %= k; if (push.back() == 0) { push.pop_back(); cur.pop_back(); } } } if (b[i] != 1) { cur.push_back(b[i]); push.push_back(1); } nb[cur].push_back(push); } long long ans = 0; for (auto &nnnn : nb) { map<vector<long long>, long long> a; for (long long i = 0; i < nnnn.second.size(); ++i) { ++a[nnnn.second[i]]; } for (auto &now : a) { vector<long long> f(nnnn.first.size()); for (long long i = 0; i < nnnn.first.size(); ++i) f[i] = (k - now.first[i]) % k; if (a.find(f) != a.end()) { if (f == now.first) ans += now.second * 1ll * (now.second - 1); else ans += a[f] * 1ll * now.second; } } } cout << ans / 2 << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(false); cin.tie(0); const int MAX = 100010; vector<int> p(MAX); iota(p.begin(), p.end(), 0); for (int i = 2; i < MAX; i++) { if (p[i] == i) { for (int j = i + i; j < MAX; j += i) { if (p[j] == j) { p[j] = i; } } } } int n, k; cin >> n >> k; vector<int> cnt(MAX); long long ans = 0; for (int i = 0; i < n; i++) { int x; cin >> x; int res = 1; long long ask = 1; while (x > 1) { int y = p[x]; int cc = 0; while (x % y == 0) { x /= y; ++cc; } cc %= k; for (int j = 0; j < cc; j++) { res *= y; } for (int j = 0; j < (k - cc) % k; j++) { ask *= y; ask = min(ask, MAX - 1LL); } } ans += cnt[ask]; ++cnt[res]; } cout << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using P = pair<ll, ll>; constexpr ll inf = 1000000000; constexpr ll mod = 1000000007; constexpr long double eps = 1e-9; template <typename T1, typename T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { os << to_string(p.first) << " " << to_string(p.second); return os; } template <typename T> ostream& operator<<(ostream& os, vector<T>& v) { for (ll i = 0; i < (int)v.size(); i++) { if (i) os << " "; os << to_string(v[i]); } return os; } struct modint { ll n; public: modint(const ll n = 0) : n((n % mod + mod) % mod) {} static modint pow(modint a, int m) { modint r = 1; while (m > 0) { if (m & 1) { r *= a; } a = (a * a); m /= 2; } return r; } modint& operator++() { *this += 1; return *this; } modint& operator--() { *this -= 1; return *this; } modint operator++(int) { modint ret = *this; *this += 1; return ret; } modint operator--(int) { modint ret = *this; *this -= 1; return ret; } modint operator~() const { return (this->pow(n, mod - 2)); } friend bool operator==(const modint& lhs, const modint& rhs) { return lhs.n == rhs.n; } friend bool operator<(const modint& lhs, const modint& rhs) { return lhs.n < rhs.n; } friend bool operator>(const modint& lhs, const modint& rhs) { return lhs.n > rhs.n; } friend modint& operator+=(modint& lhs, const modint& rhs) { lhs.n += rhs.n; if (lhs.n >= mod) lhs.n -= mod; return lhs; } friend modint& operator-=(modint& lhs, const modint& rhs) { lhs.n -= rhs.n; if (lhs.n < 0) lhs.n += mod; return lhs; } friend modint& operator*=(modint& lhs, const modint& rhs) { lhs.n = (lhs.n * rhs.n) % mod; return lhs; } friend modint& operator/=(modint& lhs, const modint& rhs) { lhs.n = (lhs.n * (~rhs).n) % mod; return lhs; } friend modint operator+(const modint& lhs, const modint& rhs) { return modint(lhs.n + rhs.n); } friend modint operator-(const modint& lhs, const modint& rhs) { return modint(lhs.n - rhs.n); } friend modint operator*(const modint& lhs, const modint& rhs) { return modint(lhs.n * rhs.n); } friend modint operator/(const modint& lhs, const modint& rhs) { return modint(lhs.n * (~rhs).n); } }; istream& operator>>(istream& is, modint m) { is >> m.n; return is; } ostream& operator<<(ostream& os, modint m) { os << m.n; return os; } long long extgcd(long long a, long long b, long long& x, long long& y) { long long d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } long long mod_inverse(long long a, long long m) { long long x, y; if (extgcd(a, m, x, y) == 1) return (m + x % m) % m; else return -1; } vector<long long> fact(1010101 + 1, inf); long long mod_fact(long long n, long long& e) { if (fact[0] == inf) { fact[0] = 1; if (1010101 != 0) fact[1] = 1; for (ll i = 2; i <= 1010101; ++i) { fact[i] = (fact[i - 1] * i) % mod; } } e = 0; if (n == 0) return 1; long long res = mod_fact(n / mod, e); e += n / mod; if ((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod; return (res * fact[n % mod]) % mod; } long long mod_comb(long long n, long long k) { if (n < 0 || k < 0 || n < k) return 0; long long e1, e2, e3; long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3); if (e1 > e2 + e3) return 0; return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod; } using mi = modint; mi mod_pow(mi a, ll n) { mi ret = 1; mi tmp = a; while (n > 0) { if (n % 2) ret *= tmp; tmp = tmp * tmp; n /= 2; } return ret; } ll gcd(ll a, ll b) { if (b == 0) return a; return gcd(b, a % b); } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, k; cin >> n >> k; vector<int> a(n); for (ll i = 0; i < (int)n; i++) cin >> a[i]; vector<vector<int>> prim(n); for (ll i = 0; i < (int)n; i++) { for (int j = 2; j * j <= a[i]; j++) { while (a[i] % j == 0) { prim[i].push_back(j); a[i] /= j; } } if (a[i] != 1) prim[i].push_back(a[i]); } ll ans = 0; map<vector<pair<int, int>>, int> ma; for (ll i = 0; i < (int)n; i++) { if (prim[i].empty()) { ans += ma[{}]; ma[{}]++; continue; } int num = prim[i].front(), strk = 1; vector<pair<int, int>> fp, tgt; for (ll j = 1; j < (int)prim[i].size(); j++) { if (prim[i][j] != num) { if (strk % k) { fp.push_back({num, strk % k}); tgt.push_back({num, k - (strk % k)}); } num = prim[i][j]; strk = 1; } else strk++; } if (strk % k) { fp.push_back({num, strk % k}); tgt.push_back({num, k - (strk % k)}); } ans += ma[tgt]; ma[fp]++; } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int a[101010], f[101010], num[101010]; inline long long power(long long a, int k) { long long ans = 1; for (; k; k >>= 1, a *= a) if (k & 1) ans *= a; return ans; } int main() { for (int i = 2; i < 101010; i++) if (!f[i]) { f[i] = i; if ((long long)i * i >= 101010) continue; for (int j = i * i; j < 101010; j += i) f[j] = i; } int n, k; scanf("%d %d", &n, &k); for (int i = 1; i <= n; i++) scanf("%d", a + i); if (k == 2) { long long ans = 0; for (int i = 1; i <= n; i++) { int u = a[i], val = 1; while (u > 1) { int p = f[u], num = 0; while (u % p == 0) u /= p, num ^= 1; if (num) val *= p; } ans += num[val]; num[val]++; } cout << ans << endl; return 0; } int mx = 0; for (int i = 1; i <= n; i++) { num[a[i]]++; mx = max(mx, a[i]); } int ed = 1; while (k * log(ed) < log((double)mx * mx + 1)) ed++; ed++; long long ans = 0; for (int i = 1; i <= ed; i++) { long long val = power((long long)i, k); for (int j = 1; j <= mx; j++) if (val % j == 0) { long long x = val / j; if (0 < x && x <= mx && x <= j) { if (x < j) ans += (long long)num[j] * num[x]; else ans += (long long)num[j] * (num[j] - 1) >> 1; } } } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 10; int n, k; int a[maxn]; map<vector<pair<int, int> >, int> mp; int main() { scanf("%d%d", &n, &k); for (int i = 0; i < n; i++) scanf("%d", &a[i]); long long ans = 0; for (int i = 0; i < n; i++) { vector<pair<int, int> > v1; for (int cur = 2; cur * cur <= a[i]; cur++) { int num = 0; while (a[i] % cur == 0) { a[i] /= cur; num++; } if (num % k) v1.push_back(make_pair(cur, num % k)); } if (a[i] > 1) v1.push_back(make_pair(a[i], 1 % k)); vector<pair<int, int> > v2; for (int j = 0; j < v1.size(); j++) { v2.push_back(make_pair(v1[j].first, k - v1[j].second)); } ans += mp[v2]; mp[v1]++; } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long read() { long long x = 0, f = 1; char c = getchar(); while (!isdigit(c)) { if (c == '-') f = -1; c = getchar(); } while (isdigit(c)) { x = (x << 3) + (x << 1) + c - 48; c = getchar(); } return x * f; } long long k, m, n; long long a[100100], check[100100], tax[100005]; vector<long long> num[100005]; long long sum; long long hh[100010][110]; signed main() { n = read(); k = read(); for (register long long i = 1; i <= 100000; i++) { hh[i][0] = 1; for (register long long j = 1; j <= 100; j++) { if (hh[i][j - 1] * i > 1e10) break; hh[i][j] = hh[i][j - 1] * i; } } for (register long long i = 1; i <= n; i++) { a[i] = read(); for (register long long j = 2; j * j <= a[i]; j++) { if (!hh[j][k]) continue; while (a[i] % hh[j][k] == 0) a[i] /= hh[j][k]; } } long long ans = 0; for (register long long i = 1; i <= n; i++) { for (register long long j = 1; j * j <= a[i]; j++) { if (a[i] % j == 0) { if (hh[j][k] && hh[j][k] % a[i] == 0 && hh[j][k] / a[i] <= 100000) { ans += check[hh[j][k] / a[i]]; } if (j * j != a[i] && hh[a[i] / j][k] && hh[a[i] / j][k] % a[i] == 0 && hh[a[i] / j][k] / a[i] <= 100000) { ans += check[hh[a[i] / j][k] / a[i]]; } } } check[a[i]]++; } printf("%I64d", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxN = 101000; bool is_prime(int x) { for (int i = 2; i * i <= x; ++i) { if (x % i == 0) { return false; } } return true; } vector<int> primes; vector<pair<int, int> > factorize(int x, int modk) { vector<pair<int, int> > ret; int y = x; for (int i = 0; primes[i] * primes[i] <= x; ++i) { if (y % primes[i] == 0) { int cnt = 0; while (y % primes[i] == 0) { ++cnt; y /= primes[i]; } if (cnt % modk != 0) { ret.push_back(make_pair(primes[i], cnt % modk)); } } } if (y > 1) { ret.push_back(make_pair(y, 1)); } return ret; } int find_equal(vector<pair<int, int> >& ret, int k) { if (ret.empty()) { return 1; } long long num = 1; for (int i = 0; i < ret.size(); ++i) { int pw = k - ret[i].second; for (int j = 0; j < pw; ++j) { num *= ret[i].first; if (num > 1e6) { return -1; } } } return num; } int comp(vector<pair<int, int> >& ret) { int res = 1; for (int i = 0; i < ret.size(); ++i) { for (int j = 0; j < ret[i].second; ++j) { res *= ret[i].first; } } return res; } void solve() { for (int i = 2; i < maxN; ++i) { if (is_prime(i)) { primes.push_back(i); } } int n, k; cin >> n >> k; map<int, int> avail; long long res = 0; for (int i = 0; i < n; ++i) { int x; cin >> x; auto fact = factorize(x, k); int eq = find_equal(fact, k); if (eq != -1) { res += avail[eq]; } ++avail[comp(fact)]; } cout << res << endl; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int t; t = 1; for (int tt = 0; tt < t; ++tt) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> fact; vector<pair<int, int>> factcnt, ifactcnt; map<vector<pair<int, int>>, int> fmap; int sieve[100005]; void buildsieve() { for (int i = 2; i < 100005; i++) { if (!sieve[i]) { for (int j = i; j < 100005; j += i) { if (!sieve[j]) sieve[j] = i; } } } } int main() { ios::sync_with_stdio(0); buildsieve(); fmap.clear(); int n, k; cin >> n >> k; long long ans = 0; for (int i = 0; i < n; i++) { int ai; cin >> ai; int ti = ai; fact.clear(); while (sieve[ti]) { fact.push_back(sieve[ti]); ti /= sieve[ti]; } factcnt.clear(); ifactcnt.clear(); int f = 0, cnt = 0; for (auto it : fact) { if (it != f) { if (cnt % k) { cnt %= k; factcnt.push_back(make_pair(f, cnt)); ifactcnt.push_back(make_pair(f, k - cnt)); } f = it; cnt = 0; } cnt++; } if (cnt % k) { cnt %= k; factcnt.push_back(make_pair(f, cnt)); ifactcnt.push_back(make_pair(f, k - cnt)); } if (fmap.find(ifactcnt) != fmap.end()) ans += fmap[ifactcnt]; fmap[factcnt]++; } cout << ans << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; void canhazfast() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); } template <typename T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; } template <typename T> T extgcd(T a, T b, T &x, T &y) { T x0 = 1, y0 = 0, x1 = 0, y1 = 1; while (b) { T q = a / b; a %= b; swap(a, b); x0 -= q * x1; swap(x0, x1); y0 -= q * y1; swap(y0, y1); } x = x0; y = y0; return a; } int ctz(unsigned x) { return __builtin_ctz(x); } int ctzll(unsigned long long x) { return __builtin_ctzll(x); } int clz(unsigned x) { return __builtin_clz(x); } int clzll(unsigned long long x) { return __builtin_clzll(x); } int popcnt(unsigned x) { return __builtin_popcount(x); } int popcntll(unsigned long long x) { return __builtin_popcountll(x); } int bsr(unsigned x) { return 31 ^ clz(x); } int bsrll(unsigned long long x) { return 63 ^ clzll(x); } vector<pair<unsigned, unsigned> > factorize(unsigned n, unsigned k) { vector<pair<unsigned, unsigned> > res; if (int e2 = ctz(n)) { if (e2 % k) res.emplace_back(2, e2 % k); n >>= e2; } for (unsigned p = 3;; p += 2) { unsigned q = n / p, r = n % p, e = 0; if (q < p) break; while (!r) { n = q; q = n / p; r = n % p; ++e; } if (e % k) res.emplace_back(p, e % k); } if (n > 1) res.emplace_back(n, 1); return res; } int main() { canhazfast(); int n, k; long long ans = 0; map<vector<pair<unsigned, unsigned> >, int> mp; cin >> n >> k; for (int i = 0; i < n; ++i) { unsigned a; cin >> a; vector<pair<unsigned, unsigned> > fsa = factorize(a, k); vector<pair<unsigned, unsigned> > fsb = fsa; for (pair<unsigned, unsigned> &f : fsb) { f.second = k - f.second; } int cnt = mp.count(fsb) ? mp[fsb] : 0; ans += cnt; ++mp[fsa]; } cout << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; int power(long long a, int b) { long long f = 1; for (; b; b >>= 1, a = a * a) { if (a > 2e5) a = 2e5; if (b & 1) { f = f * a; if (f > 2e5) f = 2e5; } } return f; } const int N = 100050; long long pk[N][102]; int mnp[N]; int p[70], q[70], top; int c[N]; int main() { int n, k; scanf("%d%d", &n, &k); for (int i = (1); i <= (N - 1); ++i) { pk[i][0] = 1; for (int j = (1); j <= (k); ++j) { pk[i][j] = pk[i][j - 1] * i; if (pk[i][j] > 2e5) pk[i][j] = 2e5; } } for (int i = (N - 1); i >= (2); --i) for (int j = i; j < N; j += i) mnp[j] = i; long long ans = 0; while (n--) { int x; scanf("%d", &x); top = 0; while (x > 1) { int i = mnp[x]; top++; p[top] = i; q[top] = 0; while (x % i == 0) { q[top]++; x /= i; } } for (int i = (1); i <= (top); ++i) q[i] %= k; long long t = 1, need = 1; for (int i = (1); i <= (top); ++i) { t *= power(p[i], q[i]); if (q[i]) { need *= pk[p[i]][k - q[i]]; if (need > 2e5) need = 2e5; } } if (need < N) ans += c[need]; c[t]++; } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; void START() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); } const int gh = 1e5 + 6; const long long mod = 1000000000100011; int n, g[gh], k; map<int, int> mp; long long kq; void sieve(int n) { for (int i = 2; i <= n; i++) if (!g[i]) for (int j = i; j <= n; j += i) g[j] = i; } inline int mu(long long a, int b) { long long c = 1; for (; b; a = (a * a) % mod, b >>= 1) if (b & 1) c = (c * a) % mod; return c; } int main() { START(); sieve(1e5); cin >> n >> k; for (int x, i = 1; i <= n; i++) { cin >> x; long long tmp1 = 1, tmp2 = 1; while (x > 1) { int dem = 0, ga = g[x]; while (x % ga == 0) x /= ga, dem++; tmp1 = (tmp1 * mu(ga, dem % k)) % mod; tmp2 = (tmp2 * mu(ga, (k - (dem % k)) % k)) % mod; } kq += mp[tmp2]; mp[tmp1]++; } cout << kq; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 1; vector<int> a, B; long long n, m, w[N], b[N], C[N], A; int main() { ios::sync_with_stdio(false); cin >> n >> m; for (int i = 1; i <= n; i++) cin >> w[i]; for (int i = 1; i <= n; i++) { a.clear(), B.clear(); for (int j = 2; j * j <= w[i]; j++) if (w[i] % j == 0) { a.push_back(j), B.push_back(0); while (w[i] % j == 0) w[i] /= j, B[B.size() - 1]++; B[B.size() - 1] %= m; } if (w[i] > 1) a.push_back(w[i]), B.push_back(1); w[i] = b[i] = 1; for (int j = 0; j < a.size(); j++) for (int k = 1; k <= B[j]; k++) w[i] *= a[j]; for (int j = 0; j < a.size(); j++) { for (int k = 1; k <= (m - B[j]) % m; k++) { b[i] *= a[j]; if (b[i] >= N) break; } if (b[i] >= N) break; } C[w[i]]++; } for (int i = 1; i <= n; i++) { if (b[i] >= N) continue; if (w[i] == b[i]) A += C[b[i]] - 1; else A += C[b[i]]; } cout << A / 2; return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 1e5; const long long M = 1e3; long long n, k, s[N << 2], bo[N << 2], ann, an2, an1, ch1, ch2, m, ans, sum, top, an, boo[N << 2]; map<pair<int, long long>, int> ma; int main() { scanf("%lld%lld", &n, &k); for (int i = 2; i <= M; i++) { if (!bo[i]) s[++top] = i; for (int j = 1; j <= top; j++) { if (i * s[j] > M) break; bo[i * s[j]] = 1; if (i % s[j] == 0) break; } } for (int i = 1; i <= n; i++) { scanf("%lld", &m); ann = 0; an2 = 1; an1 = 0; for (int j = 1; j <= top; j++) { if (m % s[j]) continue; an = 0; while (m % s[j] == 0) { m /= s[j]; an++; } an %= k; if (an > 0) { ann = ann * k + an; an2 = an2 * s[j]; an = k - an; an1 = an1 * k + an; } } if (m > 1) { an = 1; ann = ann * k + an; an2 = an2 * m; an = k - an; an1 = an1 * k + an; } if (an2 == 1ll) { sum++; continue; } ans = ans + ma[make_pair((int)an2, an1)]; ma[make_pair((int)an2, ann)]++; } printf("%lld", ans + 1ll * sum * (sum - 1) / 2ll); }
#include <bits/stdc++.h> using namespace std; const long long N = 2e5 + 3; const long long MAXN = 1e5 + 10; long long spf[MAXN + 3], store[N], _store[N], n, k; map<long long, long long> K, _K; long long power(long long base, long long exp) { long long res = 1; while (exp) { if (exp & 1) { res *= base; } exp >>= 1; base *= base; } return res; } void sieve() { spf[1] = 1; for (long long i = 2; i <= MAXN; i++) spf[i] = i; for (long long i = 4; i <= MAXN; i += 2) spf[i] = 2; for (long long i = 3; i * i <= MAXN; i++) { if (spf[i] == i) { for (long long j = i * i; j <= MAXN; j += i) if (spf[j] == j) spf[j] = i; } } } void work(long long x, long long idx) { map<long long, long long> pfactors, _pfactors; while (x != 1) { pfactors[spf[x]]++; pfactors[spf[x]] %= k; x = x / spf[x]; } long long res = 1, _res = 1; for (auto it : pfactors) { res *= power(it.first, it.second); _res *= power(it.first, (k - it.second) % k); } K[res]++; _K[res]++; store[idx] = res; _store[idx] = _res; } signed main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); sieve(); cin >> n >> k; map<long long, long long> have; for (long long i = 1; i <= n; ++i) { long long a; cin >> a; work(a, i); } long long ans = 0; for (long long i = 1; i <= n; ++i) { long long freq = _K[_store[i]] - (store[i] == _store[i]); ans += freq; } cout << ans / 2 << '\n'; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 10; int n, k; int a[maxn]; map<vector<pair<int, int> >, int> mp; int main() { scanf("%d%d", &n, &k); for (int i = 0; i < n; i++) scanf("%d", &a[i]); long long ans = 0; for (int i = 0; i < n; i++) { vector<pair<int, int> > v1; for (int cur = 2; cur * cur <= a[i]; cur++) { int num = 0; while (a[i] % cur == 0) { a[i] /= cur; num++; } if (num % k) v1.push_back(make_pair(cur, num % k)); } if (a[i] > 1) v1.push_back(make_pair(a[i], 1)); vector<pair<int, int> > v2; for (int j = 0; j < v1.size(); j++) { v2.push_back(make_pair(v1[j].first, k - v1[j].second)); } ans += mp[v2]; mp[v1]++; } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long long maxn = 102000; long long n, k, a[maxn], pri[maxn], vis[maxn], pcnt, cnt[maxn], nd[maxn]; long long pkt[maxn][102]; long long bu(long long x, bool chk = false) { long long ret = 1; auto deal = [&](long long fac, long long deg) { deg %= k; if (deg == 0) return 1ll; else return pkt[fac][k - deg]; }; while (x != 1) { long long d = vis[x], deg = 0, so; while (x % d == 0) x /= d, deg++; if (chk) { if (deg % k != 0) return -1; } else { so = deal(d, deg); if (so == -1) return -1; else { ret *= so; if (ret >= maxn) return -1; } } } return ret; } long long yu(long long x) { long long ret = 1; auto deal = [&](long long fac, long long deg) { deg %= k; return pkt[fac][deg]; }; while (x != 1) { long long d = vis[x], deg = 0, so; while (x % d == 0) x /= d, deg++; so = deal(d, deg); if (so == -1) return -1; else { ret *= so; if (ret >= maxn) return -1; } } return ret; } signed main() { memset(pkt, -1, sizeof pkt); for (long long i = 2; i < maxn; ++i) { pkt[i][0] = 1; for (long long j = 1; 1LL * pkt[i][j - 1] * i < maxn; ++j) pkt[i][j] = pkt[i][j - 1] * i; if (!vis[i]) pri[++pcnt] = i, vis[i] = i; for (long long j = 1; j <= pcnt && i * pri[j] < maxn; ++j) { vis[i * pri[j]] = pri[j]; if (i % pri[j] == 0) break; } } scanf("%lld%lld", &n, &k); for (long long i = 1; i <= n; ++i) { scanf("%lld", &a[i]); cnt[yu(a[i])]++; long long b = bu(a[i]); if (b != -1) nd[b]++; } long long ans = 0; for (long long i = 1; i <= 100000; ++i) if (nd[i]) { ans += 1LL * nd[i] * cnt[i]; } for (long long i = 1; i <= 100000; ++i) if (yu(i) == bu(i)) { ans -= cnt[i]; } ans /= 2; printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> int sign(T a) { if (a == 0) return 0; return (a > 0 ? 1 : -1); } template <typename T1, typename T2> T2 mod(T1 x, T2 MOD) { if (x < 0) x += MOD; if (x >= MOD) x -= MOD; return x; } template <typename T> T sqr(T a) { return a * a; } template <typename T> bool uax(T& a, const T b) { if (a < b) { a = b; return true; } return false; } template <typename T> bool uin(T& a, const T b) { if (a > b) { a = b; return true; } return false; } template <typename T1, typename T2> istream& operator>>(istream& in, pair<T1, T2>& p) { in >> p.first >> p.second; return in; } template <typename T1, typename T2> ostream& operator<<(ostream& out, pair<T1, T2>& p) { out << '(' << p.first << ' ' << p.second << ')'; return out; } mt19937_64 gen_rand; const int N = (int)3e5 + 7; const int LOG = 31; const int N_ = (int)507; const int MAXN = (int)8e5 + 7; const int MOD = (int)1e9 + 7; const int INF = (int)2e9 + 7; const int CONST = 5000; const long long LINF = (int64_t)1e10; const long double PI = 3.1415926535897932384626433832795; const long double EPS = 5e-1; int n, k, a[N], cnt[N]; int main() { cout << fixed << setprecision(20); ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); gen_rand.seed(time(0)); cin >> n >> k; for (int i = 0; i < n; i++) cin >> a[i]; if (k == 2) { map<int, int> cnt; for (int i = 0; i < n; i++) { int val = 1; for (int j = 2; j * j <= a[i]; j++) { int x = 0; while (a[i] % j == 0) x++, a[i] /= j; if (x & 1) val *= j; } if (a[i] != 1) val *= a[i]; cnt[val]++; } long long ans = 0; for (auto it : cnt) { if (it.second == 1) continue; ans += 1LL * it.second * (it.second - 1) / 2; } cout << ans; } else { vector<long long> pw; bool fl = true; for (int i = 1;; i++) { long long x = 1; for (int j = 0; j < k; j++) { if (x * i > LINF) { fl = false; break; } x *= i; } if (!fl) break; pw.push_back(x); } long long ans = 0; for (int i = n - 1; i >= 0; i--) { for (long long x : pw) { if (x / a[i] > (int)1e5) break; if (x % a[i] == 0) ans += cnt[x / a[i]]; } cnt[a[i]]++; } cout << ans; } }
#include <bits/stdc++.h> using namespace std; const int maxn = 100010, sq = 333; inline long long read() { char ch = getchar(); long long x = 0, f = 0; while (ch < '0' || ch > '9') f |= ch == '-', ch = getchar(); while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar(); return f ? -x : x; } int n, k, a[maxn]; vector<pair<int, int> > d[maxn], tmp; map<vector<pair<int, int> >, int> cnt; long long ans; int main() { n = read(); k = read(); for (int i = (1); i <= (n); i++) a[i] = read(); for (int i = (1); i <= (n); i++) { int x = a[i]; tmp.clear(); for (int j = (2); j <= (sqrt(x)); j++) if (x % j == 0) { int cnt = 0; while (x % j == 0) x /= j, cnt = (cnt + 1) % k; if (cnt) d[i].push_back(make_pair(j, cnt)), tmp.push_back(make_pair(j, k - cnt)); } if (x > 1) d[i].push_back(make_pair(x, 1)), tmp.push_back(make_pair(x, k - 1)); ans += cnt[tmp]; cnt[d[i]]++; } printf("%lld\n", ans); }
#include <bits/stdc++.h> using namespace std; using ll = long long; using pii = pair<int, int>; long long pk[100005]; int A[100005], C[100005], vis[100005]; vector<int> vec[100005]; int main() { ios_base::sync_with_stdio(0), cin.tie(0); int N, K; cin >> N >> K; for (int i = 1; i <= N; ++i) cin >> A[i], C[A[i]]++; for (int i = 1; i <= 100000; ++i) { for (int j = 1; j * j <= i; ++j) { if (i % j == 0) vec[i].push_back(j); } int t = 0; if (vec[i].back() * vec[i].back() == i) { t = vec[i].back(); vec[i].pop_back(); } for (int j = (int)vec[i].size() - 1; j >= 0; --j) vec[i].push_back(i / vec[i][j]); if (t) vec[i].push_back(t); } int bar = 100001; for (int i = 1; i <= 100000; ++i) { long long a = 1; int flag = 0; for (int j = 1; j <= K; ++j) { a *= i; if (a > 1e10) { flag = 1; break; } } if (flag) { bar = i; break; } pk[i] = a; } long long ans = 0; sort(A + 1, A + N + 1); if (K == 2) { for (int i = 1; i < bar; ++i) { for (auto j : vec[i]) { for (auto k : vec[i]) { if (j >= k) continue; if (1ll * i * k / j > 100000 || vis[i / k * j] == i) continue; vis[i / j * k] = i; vis[i / k * j] = i; ans += 1ll * C[i / j * k] * C[i / k * j]; } } ans += 1ll * C[i] * (C[i] - 1) / 2; } cout << ans; return 0; } for (int i = 1; i <= N; ++i) { for (int j = 1; j < bar; ++j) { if (pk[j] % A[i]) continue; if (pk[j] == 1ll * A[i] * A[i]) ans += C[A[i]] - 1; else if (pk[j] / A[i] <= 100000) ans += C[pk[j] / A[i]]; } } cout << ans / 2; return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5; int n, k, cnt[111111], a[111111], mxx, prime[111111], ct, mx[111111], cnr; long long cur, ans, ts, fuck, fk; bool f, fl[111111]; void Init() { for (int i = 2; i <= maxn; i++) { if (!fl[i]) { prime[++ct] = i; } for (int j = 1; j <= ct && i * prime[j] <= maxn; j++) { fl[i * prime[j]] = 1; if (i % prime[j] == 0) break; } } for (int i = 1; i <= ct; i++) { for (int j = prime[i]; j <= maxn; j += prime[i]) { mx[j] = i; } } } int main() { scanf("%d%d", &n, &k); for (int i = 1; i <= n; i++) scanf("%d", &a[i]); for (int i = 1; i <= n; i++) cnt[a[i]]++; for (int i = 2; i <= maxn; i++) { cur = 1; for (int j = 1; j <= k; j++) { if (cur > 100000) { f = 1; break; } cur = cur * i; } if (cur > 100000) { mxx = i - 1; break; } } Init(); for (int i = 1; i <= n; i++) { cur = a[i]; fuck = 1; while (cur > 1) { int x = mx[cur]; cnr = 0; while (cur % prime[x] == 0) { cnr++; cur /= prime[x]; } cnr = (cnr - 1) % k + 1; for (int j = 1; fuck != -1 && j <= k - cnr; j++) { fuck *= prime[x]; if (fuck > maxn) fuck = -1; } } if (fuck == -1) continue; for (int j = 1; j <= mxx; j++) { fk = fuck; for (int h = 1; fk != -1 && h <= k; h++) { fk *= j; if (fk > maxn) fk = -1; } if (~fk) { if (fk == a[i]) ans += (cnt[fk] - 1); else ans += cnt[fk]; } else break; } } printf("%lld\n", ans / 2); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100010; int n, k; long long a[N], sp[N]; map<vector<pair<int, int> >, int> f; int main() { for (int i = 2; i * i < N; ++i) { if (sp[i]) continue; sp[i] = i; for (int j = i * i; j < N; j += i) { if (!sp[j]) sp[j] = i; } } for (int i = 2; i < N; ++i) if (!sp[i]) sp[i] = i; cin >> n >> k; long long ans = 0; for (int i = 1; i <= n; ++i) { scanf("%lld", a + i); int x = a[i]; vector<pair<int, int> > one, two; while (x > 1) { int p = sp[x], e = 0; while (x % p == 0) x /= p, ++e; e %= k; if (e) { one.emplace_back(p, e); e = k - e; two.emplace_back(p, e); } } ans += f[two]; ++f[one]; } cout << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; int a[200005]; map<long long, long long> mp; vector<pair<int, int> > v; int main() { int n, k; long long ans = 0; scanf("%d%d", &n, &k); for (int i = 1; i <= n; i++) scanf("%d", &a[i]); for (int i = 1; i <= n; i++) { if (a[i] == 1) { ans += mp[1]; mp[1]++; continue; } long long now = 1; for (int j = 2; j * j <= a[i]; j++) { if (a[i] % j) continue; int num = 0; while (a[i] % j == 0) { num++; a[i] /= j; } v.push_back(pair<int, int>(j, num % k)); } if (a[i] > 1) v.push_back(pair<int, int>(a[i], 1)); long long need = 1; for (auto p : v) { if (p.second == 0) continue; for (int j = 1; j <= k - p.second; j++) need *= p.first; for (int j = 1; j <= p.second; j++) now *= p.first; if (need > 1e5) need = 0; } v.clear(); ans += mp[need]; mp[now]++; } printf("%lld\n", ans); }
#include <bits/stdc++.h> using namespace std; const int maxn = 100005; int n, k; int cnt[maxn]; int a[maxn]; int main() { while (cin >> n >> k) { memset(cnt, 0, sizeof cnt); for (int i = 1; i <= n; i++) { cin >> a[i]; cnt[a[i]]++; } long long ans = 0; for (int i = 1; i <= 1e5; i++) { if (!cnt[i]) continue; vector<pair<int, int> > v; int now = i; for (int z = 2; z * z <= now; z++) { if (now % z == 0) { int c = 0; while (now % z == 0) now /= z, c++; v.push_back(make_pair(z, c)); } } if (now > 1) v.push_back(make_pair(now, 1)); long long mi = i; long long mul = 1; bool check = true; bool wrong = false; for (auto item : v) { int mo = item.second % k; if (mo != 0) { for (int j = 0; j < k - mo; j++) { mi *= item.first, mul *= item.first; if (mul > 1e5) wrong = true; } } if (mo > 0 && mo * 2 != k) check = false; } if (check) ans += (long long)cnt[i] * (cnt[i] - 1); if (mul != i && !wrong) ans += (long long)cnt[i] * cnt[mul]; if (wrong) continue; for (int j = 2;; j++) { long long now = mul; bool is_wrong = false; for (int z = 0; z < k; z++) { now *= j; if (now > 1e5) { is_wrong = true; break; } } if (is_wrong) break; if (now != i && !is_wrong) ans += (long long)cnt[i] * cnt[now]; } } cout << ans / 2 << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; using LL = long long; using PII = pair<int, int>; const int MAX = 1e5; int main() { int n, k; scanf("%d%d", &n, &k); unordered_map<int, int> mp; LL ans = 0; for (int i = 0; i < n; i++) { int x; scanf("%d", &x); assert(x >= 1 && x <= MAX); int y = 1; LL yy = 1; for (int j = 2; j * j <= x; j++) { int cnt = 0; while (x % j == 0) { cnt++; x /= j; } if (cnt) { cnt %= k; for (int t = 1; t <= cnt; t++) y *= j; cnt = k - cnt; cnt %= k; for (int t = 1; t <= cnt; t++) { if (yy != -1) { yy *= j; if (yy > MAX) yy = -1; } else { break; } } } } if (x != 1) { y *= x; for (int t = 1; t <= k - 1; t++) { if (yy != -1) { yy *= x; if (yy > MAX) yy = -1; } else { break; } } } ans += mp[yy]; mp[y]++; } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; map<vector<pair<int, int> >, int> cnt; int main() { int n, k; cin >> n >> k; long long ans = 0; for (int i = 0; i < n; ++i) { int x; cin >> x; vector<pair<int, int> > pcnt; vector<pair<int, int> > temp; for (int p = 2; p * p <= x; ++p) { if (x % p == 0) { int cc = 0; while (x % p == 0) { ++cc; x /= p; } if (cc % k != 0) { pcnt.push_back(make_pair(p, cc % k)); } } } if (x > 1) pcnt.push_back(make_pair(x, 1)); for (int j = 0; j < pcnt.size(); ++j) { temp.push_back(make_pair(pcnt[j].first, k - pcnt[j].second)); } ans += cnt[temp]; ++cnt[pcnt]; } cout << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using vi = vector<int>; using pii = pair<int, int>; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int n, k; cin >> n >> k; const ll M = 1e5 + 1; const ll B = M * M; vector<ll> caps(M, 1); for (int j = 2; j < M; ++j) { for (int l = 0; l < k; ++l) { caps[j] *= j; if (caps[j] > B) { caps[j] = -1; break; } } } vector<int> count(M); vector<vector<ll>> factors(M); for (int p = 2; p < M; ++p) { if (!factors[p].empty()) continue; for (int j = p; j < M; j += p) { factors[j].push_back(p); } } ll ans = 0; for (int i = 0; i < n; ++i) { ll a; cin >> a; ll b = 1, c = a; for (ll p : factors[a]) { if (caps[p] == -1) { b = -1; break; } while (a % caps[p] == 0) { a /= caps[p]; c /= caps[p]; } if (a % p == 0) { b *= caps[p]; } while (a % p == 0) { a /= p; b /= p; } } if (b == -1) continue; if (b < M) { ans += count[b]; } ++count[c]; } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 43; const int maxm = 2e3 + 43; const int maxlog = 22; const int mod = 1e9 + 7; const int sq = 340; const int inf = 1e9; const long double PI = 3.141592653589793238463; long long cnt[10 * maxn]; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cout.precision(15); long long n, k; cin >> n >> k; if (k != 2) { vector<long long> nums; for (long long i = 1; i <= (long long)(1e5 + 3); i++) { long long cur = 1; for (long long j = 1; j <= k; j++) { cur *= i; if (cur > 1e10 + 34) break; } if (cur <= 1e10 + 34) nums.push_back(cur); else break; } long long ans = 0; for (long long i = 1; i <= n; i++) { long long x; cin >> x; for (long long j = 0; j < nums.size(); j++) { long long y = nums[j]; if (y % x == 0) { if (y / x < maxn) { ans += cnt[y / x]; } } } cnt[x]++; } cout << ans << endl; return 0; } else { long long ans = 0; map<vector<long long>, long long> ma; for (long long i = 0; i < n; i++) { long long x; cin >> x; vector<long long> v; long long y = x; for (long long i = 2; i * i <= x; i++) { if (y % i == 0) { bool flag = false; while (y % i == 0) { y /= i; flag ^= 1; } if (flag) v.push_back(i); } } if (y != 1) v.push_back(y); sort(v.begin(), v.end()); ans += ma[v]; ma[v]++; } cout << ans << endl; return 0; } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O3") using namespace std; const long long INF = 1e7; long long p(long long n, long long k) { if (k == 0) return 1; if (k % 2 == 1) return min(INF, n * p(min(INF, n * n), k / 2)); else return p(min(INF, n * n), k / 2); } int main() { ios_base::sync_with_stdio(false); long long n, k; cin >> n >> k; long long a[n]; for (long long i = 0; i < n; i++) { cin >> a[i]; for (long long x = 2; p(x, k) <= a[i]; x++) { while ((a[i] % p(x, k)) == 0) a[i] /= p(x, k); } } long long ans = 0; map<long long, long long> K; for (long long i = 0; i < n; i++) { long long x = a[i]; long long y = 1; for (long long p_ = 2; p_ <= 320; p_++) { long long alfa = 0; while (x % p_ == 0) { x /= p_; alfa++; } if (alfa > 0) y *= p(p_, k - alfa); y = min(y, INF); } if (x != 1) y *= p(x, k - 1); y = min(y, INF); ans += K[y]; K[a[i]]++; } cout << ans << "\n"; }
#include <bits/stdc++.h> using namespace std; const int N = 1e6 + 10; int n, k; long long a[N], b[N]; int ma[N]; long long qpow(long long a, long long n) { if (n < 0) throw; long long r = 1; for (; n; a = a * a, n >>= 1) if (n & 1) r = r * a; return r; } int main() { ma[1] = 1; for (int i = 2; i < N; ++i) if (!ma[i]) { for (int j = i; j < N; j += i) ma[j] = max(ma[j], i); } scanf("%d%d", &n, &k); for (int i = 1; i <= n; ++i) scanf("%lld", a + i); for (int i = 1; i <= n; ++i) { b[i] = 1; int first = a[i], second = 1; while (first != 1) { int p = ma[first], cnt = 0; while (first % p == 0) first /= p, ++cnt; cnt %= k; if (cnt) { b[i] *= qpow(p, k - cnt); second *= qpow(p, cnt); } } a[i] = second; } long long ans = 0; map<long long, int> vis; for (int i = 1; i <= n; ++i) { ans += vis[b[i]]; ++vis[a[i]]; } printf("%lld\n", ans); }
#include <bits/stdc++.h> using namespace std; vector<int> prime_division(int64_t n, int K) { vector<int> ret; for (int64_t i = 2; i * i <= n; i++) { int cnt = 0; while (n % i == 0) { n /= i; cnt++; } if (cnt % K) { ret.push_back(i); ret.push_back(cnt % K); } } if (n > 1) { ret.push_back(n); ret.push_back(1); } return ret; } int main() { int N, K, A[100000]; cin >> N >> K; for (int i = 0; i < N; i++) cin >> A[i]; int64_t ans = 0; map<vector<int>, int> mp; for (int i = 0; i < N; i++) { auto v = prime_division(A[i], K); int sz = v.size(); auto v2 = v; for (int i = 1; i < sz; i += 2) { v2[i] = K - v[i]; } if (mp.count(v2)) ans += mp[v2]; mp[v]++; } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; template <class t, class u> void chmax(t& first, u second) { if (first < second) first = second; } template <class t, class u> void chmin(t& first, u second) { if (second < first) first = second; } template <class t> using vc = vector<t>; template <class t> using vvc = vc<vc<t>>; using pi = pair<ll, ll>; using vi = vc<ll>; template <class t, class u> ostream& operator<<(ostream& os, const pair<t, u>& p) { return os << "{" << p.first << "," << p.second << "}"; } template <class t> ostream& operator<<(ostream& os, const vc<t>& v) { os << "{"; for (auto e : v) os << e << ","; return os << "}"; } using uint = unsigned; using ull = unsigned long long; template <ll i, class T> void print_tuple(ostream&, const T&) {} template <ll i, class T, class H, class... Args> void print_tuple(ostream& os, const T& t) { if (i) os << ","; os << get<i>(t); print_tuple<i + 1, T, Args...>(os, t); } template <class... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) { os << "{"; print_tuple<0, tuple<Args...>, Args...>(os, t); return os << "}"; } void print(ll x, ll suc = 1) { cout << x; if (suc == 1) cout << "\n"; if (suc == 2) cout << " "; } ll read() { ll i; cin >> i; return i; } vi readvi(ll n, ll off = 0) { vi v(n); for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off; return v; } template <class T> void print(const vector<T>& v, ll suc = 1) { for (ll i = ll(0); i < ll(v.size()); i++) print(v[i], i == ll(v.size()) - 1 ? suc : 2); } string readString() { string s; cin >> s; return s; } template <class T> T sq(const T& t) { return t * t; } void yes(bool ex = true) { cout << "Yes" << endl; if (ex) exit(0); } void no(bool ex = true) { cout << "No" << endl; if (ex) exit(0); } constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; } const ll infLL = LLONG_MAX / 3; const ll inf = infLL; ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); } ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); } ll popcount(signed t) { return __builtin_popcount(t); } ll popcount(ll t) { return __builtin_popcountll(t); } bool ispow2(ll i) { return i && (i & -i) == i; } ll mask(ll i) { return (ll(1) << i) - 1; } bool inc(ll first, ll second, ll c) { return first <= second && second <= c; } template <class t> void mkuni(vc<t>& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); } ll rand_int(ll l, ll r) { static random_device rd; static mt19937_64 gen(rd()); return uniform_int_distribution<ll>(l, r)(gen); } const ll vmax = 100010; bool pri[vmax]; void initprime() { for (ll i = ll(2); i < ll(vmax); i++) pri[i] = 1; for (ll i = ll(2); i < ll(vmax); i++) if (pri[i]) for (ll j = i * 2; j < vmax; j += i) pri[j] = 0; } vi factors[vmax]; void initfactor() { for (ll i = ll(2); i < ll(vmax); i++) if (pri[i]) for (ll j = i; j < vmax; j += i) factors[j].push_back(i); } ll y[vmax], z[vmax]; void mult(ll& first, ll second) { first = min(first * second, vmax); } ll mypow(ll first, ll n) { ll res = 1; while (n) { if (n & 1) mult(res, first); mult(first, first); n >>= 1; } return res; } signed main() { cin.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(20); initprime(); initfactor(); ll n, k; cin >> n >> k; for (ll i = ll(1); i < ll(vmax); i++) { ll x = i; ll p = 1, w = 1; for (auto f : factors[i]) { ll c = 0; while (x % f == 0) { c++; x /= f; } c %= k; mult(p, mypow(f, c)); c = (k - c % k) % k; mult(w, mypow(f, c)); } if (i < 10) { void(0); void(0); } y[i] = p; z[i] = w; } vi cnt(vmax + 1); ll ans = 0; for (ll i = ll(0); i < ll(n); i++) { ll first; cin >> first; first = y[first]; ans += cnt[z[first]]; cnt[first]++; } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; using ll = long long; constexpr int NMAX = 100010; int pfac[NMAX]; ll byKFreePart[NMAX]; int kFreeConjugate[NMAX]; int kFreePart[NMAX]; void fillWithPFactors(int x, map<int, int> &m) { if (x == 1) return; ++m[pfac[x]]; fillWithPFactors(x / pfac[x], m); } int main() { int n, k; scanf("%d %d", &n, &k); for (int i = 2; i < NMAX; ++i) pfac[i] = i; for (int i = 2; i < NMAX; ++i) { if (pfac[i] < i) continue; for (int toMark = 2 * i; toMark < NMAX; toMark += i) pfac[toMark] = i; } for (int i = 1; i < NMAX; ++i) { map<int, int> cpf; fillWithPFactors(i, cpf); for (auto &p_e : cpf) p_e.second %= k; kFreePart[i] = 1; for (auto p_e : cpf) { for (int k = 0; k < p_e.second; ++k) kFreePart[i] *= p_e.first; } for (auto &p_e : cpf) p_e.second = (k - p_e.second) % k; ll cprod = 1; for (auto p_e : cpf) { for (int k = 0; k < p_e.second && cprod < NMAX; ++k) cprod *= p_e.first; } if (cprod < NMAX) kFreeConjugate[i] = cprod; else kFreeConjugate[i] = -1; } ll ans = 0; for (int i = 0; i < n; ++i) { int x; scanf("%d", &x); if (kFreeConjugate[x] > -1) ans += byKFreePart[kFreeConjugate[x]]; ++byKFreePart[kFreePart[x]]; } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 5, limit = 1e6; long long pw[N][101], sv[N]; int main() { ios_base::sync_with_stdio(0); cin.tie(0); for (int i = 1; i < N; i++) { pw[i][0] = 1; for (int j = 1; j < 101; j++) { if (limit / i < pw[i][j - 1] || pw[i][j - 1] == 0) pw[i][j] = 0; else pw[i][j] = pw[i][j - 1] * 1LL * i; } } int n, k; cin >> n >> k; long long ans = 0; for (int i = 0, x; i < n; i++) { vector<pair<int, int> > pr; cin >> x; for (int j = 2; j * j <= x; j++) { int cnt = 0; while (x % j == 0) x /= j, cnt++; if (cnt % k) pr.emplace_back(j, cnt % k); } if (x > 1) pr.emplace_back(x, 1); long long num = 1; int num2 = 1; for (auto &y : pr) { num = num * 1LL * pw[y.first][k - y.second]; num2 *= pw[y.first][y.second]; } if (num < N) ans += sv[num]; sv[num2]++; } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long long int maxn = 220010, p = 179, mod = 17917917911791; long long int predp[maxn]; map<long long int, long long int> mp; int main() { cin.tie(0), cout.tie(0), ios_base::sync_with_stdio(false); long long int n, k; cin >> n >> k; predp[0] = 1; for (int d = 1; d < maxn; d++) { predp[d] = (predp[d - 1] * p) % mod; } vector<long long int> mas(n, 0); for (int d = 0; d < n; d++) { cin >> mas[d]; } long long int ans = 0; for (int d = 0; d < n; d++) { vector<pair<long long int, long long int> > del; long long int n1 = mas[d]; long long int hash1 = 0; long long int hash2 = 0; for (int i = 2; i * i <= mas[d] && i <= n1; i++) { if (n1 % i == 0) { long long int cnt = 0; while (n1 % i == 0) { n1 /= i; cnt++; } cnt %= k; hash1 += predp[i] * cnt; hash1 %= mod; hash2 += predp[i] * ((k - cnt) % k); hash2 %= mod; } } if (n1 != 1) { hash1 += predp[n1]; hash1 %= mod; hash2 += predp[n1] * (k - 1); hash2 %= mod; } ans += mp[hash2]; mp[hash1]++; } cout << ans; }
#include <bits/stdc++.h> using namespace std; const long long MOD = 1000000007; const long long INF = 1000000001; const long long INF2 = 1000000000000000001LL; const double PI = acos(-1); const double ERR = 1e-10; const int N = 100005; long long n, k; int a[N]; vector<pair<int, char> > v1[N]; vector<pair<int, char> > v[N]; const int PN = 100005; bool isprime[PN]; void primechk() { for (int i = 2; i < PN; i++) isprime[i] = true; for (long long i = 2; i < PN; i++) if (isprime[i]) { v[i].push_back(pair<int, char>(i, 1)); for (long long j = i * i; j < PN; j += i) isprime[j] = false; for (long long j = 2 * i; j < PN; j += i) { v[j].push_back(pair<int, char>(i, 1)); long long j1 = j / i; while (j1 != 0 && j1 % i == 0) { j1 /= i; v[j][(int)v[j].size() - 1].second++; } } } } map<vector<pair<int, char> >, long long> m; int main() { primechk(); scanf("%lld", &n); scanf("%lld", &k); for (int i = 0; i < n; i++) { scanf("%d", &a[i]); vector<pair<int, char> > vv; vv.push_back(pair<int, char>(0, 0)); unsigned long long m1 = 1; for (int j = 0; j < v[a[i]].size(); j++) { pair<int, char> now = v[a[i]][j]; if (now.second % k != 0) { now.second = now.second % k; vv.push_back(now); } } if (m.find(vv) == m.end()) { m[vv] = 1; } else m[vv]++; } long long ans = 0; for (int i = 0; i < n; i++) { vector<pair<int, char> > vv; vector<pair<int, char> > vv1; vv.push_back(pair<int, char>(0, 0)); vv1.push_back(pair<int, char>(0, 0)); unsigned long long m1 = 1, m2 = 1; for (int j = 0; j < v[a[i]].size(); j++) { pair<int, char> now = v[a[i]][j]; if (now.second % k != 0) { now.second = now.second % k; vv.push_back(now); vv1.push_back(now); vv[(int)vv.size() - 1].second = k - vv[(int)vv.size() - 1].second; } } m[vv1]--; if (m.find(vv) != m.end()) { ans += m[vv]; } m[vv1]++; } printf("%lld", ans / 2); return 0; }
#include <bits/stdc++.h> using namespace std; int a[600030], n, k; int f(int x) { int ret = 1; for (int i = 2; i * i <= x; ++i) { if (x % i) continue; int t = 0; while (x % i == 0) { x /= i; t += 1; } t %= k; while (t--) ret *= i; } if (x > 1) { ret *= x; } return ret; } bool check(int t, int x, int k) { for (int i = 1; i <= k; ++i) { if (1LL * t * x > 600030) { return false; } t *= x; } return true; } int g(int x) { int ret = 1; for (int i = 2; i * i <= x; ++i) { if (x % i) continue; int t = 0; while (x % i == 0) { x /= i; ++t; } t = (k - t) % k; if (!check(ret, i, t)) { return -1; } while (t--) ret *= i; } if (x > 1) { if (!check(ret, x, k - 1)) { return -1; } for (int i = 1; i <= k - 1; ++i) ret *= x; } return ret; } int main() { map<int, int> mp; scanf("%d%d", &n, &k); for (int i = 1; i <= n; ++i) { scanf("%d", &a[i]); a[i] = f(a[i]); mp[a[i]]++; } long long ans = 0; for (int i = 1; i <= n; ++i) { int v = g(a[i]); ans += mp[v]; if (v == a[i]) ans--; } printf("%lld\n", ans / 2); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 5; long long n, k, a[N]; map<vector<pair<int, int> >, int> cnt; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n >> k; long long ans = 0; for (int i = 1; i <= n; i++) { cin >> a[i]; long long tmp = a[i]; vector<pair<int, int> > prDiv, findDiv; for (int j = 2; j <= sqrt(tmp); j++) { if (tmp % j == 0) { int cnt = 0; while (tmp % j == 0) { tmp /= j; cnt++; } if (cnt % k != 0) { prDiv.push_back({j, cnt % k}); findDiv.push_back({j, k - (cnt % k)}); } } } if (tmp > 1) { prDiv.push_back({tmp, 1}); findDiv.push_back({tmp, k - 1}); } ans += cnt[findDiv]; cnt[prDiv]++; } cout << ans; }
#include <bits/stdc++.h> using namespace std; const int INF = 1000000001; const long long int INFLL = 10000000001; const long double EPS = 1e-6; const int MAXN = 100005; const int FACTORS_THRESHOLD = 100005; int A[MAXN]; int T[MAXN]; long long int Power(int x, int y) { long long int r = 1; for (int i = 0; i < y; i++) { r = min(INFLL, r * x); if (r >= INFLL) break; } return r; } void Sieve(int n, vector<int>* primes, vector<int>* factors) { factors->resize(n + 1); for (int i = 2; i * i <= n; i++) { if ((*factors)[i] != 0) continue; for (int j = 2 * i; j <= n; j += i) if ((*factors)[j] == 0) (*factors)[j] = i; } (*factors)[1] = 1; for (int i = 2; i <= n; i++) if ((*factors)[i] == 0) { (*factors)[i] = i; primes->push_back(i); } } int SmallestFactor(long long int n, const vector<int>& primes, const vector<int>& factors) { if (n <= FACTORS_THRESHOLD) { if (factors[n] == n) return 1; return factors[n]; } else { for (int i = 0; i < primes.size(); i++) if (n % primes[i] == 0) return primes[i]; return 1; } } void Factorize(long long int n, const vector<int>& primes, const vector<int>& factors, unordered_map<long long int, int>* factorization) { if (n == 1) return; long long int d = SmallestFactor(n, primes, factors); if (d == 1) { (*factorization)[n]++; return; } Factorize(d, primes, factors, factorization); Factorize(n / d, primes, factors, factorization); } unordered_map<long long int, int> Factorize(long long int n, const vector<int>& primes, const vector<int>& factors) { unordered_map<long long int, int> factorization; Factorize(n, primes, factors, &factorization); return factorization; } void Divisors(const unordered_map<long long int, int>& factorization, unordered_map<long long int, int>::iterator it, long long int divisor, vector<long long int>* result) { if (it == factorization.end()) { result->push_back(divisor); return; } for (int i = 0; i <= it->second; i++) { Divisors(factorization, next(it), divisor, result); divisor *= it->first; } } vector<long long int> Divisors(long long int n, const vector<int>& primes, const vector<int>& factors) { unordered_map<long long int, int> factorization = Factorize(n, primes, factors); vector<long long int> divisors; Divisors(factorization, factorization.begin(), 1LL, &divisors); return divisors; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); vector<int> primes, factors; Sieve(FACTORS_THRESHOLD, &primes, &factors); int n, k; cin >> n >> k; for (int i = 0; i < n; i++) { cin >> T[i]; A[T[i]]++; } long long int result = 0; for (int i = 1;; i++) { long long int pwr = Power(i, k); if (pwr >= INFLL) break; vector<long long int> dvs = Divisors(pwr, primes, factors); for (long long int x : dvs) { long long int y = pwr / x; if (x >= MAXN) continue; if (y >= MAXN) continue; if (x > y) continue; if (x != y) result += (long long int)A[x] * A[y]; if (x == y) result += ((long long int)A[x] * (A[x] - 1)) / 2; } } cout << result << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> class RangeCountExact { map<T, int> mp; vector<vector<int>> idxs; int get(int r, T x) { if (mp.count(x) == 0) return 0; int a = mp[x]; return lower_bound(idxs[a].begin(), idxs[a].end(), r) - idxs[a].begin(); } public: RangeCountExact(const vector<T> &as) { for (auto &a : as) mp[a]; int N = 0; for (auto &p : mp) { p.second = N++; } idxs.resize(N); for (int i = 0; i < as.size(); i++) { idxs[mp[as[i]]].push_back(i); } } int get(int l, int r, T x) { return get(r, x) - get(l, x); } }; int main() { ios::sync_with_stdio(false); cin.tie(0); int n, k; cin >> n >> k; vector<set<int>> as; map<int, int> kesu; for (int i = 0; i < n; i++) { set<int> ps; int a; cin >> a; for (int j = 2; j * j <= a; j++) { if (a % j == 0) { int cnt = 0; while (a % j == 0) { a /= j; cnt++; } cnt %= k; if (cnt) { int b = 1; for (int q = 0; q < cnt; q++) b *= j; ps.insert(b); long long c = 1; bool ok = true; for (int q = 0; q < k - cnt; q++) { c *= j; if (c > 1e5) { ok = false; break; } } if (ok) { kesu[b] = c; kesu[c] = b; } } } } if (a > 1) { ps.insert(a); long long c = 1; bool ok = true; for (int q = 0; q < k - 1; q++) { c *= a; if (c > 1e5) { ok = false; break; } } if (ok) { kesu[a] = c; kesu[c] = a; } } as.push_back(ps); } RangeCountExact<set<int>> cnt(as); long long ans = 0; for (int i = 0; i < n; i++) { set<int> need; bool ok = true; for (auto &p : as[i]) { if (kesu.count(p) == 0) { ok = false; break; } need.insert(kesu[p]); } if (ok) ans += cnt.get(i + 1, n, need); } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; long long a[500005], tt[500005], t[500005]; signed main() { long long n, k, ans = 0; scanf("%lld%lld", &n, &k); if (k == 2) { for (long long i = 1; i <= n; i++) { scanf("%lld", a + i); for (long long j = 2; j * j <= a[i]; j++) { while (a[i] % (j * j) == 0) a[i] /= (j * j); } t[a[i]]++; } for (long long i = 1; i <= 100000; i++) ans += t[i] * (t[i] - 1) / 2; printf("%lld\n", ans); } else { long long tot = 0; for (long long i = 1;; i++) { long long now = 1, flag = 0; for (long long j = 1; j <= k; j++) { now *= i; if (now > 10000000000ll) { flag = 1; break; } } if (flag) break; t[++tot] = now; } for (long long i = 1; i <= n; i++) { scanf("%lld", a + i); } sort(a + 1, a + 1 + n); for (long long i = 1; i <= n; i++) { for (long long j = 1; j <= tot; j++) { if (t[j] % a[i] != 0) continue; if (t[j] / a[i] > a[i]) continue; ans += tt[t[j] / a[i]]; } tt[a[i]]++; } printf("%lld\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; template <typename T> vector<pair<T, int>> factorize(T x) { vector<pair<T, int>> res; for (T i = 2; i * i <= x; i++) { if (x % i == 0) { res.emplace_back(i, 0); while (x % i == 0) { res.back().second++; x /= i; } } } if (x > 1) { if (!res.empty() && res.back().first == x) res.back().second++; else res.emplace_back(x, 1); } return res; } int main() { ios::sync_with_stdio(false), cin.tie(0); int n, k; cin >> n >> k; map<vector<pair<int, int>>, int> cnt; ll res = 0; for (int i = 0; i < n; i++) { int a; cin >> a; auto fs = factorize(a); vector<pair<int, int>> tf; for (auto p : fs) { p.second %= k; if (p.second != 0) tf.push_back(p); } res += cnt[tf]; for (auto& p : tf) { p.second = k - p.second; } cnt[tf] += 1; } cout << res << endl; return 0; }
#include <bits/stdc++.h> using namespace std; char ch[2010]; int i, j, n, g[2010][2010], f[2010][2010], ans; int main() { scanf("%s", ch + 1); n = strlen(ch + 1); for (i = 0; i <= n + 1; i++) { if (ch[i] == '(') break; f[i][0] = 1; } for (i = n + 1; i >= 1; i--) { if (ch[i] == ')') break; g[i][0] = 1; } for (i = 1; i <= n; i++) for (j = 1; j <= i; j++) { if (ch[i] == '(') f[i][j] = f[i - 1][j - 1]; else if (ch[i] == ')') f[i][j] = f[i - 1][j]; else f[i][j] = (f[i - 1][j] + f[i - 1][j - 1]) % 998244353; } for (i = n; i >= 1; i--) for (j = 1; j <= n - i + 1; j++) { if (ch[i] == ')') g[i][j] = g[i + 1][j - 1]; else if (ch[i] == '(') g[i][j] = g[i + 1][j]; else g[i][j] = (g[i + 1][j] + g[i + 1][j - 1]) % 998244353; } for (i = 1; i < n; i++) { for (j = 1; j <= min(i, n - i); j++) { ans += 1ll * f[i][j] * g[i + 1][j] % 998244353 * j % 998244353; ans %= 998244353; } } printf("%d\n", ans); }
#include <bits/stdc++.h> using namespace std; int i, j, k, n, m, t; long long res, l[1000050][3], r[1000050][3], p[1005000]; char s[1005000]; long long jc[1005000], inv[1005000]; long long ksm(long long a, int p) { long long res = 1; while (p) { if (p & 1) { res = res * a % 998244353; } a = a * a % 998244353; p >>= 1; } return res; } long long c(int n, int m) { if (n < 0 || m < 0 || n < m) { return 0; } return jc[n] * inv[m] % 998244353 * inv[n - m] % 998244353; } int main() { jc[0] = inv[0] = 1; for (i = 1; i <= 1000000; i++) { jc[i] = jc[i - 1] * i % 998244353; } inv[1000000] = ksm(jc[1000000], 998244353 - 2); for (i = 999999; i >= 1; i--) { inv[i] = inv[i + 1] * (i + 1) % 998244353; } gets(s + 1); n = strlen(s + 1); for (i = n; i >= 1; i--) { r[i][1] = r[i + 1][1]; r[i][2] = r[i + 1][2]; if (s[i] == ')') { r[i][1]++; } if (s[i] == '?') { r[i][2]++; } } for (i = 1; i <= n; i++) { l[i][1] = l[i - 1][1]; l[i][2] = l[i - 1][2]; if (s[i] == '(') { l[i][1]++; } if (s[i] == '?') { l[i][2]++; } for (j = max(l[i][1], r[i + 1][1]); j <= min(l[i][1] + l[i][2], r[i + 1][1] + r[i + 1][2]); j++) { res += c(l[i][2], j - l[i][1]) * c(r[i + 1][2], j - r[i + 1][1]) % 998244353 * j % 998244353; } } printf("%lld", res % 998244353); }
#include <bits/stdc++.h> using namespace std; #pragma GCC optimize("O3") const int mods[10] = {1000000007, 999999937, 999999929, 999999893, 999999883, 999999797, 999999761, 999999757, 999999751, 999999739}; const int mod = 998244353; int rand_mods[2]; const long double eps = 1e-10; const int siz = 2e3 + 5, siz2 = 3e5 + 5, lg = 20, block = 300, block2 = 1000, mxv = 1e5 + 1, sqrt_mod = 31630; const int alpha_sz = 26; char arr[siz]; int dp[siz][siz][4], qcmu[siz]; int mul(long long a, long long b) { return (a * b) % mod; } int powmod(int a, int b) { if (b == 0) { return 1; } int p = powmod(a, b / 2); p = mul(p, p); return b % 2 ? mul(p, a) : p; } int add(long long a, long long b) { return (a + b) % mod; } int sum(int l, int r) { int ret = 0; for (int i = 0; i < 4; i++) { ret = add(ret, dp[l][r][i]); } return ret; } int main() { scanf("%s", arr + 1); int sz = strlen(arr + 1); for (int i = 1; i <= sz; i++) { qcmu[i] = (arr[i] == '?') + qcmu[i - 1]; } for (int i = 1; i < sz; i++) { dp[i][i + 1][1] = arr[i] != ')' && arr[i + 1] != '('; } for (int len = 3; len <= sz; len++) { for (int i = 1; i + len - 1 <= sz; i++) { int l = i, r = i + len - 1; if (arr[l] != ')' && arr[r] != '(') { dp[l][r][1] = add(sum(l + 1, r - 1), powmod(2, qcmu[r - 1] - qcmu[l])); } if (arr[l] != '(' && arr[r] != '(') { dp[l][r][3] = add(dp[l + 1][r][1], dp[l + 1][r][3]); } if (arr[l] != ')' && arr[r] != ')') { dp[l][r][0] = add(dp[l][r - 1][0], dp[l][r - 1][1]); } if (arr[l] != '(' && arr[r] != ')') { dp[l][r][2] = sum(l + 1, r - 1); } } } printf("%d\n", sum(1, sz)); return 0; }
#include <bits/stdc++.h> const int maxn = 2e3 + 10; const int maxm = 1e5 + 10; const long long int mod = 998244353; const long long int INF = 1e18 + 100; const int inf = 0x3f3f3f3f; const double pi = acos(-1.0); const double eps = 1e-8; using namespace std; int n, m; int cas, tol, T; char ch[maxn]; long long int pow(long long int a, long long int b) { long long int ans = 1; while (b) { if (b & 1) ans = ans * a % mod; a = a * a % mod; b /= 2; } return ans; } long long int dp[maxn][maxn], a[maxn]; int main() { scanf("%s", ch + 1); int len = strlen(ch + 1); a[0] = 0; for (int i = 1; i <= len; i++) { a[i] = a[i - 1] + (ch[i] == '?' ? 1 : 0); if (i != len && ch[i] != ')' && ch[i + 1] != '(') dp[i][i + 1] = 1; } for (int d = 3; d <= len; d++) { for (int i = 1; i + d - 1 <= len; i++) { int j = i + d - 1; dp[i][j] = 0; if (ch[i] != '(') dp[i][j] += dp[i + 1][j]; if (ch[j] != ')') dp[i][j] += dp[i][j - 1]; if (ch[i] != '(' && ch[j] != ')') dp[i][j] -= dp[i + 1][j - 1]; if (ch[i] != ')' && ch[j] != '(') dp[i][j] += dp[i + 1][j - 1] + pow(2ll, a[j - 1] - a[i]); dp[i][j] %= mod; } } printf("%lld\n", dp[1][len]); return 0; }
#include <bits/stdc++.h> using namespace std; const long long maxn = 2010; const long long mod = 998244353; long long pw(long long a, long long b) { if (b == 0) return 1; long long k = pw(a, b / 2); k = (k * k) % mod; if (b & 1) k = (k * a) % mod; return k; } long long n, m; long long dp[maxn][maxn], cnt[maxn], f[maxn][maxn]; string s; signed main() { s += "."; string ss; cin >> ss; n = ss.size(); s += ss; for (long long i = 1; i <= n; i++) cnt[i] = cnt[i - 1] + (s[i] == '?'); for (long long t = 2; t <= n; t++) for (long long l = 1; l + t - 1 <= n; l++) { long long r = l + t - 1; if (t == 2) f[l][r] = (s[l] != ')'); if (s[l] == ')') { dp[l][r] = dp[l + 1][r]; f[l][r] = f[l + 1][r]; continue; } if (s[r] == '(') { dp[l][r] = dp[l][r - 1]; continue; } if (t == 2) { dp[l][r] = 1; continue; } long long K = pw(2, cnt[r - 1] - cnt[l]); f[l][r] = K + dp[l + 1][r - 1]; if (s[l] == '?') f[l][r] += f[l + 1][r]; f[l][r] %= mod; if (s[l] == '(' && s[r] == ')') dp[l][r] = (dp[l + 1][r - 1] + K) % mod; if (s[l] == '?' && s[r] == ')') dp[l][r] = (dp[l + 1][r] + dp[l + 1][r - 1] + K) % mod; if (s[l] == '(' && s[r] == '?') dp[l][r] = (dp[l][r - 1] + dp[l + 1][r - 1] + K) % mod; if (s[l] == '?' && s[r] == '?') dp[l][r] = (K + dp[l + 1][r - 1] + dp[l][r - 1] + f[l + 1][r]) % mod; } cout << dp[1][n]; }
#include <bits/stdc++.h> using namespace std; const int N = 2005; const int mod = 998244353; char str[N]; long long l[N], r[N], s[N]; long long q_pow(long long a, long long b) { long long res = 1; while (b) { if (b & 1) (res *= a) %= mod; (a *= a) %= mod; b >>= 1; } return res; } long long c(long long a, long long b) { if (a < b) return 0; long long x = 1, y = 1; for (long long i = a, j = 1; j <= b; i--, j++) x = x * i % mod, y = y * j % mod; return (x * q_pow(y, mod - 2)) % mod; } long long lu(long long a, long long b) { if (a < mod && b < mod) return c(a, b); return (long long)c(a % mod, b % mod) * lu(a / mod, b / mod) % mod; } long long cal[2][N]; void init(long long n, long long a[]) { a[0] = 1; for (long long i = 1; i <= n; i++) { a[i] = (((a[i - 1] * (n - i + 1)) % mod) * q_pow(i, mod - 2)) % mod; } for (long long i = 1; i <= n; i++) { (a[i] += a[i - 1]) %= mod; } } int main() { long long ans = 0; scanf("%s", str + 1); long long n = strlen(str + 1); for (int i = 1; i <= n; i++) { l[i] = l[i - 1]; r[i] = r[i - 1]; s[i] = s[i - 1]; if (str[i] == '(') l[i]++; else if (str[i] == ')') r[i]++; else if (str[i] == '?') s[i]++; } init(s[n], cal[s[n] & 1]); init(s[n] - 1, cal[(s[n] - 1) & 1]); long long ss = s[n]; for (int i = 1; i <= n; i++) { long long le = -l[i] + r[n] - r[i] + s[n] - s[i]; if (str[i] == '(') { le = min(le, ss); if (le < 0) continue; (ans += (cal[ss & 1][le])) %= mod; } else if (str[i] == '?') { le = min(le - 1, ss - 1); if (le < 0) continue; (ans += (cal[(ss - 1) & 1][le])) %= mod; } } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; const int mod = 998244353; int n; char s[2010]; int num[2010], sum[2010]; int dp[2010][2010]; int main() { ios::sync_with_stdio(false); cin.tie(0), cout.tie(0); int i, j; cin >> s + 1; n = strlen(s + 1); num[0] = 1; for (i = 1; i <= n; i++) { sum[i] = sum[i - 1] + (s[i] == '?'); num[i] = (2LL * num[i - 1]) % mod; } for (i = 1; i <= n; i++) for (j = i - 1; j > 0; j--) { if (s[j] != '(') dp[j][i] = (dp[j][i] + dp[j + 1][i]) % mod; if (s[i] != ')') dp[j][i] = (dp[j][i] + dp[j][i - 1]) % mod; if (s[j] != '(' && s[i] != ')') dp[j][i] = (dp[j][i] - dp[j + 1][i - 1]) % mod; if (s[j] != ')' && s[i] != '(') dp[j][i] = ((dp[j][i] + dp[j + 1][i - 1]) % mod + num[sum[i - 1] - sum[j]]) % mod; } cout << (dp[1][n] + mod) % mod << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long int MOD = 998244353; long long int power(long long int x, long long int n, long long int &m) { x %= m; long long int ans = 1; while (n > 0) { if (n & 1) (ans *= x) %= m; (x = x * x) %= m; n >>= 1; } return ans; } const long long int mxn = 2000; vector<vector<long long int>> dp(mxn + 1, vector<long long int>(mxn + 1, 0)); vector<long long int> prefix(mxn + 1, 0); long long int len; long long int getSum(vector<long long int> &prefix, long long int f, long long int t) { if (f == 0) return prefix[t]; return (prefix[t] - prefix[f - 1]); } void TESTCASE() { string s; cin >> s; len = s.size(); prefix[0] = (s[0] == '?'); for (long long int i = 1; i < len; i++) prefix[i] = prefix[i - 1] + (s[i] == '?'); for (long long int l = 2; l <= len; l++) { for (long long int i = 0; i < len - l + 1; i++) { long long int j = i + l - 1; if (s[i] == ')' || s[i] == '?') { dp[i][j] += dp[i + 1][j]; dp[i][j] %= MOD; } if (s[j] == '(' || s[j] == '?') { dp[i][j] += dp[i][j - 1]; dp[i][j] %= MOD; } if ((s[i] == '?' && s[j] == '?') || (s[i] == ')' && s[j] == '(') || (s[i] == '?' && s[j] == '(') || (s[i] == ')' && s[j] == '?')) { dp[i][j] -= dp[i + 1][j - 1]; dp[i][j] += MOD; dp[i][j] %= MOD; } if ((s[i] == '?' && s[j] == '?') || (s[i] == '(' && s[j] == ')') || (s[i] == '(' && s[j] == '?') || (s[i] == '?' && s[j] == ')')) { dp[i][j] += dp[i + 1][j - 1] + power(2, getSum(prefix, i + 1, j - 1), MOD); dp[i][j] %= MOD; } } } cout << dp[0][len - 1] << "\n"; } signed main() { long long int TESTS = 1; while (TESTS--) { TESTCASE(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 998244353; int dp[2005][2005], dp2[2005][2005]; inline void add(int &x, int y) { x += y; if (x >= mod) x -= mod; } int main() { ios_base::sync_with_stdio(0), cin.tie(0); string s; cin >> s; int n = s.length(); if (s[0] == '(' || s[0] == '?') dp[0][1] = 1; if (s[0] == ')' || s[0] == '?') dp[0][0] = 1; for (int i = 0; i + 1 < n; ++i) for (int d = 0; d <= i + 1; ++d) { if (s[i + 1] == '(' || s[i + 1] == '?') add(dp[i + 1][d + 1], dp[i][d]); if (s[i + 1] == ')' || s[i + 1] == '?') add(dp[i + 1][d], dp[i][d]); } if (s.back() == '(' || s.back() == '?') dp2[n - 1][0] = 1; if (s.back() == ')' || s.back() == '?') dp2[n - 1][1] = 1; for (int i = n - 1; i - 1 >= 0; --i) for (int d = 0; d <= n - i; ++d) { if (s[i - 1] == '(' || s[i - 1] == '?') add(dp2[i - 1][d], dp2[i][d]); if (s[i - 1] == ')' || s[i - 1] == '?') add(dp2[i - 1][d + 1], dp2[i][d]); } int ans = 0; for (int i = 0; i + 1 < n; ++i) for (int d = 1; d <= n; ++d) add(ans, (long long)dp[i][d] * dp2[i + 1][d] % mod * d % mod); cout << ans << "\n"; return 0; }
#include <bits/stdc++.h> const int mod = 998244353; using namespace std; string s; int dp1[3000][3000], dp2[3000][3000]; void sol() { memset(dp2, 0, sizeof(dp2)); memset(dp1, 0, sizeof(dp1)); int n = s.size(); dp1[0][0] = 1; dp2[n + 1][0] = 1; for (int i = 1; i <= n; ++i) { for (int j = 0; j <= n; ++j) { if (s[i - 1] == '(') { if (j) dp1[i][j] = (dp1[i][j] + dp1[i - 1][j - 1]) % mod; } else if (s[i - 1] == ')') { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j]) % mod; } else { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j]) % mod; if (j) { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j - 1]) % mod; } } } } for (int i = n; i > 0; --i) { for (int j = 0; j <= n; ++j) { if (s[i - 1] == ')') { if (j) dp2[i][j] = (dp2[i][j] + dp2[i + 1][j - 1]) % mod; } else if (s[i - 1] == '(') { dp2[i][j] = (dp2[i][j] + dp2[i + 1][j]) % mod; } else { dp2[i][j] = (dp2[i][j] + dp2[i + 1][j]) % mod; if (j) dp2[i][j] = (dp2[i][j] + dp2[i + 1][j - 1]) % mod; } } } long long ans = 0; for (int i = 1; i <= n; ++i) { for (int j = 1; j <= n; ++j) { ans = (ans + ((1ll * j * dp1[i][j]) % mod) * dp2[i + 1][j]) % mod; } } cout << ans << endl; } int main() { cin >> s; sol(); }
#include <bits/stdc++.h> using namespace std; long long int mod = 998244353; int main() { string s; cin >> s; int n = s.size(); vector<long long int> power_2(n + 1, 1); for (int i = 1; i < n + 1; i++) { power_2[i] = (2 * power_2[i - 1]) % mod; } vector<long long int> cnt(n + 1, 0); for (int i = 0; i < n; i++) { cnt[i + 1] = cnt[i]; if (s[i] == '?') cnt[i + 1]++; } vector<vector<long long int> > dp(n, vector<long long int>(n, 0)); for (int length = 2; length < n + 1; length++) { for (int i = 0; i < n - length + 1; i++) { int j = i + length - 1; if (s[i] != '(') dp[i][j] = (dp[i][j] + dp[i + 1][j]) % mod; if (s[j] != ')') dp[i][j] = (dp[i][j] + dp[i][j - 1]) % mod; if (s[i] != '(' && s[j] != ')') dp[i][j] = (dp[i][j] - dp[i + 1][j - 1] + mod) % mod; if (s[i] != ')' && s[j] != '(') { dp[i][j] = (dp[i][j] + dp[i + 1][j - 1]) % mod; dp[i][j] = (dp[i][j] + power_2[cnt[j] - cnt[i + 1]]) % mod; } } } long long int ans = dp[0][n - 1]; while (ans < 0) ans += mod; cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 2e3 + 10; const int mod = 998244353; char s[MAXN]; int n, bk[MAXN]; long long f[MAXN][MAXN]; long long qpow(long long x, long long k) { long long res = 1; while (k) { if (k & 1) res = res * x % mod; k >>= 1; x = x * x % mod; } return res; } int main() { scanf("%s", s + 1); n = strlen(s + 1); for (int i = 1; i <= n; i++) bk[i] = bk[i - 1] + (s[i] == '?'); for (int len = 2; len <= n; len++) for (int l = 1, r = l + len - 1; r <= n; l++, r++) { if (s[l] != '(') f[l][r] = (f[l][r] + f[l + 1][r]) % mod; if (s[r] != ')') f[l][r] = (f[l][r] + f[l][r - 1]) % mod; if (s[l] != '(' && s[r] != ')') f[l][r] = (f[l][r] - f[l + 1][r - 1] + mod) % mod; if (s[l] != ')' && s[r] != '(') f[l][r] = (f[l][r] + f[l + 1][r - 1] + qpow(2, bk[r - 1] - bk[l])) % mod; } printf("%lld\n", f[1][n]); return 0; }
#include <bits/stdc++.h> using namespace std; const int nmax = 2005; const int mod = 998244353; int sum[nmax]; long long dp[nmax][nmax]; int pow2[nmax]; int main() { string s; cin >> s; pow2[0] = 1; for (int i = 1; i < nmax; ++i) pow2[i] = (2LL * pow2[i - 1]) % mod; for (int i = 0; i < s.size(); ++i) { if (i) sum[i] += sum[i - 1]; if (s[i] == '?') ++sum[i]; } for (int l = 2; l <= s.size(); ++l) for (int i = 0; i < s.size() - l + 1; ++i) { int j = i + l - 1; int add = sum[j - 1] - sum[i]; if (s[i] != '(') { dp[i][j] += dp[i + 1][j]; dp[i][j] %= mod; } if (s[j] != ')') { dp[i][j] += dp[i][j - 1]; dp[i][j] %= mod; } if (s[i] != '(' && s[j] != ')') { dp[i][j] -= dp[i + 1][j - 1]; if (dp[i][j] < 0) dp[i][j] += mod; dp[i][j] %= mod; } if (s[i] != ')' && s[j] != '(') { dp[i][j] += dp[i + 1][j - 1] + pow2[add]; dp[i][j] %= mod; } } cout << dp[0][s.size() - 1]; }
#include <bits/stdc++.h> using namespace std; long long mod_pow(long long b, int x) { if (!x) return 1; if (x & 1) return (b * mod_pow(b, x - 1)) % 998244353; long long tmp = mod_pow(b, x / 2); return (tmp * tmp) % 998244353; } char s[2010]; int memo[2010][2010], acum[2010]; long long sum_depths(int l, int r) { if (l >= r) return 0; if (memo[l][r] != -1) return memo[l][r]; long long ret = 0; if (s[l] != '(') { ret = (ret + sum_depths(l + 1, r)) % 998244353; } if (s[r] != ')') { ret = (ret + sum_depths(l, r - 1)) % 998244353; } if (s[l] != '(' and s[r] != ')') { ret = (ret - sum_depths(l + 1, r - 1) + 998244353) % 998244353; } if (s[l] != ')' and s[r] != '(') { int k = acum[r - 1] - acum[l]; ret = (ret + sum_depths(l + 1, r - 1) + mod_pow(2, k)) % 998244353; } return memo[l][r] = ret; } int main() { while (scanf("%s", s) > 0) { for (int i = 0; s[i]; i++) { acum[i] = (s[i] == '?'); if (i) acum[i] += acum[i - 1]; } memset(memo, -1, sizeof memo); printf("%lld\n", sum_depths(0, strlen(s) - 1)); } }
#include <bits/stdc++.h> using namespace std; const long long N = 998244353; long long EXP(long long x, long long p) { if (p == 0) return 1; long long Ans = EXP(x, p / 2); Ans = (Ans * Ans) % N; if (p % 2 == 1) Ans *= x; return Ans % N; } string s; long long dp[2005][2005]; long long k[2005][2005]; long long F(int i, int j) { if (i >= j) return 0; if (dp[i][j] != -1) return dp[i][j]; long long ans = 0; if (s[i] == ')') ans = F(i + 1, j); if (s[j] == '(') ans = F(i, j - 1); if (s[i] == '(' && s[j] == ')') { ans = (F(i + 1, j - 1) + EXP(2, k[i + 1][j - 1])) % N; } if (s[i] == '(' && s[j] == '?') ans = ((F(i + 1, j - 1) + EXP(2, k[i + 1][j - 1])) % N + F(i, j - 1)) % N; if (s[i] == '?' && s[j] == ')') ans = ((F(i + 1, j - 1) + EXP(2, k[i + 1][j - 1])) % N + F(i + 1, j)) % N; if (s[i] == '?' && s[j] == '?') { ans = ((F(i + 1, j - 1) + EXP(2, k[i + 1][j - 1])) % N + (F(i + 1, j) + F(i, j - 1) - F(i + 1, j - 1)) % N) % N; } return dp[i][j] = ans; } int main() { ios::sync_with_stdio(false); cin.tie(0), cout.tie(0); cin >> s; for (int i = 0; i < 2005; i++) { for (int j = 0; j < 2005; j++) { dp[i][j] = -1; } } for (int i = 0; i < s.length(); i++) { long long cons = 0; for (int j = i; j < s.length(); j++) { if (s[j] == '?') cons++; k[i][j] = cons; } } cout << (F(0, s.length() - 1) + N) % N << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long long maxn = 2010; const long long Mod = 998244353; long long f[maxn][maxn], g[maxn][maxn], n; char s[maxn]; inline long long power(long long a, long long b) { long long r = 1; while (b) { if (b & 1) r = r * a % Mod; a = a * a % Mod; b >>= 1; } return r; } signed main() { scanf("%s", s + 1); n = strlen(s + 1); for (long long i = (1), _end_ = (n); i <= _end_; ++i) for (long long j = (i), _end_ = (n); j <= _end_; ++j) g[i][j] = g[i][j - 1] + (s[j] == '?'); for (long long len = (2), _end_ = (n); len <= _end_; ++len) for (long long i = (1), _end_ = (n - len + 1); i <= _end_; ++i) { long long j = i + len - 1; if (s[i] != '(') f[i][j] += f[i + 1][j]; if (s[j] != ')') f[i][j] += f[i][j - 1]; if (s[i] != '(' && s[j] != ')') f[i][j] -= f[i + 1][j - 1]; if (s[i] != ')' && s[j] != '(') f[i][j] += f[i + 1][j - 1] + power(2, g[i + 1][j - 1]); f[i][j] %= Mod; } printf("%lld\n", (f[1][n] + Mod) % Mod); return 0; }
#include <bits/stdc++.h> const int mod = 998244353; using namespace std; char s[3000]; int dp1[3000][3000], dp2[3000][3000]; void sol() { memset(dp2, 0, sizeof(dp2)); memset(dp1, 0, sizeof(dp1)); int n = strlen(s + 1); dp1[0][0] = 1; dp2[n + 1][0] = 1; for (int i = 0; i <= n; ++i) { for (int j = 0; j <= n; ++j) { if (s[i] == '(') { if (j) dp1[i][j] = (dp1[i][j] + dp1[i - 1][j - 1]) % mod; } else if (s[i] == ')') { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j]) % mod; } else { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j]) % mod; if (j) { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j - 1]) % mod; } } } } for (int i = n; i >= 0; --i) { for (int j = 0; j <= n; ++j) { if (s[i] == ')') { if (j) dp2[i][j] = (dp2[i][j] + dp2[i + 1][j - 1]) % mod; } else if (s[i] == '(') { dp2[i][j] = (dp2[i][j] + dp2[i + 1][j]) % mod; } else { dp2[i][j] = (dp2[i][j] + dp2[i + 1][j]) % mod; if (j) dp2[i][j] = (dp2[i][j] + dp2[i + 1][j - 1]) % mod; } } } long long ans = 0; for (int i = 1; i <= n; ++i) { for (int j = 1; j <= n; ++j) { ans = (ans + ((1ll * j * dp1[i][j]) % mod) * dp2[i + 1][j]) % mod; } } cout << ans << endl; } int main() { cin >> s + 1; sol(); }
#include <bits/stdc++.h> const int mod = 998244353; using namespace std; char s[3000]; int dp1[3000][3000], dp2[3000][3000]; void sol() { memset(dp2, 0, sizeof(dp2)); memset(dp1, 0, sizeof(dp1)); int n = strlen(s + 1); for (int i = 0; i <= n + 1; ++i) { if (s[i] == '(') break; dp1[i][0] = 1; } for (int i = n + 1; i > 0; --i) { if (s[i] == ')') break; dp2[i][0] = 1; } for (int i = 1; i <= n; ++i) { for (int j = 1; j <= i; ++j) { if (s[i] == '(') { if (j) dp1[i][j] = (dp1[i][j] + dp1[i - 1][j - 1]) % mod; } else if (s[i] == ')') { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j]) % mod; } else { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j]) % mod; if (j) { dp1[i][j] = (dp1[i][j] + dp1[i - 1][j - 1]) % mod; } } } } for (int i = n; i > 0; --i) { for (int j = 1; j <= n - i + 1; ++j) { if (s[i] == ')') { if (j) dp2[i][j] = (dp2[i][j] + dp2[i + 1][j - 1]) % mod; } else if (s[i] == '(') { dp2[i][j] = (dp2[i][j] + dp2[i + 1][j]) % mod; } else { dp2[i][j] = (dp2[i][j] + dp2[i + 1][j]) % mod; if (j) dp2[i][j] = (dp2[i][j] + dp2[i + 1][j - 1]) % mod; } } } long long ans = 0; for (int i = 1; i <= n; ++i) { for (int j = 1; j <= (i, n - i); ++j) { ans = (ans + ((1ll * j * dp1[i][j]) % mod) * dp2[i + 1][j]) % mod; } } cout << ans << endl; } int main() { cin >> s + 1; sol(); }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e3 + 5; const int mod = 998244353; long long dp[maxn][maxn]; char s[maxn]; long long qpow(long long a, int b) { long long res = 1; for (int i = 0; b; b >>= 1) { if (b & 1) res = res * a % mod; a = a * a % mod; } return res; } int cnt[maxn]; int main() { int n; scanf("%s", s + 1); n = strlen(s + 1); for (int i = 1; i <= n; ++i) cnt[i] = cnt[i - 1] + (s[i] == '?'); for (int len = 2; len <= n; ++len) { for (int i = 1; i <= n; ++i) { int j = i + len - 1; if (j > n) break; if (s[i] != '(') dp[i][j] += dp[i + 1][j], dp[i][j] %= mod; if (s[j] != ')') dp[i][j] += dp[i][j - 1], dp[i][j] %= mod; if (s[i] != '(' && s[j] != ')') { dp[i][j] -= dp[i + 1][j - 1]; dp[i][j] += mod; dp[i][j] %= mod; } if (s[i] != ')' && s[j] != '(') dp[i][j] += dp[i + 1][j - 1] + qpow(2, cnt[j - 1] - cnt[i]); dp[i][j] %= mod; } } printf("%lld\n", dp[1][n]); return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 119 << 23 | 1; int fpow(int a, int k) { int r = 1, t = a; while (k) { if (k & 1) r = (long long)r * t % MOD; t = (long long)t * t % MOD; k >>= 1; } return r; } int main() { string s; cin >> s; int n = s.size(); vector<vector<int>> dp(n, vector<int>(n)); vector<int> f(n + 1); for (int i = 0; i < n; i++) { f[i + 1] = f[i]; f[i + 1] += s[i] == '?'; } for (int len = 2; len <= n; len++) { for (int i = 0; i < n - len + 1; i++) { int j = i + len - 1; if (s[i] != '(') { dp[i][j] += dp[i + 1][j]; dp[i][j] %= MOD; } if (s[j] != ')') { dp[i][j] += dp[i][j - 1]; dp[i][j] %= MOD; } if (s[i] != '(' && s[j] != ')') { dp[i][j] -= dp[i + 1][j - 1]; dp[i][j] += MOD; dp[i][j] %= MOD; } if (s[i] != ')' && s[j] != '(') { dp[i][j] += dp[i + 1][j - 1]; dp[i][j] %= MOD; dp[i][j] += fpow(2, f[j] - f[i + 1]); dp[i][j] %= MOD; } } } cout << dp[0][n - 1] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; int n, *k; int64_t** dp; const int64_t M = 998244353; string s; int64_t modpow(int x) { if (x == 0) return 1; if (x == 1) return 2; if (x % 2 == 0) { int64_t val = modpow(x / 2); return (val * val) % M; } else { int64_t val = modpow(x / 2); return (((val * val) % M) * 2) % M; } } int64_t get_dp(int i, int j) { int pi = i, pj = j; if (i >= j) return 0; if (dp[i][j] != -1) return dp[i][j]; int64_t ans = 0; int ki = k[j - 1] - k[i]; if (s[j] != ')') { ans += get_dp(i, j - 1); ans %= M; } if (s[i] != '(') { ans += get_dp(i + 1, j); ans %= M; } if (s[i] != '(' && s[j] != ')') { ans -= get_dp(i + 1, j - 1); ans = (M + ans) % M; } if (s[i] != ')' && s[j] != '(') { ans += modpow(ki); ans %= M; ans += get_dp(i + 1, j - 1); ans %= M; } dp[pi][pj] = ans; return ans; } int main() { ios::sync_with_stdio(false); cin >> s; n = s.length(); dp = new int64_t*[n]; for (int i = 0; i < n; i++) { dp[i] = new int64_t[n]; for (int j = 0; j < n; j++) { dp[i][j] = -1; } } k = new int[n]; for (int i = 0; i < n; i++) { k[i] = (i > 0 ? k[i - 1] : 0) + (s[i] == '?' ? 1 : 0); } cout << get_dp(0, n - 1); return 0; }
#include <bits/stdc++.h> using namespace std; string S; long long int cnt[2020], dp[2020][2020]; long long int M = 998244353; long long int fast(long long int a, long long int b) { long long int ret = 1, t = a; while (b) { if (b & 1) ret = (ret * t) % M; t = (t * t) % M; b >>= 1; } return ret; } long long int get(int l, int r) { long long int p = cnt[r] - (l == 0 ? 0 : cnt[l - 1]); return fast(2, p); } long long int solve(int l, int r) { if (l >= r) return 0; if (dp[l][r] != -1) return dp[l][r]; dp[l][r] = 0; if (S[l] != ')' && S[r] != '(') { dp[l][r] += solve(l + 1, r - 1) + get(l + 1, r - 1); } if (S[l] != '(' && S[r] != ')') { dp[l][r] += solve(l + 1, r - 1); } int reduce = 0; if (S[l] != ')' && S[r] != ')') { dp[l][r] += solve(l, r - 1); if (S[l] == '?') reduce++; } if (S[l] != '(' && S[r] != '(') { dp[l][r] += solve(l + 1, r); if (S[r] == '?') reduce++; } dp[l][r] = dp[l][r] % M - (reduce * solve(l + 1, r - 1)) % M + M; dp[l][r] %= M; return dp[l][r]; } int main() { while (cin >> S) { memset(dp, -1, sizeof(dp)); memset(cnt, 0, sizeof(cnt)); for (int i = 0; i < S.length(); ++i) cnt[i] = i == 0 ? (S[i] == '?') : (S[i] == '?') + cnt[i - 1]; long long int ret = solve(0, S.length() - 1); cout << ret << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; inline int read() { int x = 0, y = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') y = -1; c = getchar(); } while (c >= '0' && c <= '9') x = (x << 1) + (x << 3) + (c ^ 48), c = getchar(); return x * y; } const int N = 2005, mod = 998244353; int n, f[N][N], num[N]; char s[N]; inline int qpow(long long x, int y) { long long res = 1; while (y) { if (y & 1) res = res * x % mod; x = x * x % mod; y >>= 1; } return res; } int main() { scanf("%s", s + 1); n = strlen(s + 1); for (int i = 1; i <= n; i++) f[i][i] = 0; for (int i = 1; i <= n; i++) if (s[i] == '?') num[i]++; for (int i = 1; i <= n; i++) num[i] += num[i - 1]; for (int t = 1; t <= n; t++) { for (int i = 1; i <= n - t; i++) { int j = i + t; if (s[i] != '(') f[i][j] = (1ll * f[i][j] + f[i + 1][j]) % mod; if (s[j] != ')') f[i][j] = (1ll * f[i][j] + f[i][j - 1]) % mod; if (s[i] != '(' && s[j] != ')') f[i][j] = (1ll * f[i][j] + mod - f[i + 1][j - 1]) % mod; if (s[i] != ')' && s[j] != '(') f[i][j] = (1ll * f[i][j] + f[i + 1][j - 1] + qpow(2, num[j - 1] - num[i])) % mod; } } printf("%d\n", f[1][n]); return 0; }
#include <bits/stdc++.h> using namespace std; const long long MOD = 998244353; char S[100005]; int N; long long pow2[100005]; int prefixSum[100005]; int val[256]; int memo[2005][2005][3][3]; int cntQ(int i, int j) { if (i > j) { return 0; } return prefixSum[j + 1] - prefixSum[i]; } long long dp(int i, int j, char chL, char chR) { if (i >= j) { return 0; } if (i + 1 == j) { return chL != ')' && chR != '('; } int dirX = val[chL]; int dirY = val[chR]; if (memo[i][j][dirX][dirY] != -1) { return memo[i][j][dirX][dirY]; } else { long long ans = 0; if (chL != ')' && chR != '(') { ans += pow2[cntQ(i + 1, j - 1)] + dp(i + 1, j - 1, S[i + 1], S[j - 1]); } if (chL != ')' && chR != ')') { ans += dp(i, j - 1, '(', S[j - 1]); } if (chL != '(' && chR != '(') { ans += dp(i + 1, j, S[i + 1], ')'); } if (chL != '(' && chR != ')') { ans += dp(i + 1, j - 1, S[i + 1], S[j - 1]); } ans %= MOD; memo[i][j][dirX][dirY] = ans; return ans; } } int main() { scanf(" %s", S); N = strlen(S); val['('] = 0; val[')'] = 1; val['?'] = 2; pow2[0] = 1; for (int i = 1; i <= N; i++) { pow2[i] = (pow2[i - 1] << 1) % MOD; } prefixSum[0] = 0; for (int i = 1; i <= N; i++) { prefixSum[i] = prefixSum[i - 1] + (S[i - 1] == '?'); } memset(memo, -1, sizeof(memo)); printf("%lld\n", dp(0, N - 1, S[0], S[N - 1])); return 0; }
#include <bits/stdc++.h> #pragma warning(disable : 4996) const long long MOD = 998244353; using namespace std; long long mpow(long long x, long long n) { long long ans = 1; while (n != 0) { if (n & 1) ans = ans * x % MOD; x = x * x % MOD; n = n >> 1; } return ans; } long long minv(long long x) { return mpow(x, MOD - 2); } char str[2005]; long long a0[2005][2005]; long long a1[2005][2005]; int main(int argc, char* argv[]) { scanf("%s", str); int n = strlen(str); int i, j; a0[0][0] = 1; for (i = 0; i < n; i++) { for (j = 0; j <= i; j++) { if (a0[i][j]) { if (str[i] != ')') a0[i + 1][j + 1] = (a0[i + 1][j + 1] + a0[i][j]) % MOD; if (str[i] != '(') a0[i + 1][j] = (a0[i + 1][j] + a0[i][j]) % MOD; } } } a1[0][0] = 1; for (i = 0; i < n; i++) { for (j = 0; j <= i; j++) { if (a1[i][j]) { if (str[n - 1 - i] != '(') a1[i + 1][j + 1] = (a1[i + 1][j + 1] + a1[i][j]) % MOD; if (str[n - 1 - i] != ')') a1[i + 1][j] = (a1[i + 1][j] + a1[i][j]) % MOD; } } } long long ans = 0; for (i = 0; i < n; i++) { int k; for (k = 1; k <= n; k++) { long long tmp = a0[i][k] * a1[n - i][k] % MOD; ans = (ans + tmp * k) % MOD; } } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2123; const long long mod = 998244353; int n; long long dp[maxn][maxn], sum[maxn], p2[maxn]; char s[maxn]; int main() { p2[0] = 1; for (int i = 1; i < maxn; ++i) p2[i] = (p2[i - 1] + p2[i - 1]) % mod; scanf("%s", s + 1); n = strlen(s + 1); for (int i = 1; i <= n; ++i) sum[i] = sum[i - 1] + (s[i] == '?'); for (int i = 2; i <= n; ++i) for (int l = 1; l + i - 1 <= n; ++l) { int r = l + i - 1; if (s[l] == ')' || s[l] == '?') dp[l][r] = (dp[l][r] + dp[l + 1][r]) % mod; if (s[r] == '(' || s[r] == '?') dp[l][r] = (dp[l][r] + dp[l][r - 1]) % mod; if ((s[l] == ')' || s[l] == '?') && (s[r] == '(' || s[r] == '?')) dp[l][r] = (dp[l][r] - dp[l + 1][r - 1]) % mod; if ((s[l] == '(' || s[l] == '?') && (s[r] == ')' || s[r] == '?')) dp[l][r] = (dp[l][r] + dp[l + 1][r - 1] + p2[sum[r - 1] - sum[l]]) % mod; dp[l][r] %= mod; if (dp[l][r] < 0) dp[l][r] += mod; } cout << dp[1][n] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = 1 << 30; const int MOD = 998244353; const int N = 2e3 + 7; int dp[N][N], bin[N], q[N]; string s; int add(int x, int y) { int res = ((long long)x + y) % MOD; if (res < 0) res += MOD; return res; } int mul(int x, int y) { return (long long)x * y % MOD; } int get(int x, int y) { if (x > y) return 0; return q[y] - q[x - 1]; } int solve(int l, int r) { if (l >= r) return 0; if (dp[l][r] != -1) return dp[l][r]; int& ans = dp[l][r] = 0; if (s[l - 1] != '(') ans = add(ans, solve(l + 1, r)); if (s[r - 1] != ')') ans = add(ans, solve(l, r - 1)); auto k = get(l + 1, r - 1); auto nxt = solve(l + 1, r - 1); if (s[l - 1] != '(' && s[r - 1] != ')') ans = add(ans, -nxt); if (s[l - 1] != ')' && s[r - 1] != '(') { ans = add(ans, nxt); ans = add(ans, bin[k]); } return ans; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int tt = clock(); cin >> s; bin[0] = 1; for (int i = 1; i <= s.size(); ++i) { bin[i] = mul(2, bin[i - 1]); } for (int i = 1; i <= s.size(); ++i) { if (s[i - 1] == '?') { q[i] = q[i - 1] + 1; } else q[i] = q[i - 1]; } for (int i = 0; i <= s.size(); ++i) { cerr << q[i] << " \n"[i == s.size()]; } memset(dp, -1, sizeof dp); cout << solve(1, s.size()) << '\n'; cerr << "TIME = " << (double)1.0 * (clock() - tt) / CLOCKS_PER_SEC << " seconds" << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long int expo(long long int a, long long int b) { if (b == 0) return 1; if (b % 2 == 0) return expo((a % 998244353 * a % 998244353) % 998244353, b / 2); return (expo(a, b - 1) % 998244353 * a % 998244353) % 998244353; } int main() { string s; cin >> s; long long int n = s.length(); long long int fact[n + 1]; long long int inv_fact[n + 1]; fact[0] = 1; inv_fact[0] = 1; for (long long int i = 1; i <= n; i++) { fact[i] = (fact[i - 1] % 998244353 * (i) % 998244353) % 998244353; inv_fact[i] = expo(fact[i] % 998244353, 998244353 - 2) % 998244353; } long long int pre[n]; long long int pre1[n]; pre[0] = (s[0] == '?'); pre1[0] = (s[0] == '('); for (long long int i = 1; i < n; i++) { pre[i] = pre[i - 1] + (s[i] == '?'); pre1[i] = pre1[i - 1] + (s[i] == '('); } long long int post[n + 1]; long long int post1[n + 1]; post[n] = 0; post1[n] = 0; post1[n - 1] = (s[n - 1] == ')'); post[n - 1] = (s[n - 1] == '?'); for (long long int i = n - 2; i >= 0; i--) { post[i] = post[i + 1] + (s[i] == '?'); post1[i] = post1[i + 1] + (s[i] == ')'); } long long int ans = 0; for (long long int i = 0; i < n; i++) { for (long long int c = 1; c <= n / 2; c++) { if (max(pre1[i], post1[i + 1]) > c) continue; if (pre[i] + pre1[i] < c) continue; if (post[i + 1] + post1[i + 1] < c) continue; long long int tmp = (fact[pre[i]] % 998244353 * inv_fact[c - pre1[i]] % 998244353 * inv_fact[pre[i] - c + pre1[i]]) % 998244353; tmp = (tmp % 998244353 * fact[post[i + 1]] % 998244353 * inv_fact[c - post1[i + 1]] % 998244353 * inv_fact[post[i + 1] - c + post1[i + 1]] % 998244353) % 998244353; tmp = (tmp % 998244353 * c % 998244353) % 998244353; ans = (ans % 998244353 + tmp % 998244353) % 998244353; } } cout << ans; }
#include <bits/stdc++.h> using namespace std; const int MOD = 119 << 23 | 1; int fpow(int a, int k) { int r = 1, t = a; while (k) { if (k & 1) r = (long long)r * t % MOD; t = (long long)t * t % MOD; k >>= 1; } return r; } int main() { string s; cin >> s; int n = s.size(); vector<vector<int>> dp(n, vector<int>(n)); vector<int> f(n + 1); for (int i = 0; i < n; i++) f[i + 1] = f[i], f[i + 1] += s[i] == '?'; for (int len = 2; len <= n; len++) { for (int i = 0; i < n - len + 1; i++) { int j = i + len - 1; if (s[i] != '(') dp[i][j] += dp[i + 1][j], dp[i][j] %= MOD; if (s[j] != ')') dp[i][j] += dp[i][j - 1], dp[i][j] %= MOD; if (s[i] != '(' && s[j] != ')') dp[i][j] -= dp[i + 1][j - 1], dp[i][j] += MOD, dp[i][j] %= MOD; if (s[i] != ')' && s[j] != '(') { dp[i][j] += dp[i + 1][j - 1], dp[i][j] %= MOD; dp[i][j] += fpow(2, f[j] - f[i + 1]), dp[i][j] %= MOD; } } } cout << dp[0][n - 1]; return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = 0x3f3f3f3f; const int N = 2005; const long long MOD = 998244353; int n; char s[N]; long long dp[N][N][2][2], cnt[N][N]; long long mul(long long a, long long b) { return (a * b) % MOD; } long long add(long long a, long long b) { return (a + b) % MOD; } long long rek(int l, int r, int fl1, int fl2) { if (l >= r) return 0; long long &ret = dp[l][r][fl1][fl2]; if (ret != -1) return ret; ret = 0; if (s[l] == ')') ret = rek(l + 1, r, 0, fl2); else if (s[r] == '(') ret = rek(l, r - 1, fl1, 0); else if (s[l] == '(' || fl1) { ret = add(rek(l + 1, r - 1, 0, 0), cnt[l + 1][r - 1]); if (s[r] == '?' && !fl2) ret = add(ret, rek(l, r - 1, fl1, 0)); } else { if (s[r] == ')' || fl2) { ret = add(rek(l + 1, r - 1, 0, 0), cnt[l + 1][r - 1]); ret = add(ret, rek(l + 1, r, 0, fl2)); } else { ret = add(rek(l + 1, r - 1, 0, 0), cnt[l + 1][r - 1]); ret = add(ret, rek(l + 1, r, 0, 1)); ret = add(ret, rek(l, r - 1, 1, 0)); ret = add(ret, rek(l + 1, r - 1, 0, 0)); } } return ret; } int main() { memset(dp, -1, sizeof dp); scanf("%s", s); n = strlen(s); for (int i = 0; i < n; ++i) { if (i != 0) cnt[i][i - 1] = 1; for (int j = i; j < n; ++j) { long long dod = 1LL + (s[j] == '?'); if (j == i) cnt[i][j] = dod; else cnt[i][j] = mul(dod, cnt[i][j - 1]); } } memset(dp, -1, sizeof dp); printf("%lld\n", rek(0, n - 1, 0, 0)); return 0; }
#include <bits/stdc++.h> using namespace std; #pragma GCC optimize("O3") const int mods[10] = {1000000007, 999999937, 999999929, 999999893, 999999883, 999999797, 999999761, 999999757, 999999751, 999999739}; const int mod = 998244353; int rand_mods[2]; const long double eps = 1e-10; const int siz = 2e3 + 5, siz2 = 3e5 + 5, lg = 20, block = 300, block2 = 1000, mxv = 1e5 + 1, sqrt_mod = 31630; const int alpha_sz = 26; char arr[siz]; int dp[siz][siz], qcmu[siz]; int mul(long long a, long long b) { return (a * b) % mod; } int sub(long long a, long long b) { return ((a - b) % mod + mod) % mod; } int powmod(int a, int b) { if (b == 0) { return 1; } int p = powmod(a, b / 2); p = mul(p, p); return b % 2 ? mul(p, a) : p; } int add(long long a, long long b) { return (a + b) % mod; } int main() { scanf("%s", arr + 1); int sz = strlen(arr + 1); for (int i = 1; i <= sz; i++) { qcmu[i] = (arr[i] == '?') + qcmu[i - 1]; } for (int i = 1; i < sz; i++) { dp[i][i + 1] = arr[i] != ')' && arr[i + 1] != '('; } for (int len = 3; len <= sz; len++) { for (int i = 1; i + len - 1 <= sz; i++) { int l = i, r = i + len - 1; if (arr[l] != ')' && arr[r] != '(') { dp[l][r] = add(dp[l + 1][r - 1], powmod(2, qcmu[r - 1] - qcmu[l])); } if (arr[l] != '(') { dp[l][r] = add(dp[l][r], dp[l + 1][r]); } if (arr[r] != ')') { dp[l][r] = add(dp[l][r], dp[l][r - 1]); } if (arr[l] != '(' && arr[r] != ')') { dp[l][r] = sub(dp[l][r], dp[l + 1][r - 1]); } } } printf("%d\n", dp[1][sz]); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e3 + 10; const int P = 998244353; const int INF = 0x3f3f3f3f; int n, dp[N][N], f[N]; char s[N]; int qsm(int n, int q = P - 2) { int ans = 1; while (q) { if (q & 1) { ans = 1LL * ans * n % P; } n = 1LL * n * n % P; q >>= 1; } return ans; } void solve() { n = strlen(s); for (int i = 0; i < n; ++i) { f[i + 1] = f[i] + (s[i] == '?'); } for (int len = 2; len <= n; ++len) { for (int i = 0; i + len - 1 < n; ++i) { int j = i + len - 1; if (s[i] != '(') { dp[i][j] = (dp[i][j] + dp[i + 1][j]) % P; } if (s[j] != ')') { dp[i][j] = (dp[i][j] + dp[i][j - 1]) % P; } if (s[i] != '(' && s[j] != ')') { dp[i][j] = (1LL * dp[i][j] - dp[i + 1][j - 1] + P) % P; } if (s[i] != ')' && s[j] != '(') { dp[i][j] = (1LL * dp[i][j] + dp[i + 1][j - 1] + qsm(2, f[j] - f[i + 1])) % P; } } } printf("%d\n", dp[0][n - 1]); } int main() { scanf("%s", s); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const long long CONST = 998244353; long long pow1(long long n) { long long rez = 1, p = 2; while (n) { if (n % 2 == 1) { rez = rez * p % CONST; } p = p * p % CONST; n = n / 2; } return rez; } signed main() { string s; cin >> s; long long n = s.size(); vector<vector<long long> > dp(n, vector<long long>(n)); vector<vector<long long> > ans(n, vector<long long>(n, 0)); for (long long len = 1; len <= n; len++) { for (long long i = 0; i <= n - len; i++) { if (s[i] == '?') { if (len == 1) { ans[i][i + len - 1] = 1; } else { ans[i][i + len - 1] = ans[i + 1][i + len - 1] + 1; } } else { if (len == 1) { ans[i][i + len - 1] = 0; } else { ans[i][i + len - 1] = ans[i + 1][i + len - 1]; } } if (s[i] != '(' && len >= 2 && i + len - 1 < n) { dp[i][i + len - 1] += dp[i + 1][i + len - 1]; } if (s[i + len - 1] != ')' && len >= 2) { dp[i][i + len - 1] += dp[i][i + len - 2]; } if (s[i] != '(' && s[i + len - 1] != ')' && len >= 2 && i + len - 1 < n) { dp[i][i + len - 1] -= dp[i + 1][i + len - 2]; } if (s[i] != ')' && s[i + len - 1] != '(' && len >= 2 && i + len - 1 < n) { dp[i][i + len - 1] += dp[i + 1][i + len - 2] + pow1(ans[i + 1][i + len - 2]); } dp[i][i + len - 1] %= CONST; } } cout << dp[0][n - 1]; return 0; }
#include <bits/stdc++.h> using namespace std; const int p = 998244353; template <typename T> inline T read() { register T sum = 0; register char cc = getchar(); int sym = 1; while (cc != '-' && (cc > '9' || cc < '0')) cc = getchar(); if (cc == '-') sym = -1, cc = getchar(); sum = sum * 10 + cc - '0'; cc = getchar(); while (cc >= '0' && cc <= '9') sum = sum * 10 + cc - '0', cc = getchar(); return sym * sum; } template <typename T> inline T read(T& a) { a = read<T>(); return a; } template <typename T, typename... Others> inline void read(T& a, Others&... b) { a = read(a); read(b...); } int n, s[2010], f[2010][2010]; char str[2010]; int add(int x, int y) { return (x + y) % p; } int sub(int x, int y) { return (x - y + p) % p; } int mul(int x, int y) { return 1ll * x * y % p; } int fpow(int x, int y) { int res = 1; while (y) { if (y & 1) res = mul(res, x); x = mul(x, x); y >>= 1; } return res; } int Get(int l, int r) { if (l > r) return 0; return s[r] - s[l - 1]; } int main() { scanf("%s", str + 1); n = strlen(str + 1); for (int i = 1; i <= n; i++) s[i] = s[i - 1] + (str[i] == '?'); for (int len = 2; len <= n; len++) for (int l = 1; l + len - 1 <= n; l++) { int r = l + len - 1; if (str[l] != '(') f[l][r] = add(f[l][r], f[l + 1][r]); if (str[r] != ')') f[l][r] = add(f[l][r], f[l][r - 1]); if (str[l] != '(' && str[r] != ')') f[l][r] = sub(f[l][r], f[l + 1][r - 1]); if (str[l] != ')' && str[r] != '(') f[l][r] = add(f[l][r], add(f[l + 1][r - 1], fpow(2, Get(l + 1, r - 1)))); } printf("%d\n", f[1][n]); return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1); const int maxn = 2005; const long long Mod = 998244353; long long dp[maxn][maxn]; long long sum[maxn]; char s[maxn]; long long p[maxn]; int main() { p[0] = 1; for (int i = 1; i <= maxn; i++) p[i] = (p[i - 1] * 2) % Mod; scanf("%s", s + 1); int n = strlen(s + 1); for (int i = 1; i <= n; i++) { if (s[i] == '?') sum[i] = sum[i - 1] + 1; else sum[i] = sum[i - 1]; } memset(dp, 0, sizeof(dp)); for (int len = 2; len <= n; len++) { for (int l = 1; l <= n + 1 - len; l++) { int r = l + len - 1; if (s[l] != '(') dp[l][r] = (dp[l][r] + dp[l + 1][r]) % Mod; if (s[r] != ')') dp[l][r] = (dp[l][r] + dp[l][r - 1]) % Mod; if (s[l] != '(' && s[r] != ')') dp[l][r] = (dp[l][r] - dp[l + 1][r - 1] + Mod) % Mod; if (s[l] != ')' && s[r] != '(') dp[l][r] = (dp[l][r] + dp[l + 1][r - 1] + p[sum[r - 1] - sum[l]]) % Mod; } } printf("%lld\n", dp[1][n]); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e3 + 5; const long long mod = 998244353; long long f[maxn][maxn], sum[maxn]; char s[maxn]; long long fpow(long long a, long long b) { long long ans = 1; a %= mod; while (b) { if (b & 1) ans = ans * a % mod; b >>= 1; a = a * a % mod; } return ans; } int main() { scanf("%s", s + 1); int n = strlen(s + 1); for (int i = 1; i <= n; i++) { sum[i] = sum[i - 1]; if (s[i] == '?') sum[i]++; } for (int len = 2; len <= n; len++) { for (int i = 1; i <= n; i++) { int j = i + len - 1; if (j > n) break; if (s[i] != '(') f[i][j] = (f[i][j] + f[i + 1][j]) % mod; if (s[j] != ')') f[i][j] = (f[i][j] + f[i][j - 1]) % mod; if (s[i] != '(' && s[j] != ')') f[i][j] = (f[i][j] + mod - f[i + 1][j - 1]) % mod; if (s[i] != ')' && s[j] != '(') f[i][j] = (f[i][j] + f[i + 1][j - 1] + fpow(2, sum[j - 1] - sum[i])) % mod; } } printf("%lld\n", f[1][n]); return 0; }
#include <bits/stdc++.h> using namespace std; long long bigmod(long long a, long long p) { a %= 998244353ll; long long r = 1; while (p) { if ((p & 1)) { r = (r * a) % 998244353ll; } a = (a * a) % 998244353ll; p >>= 1; } return r; } struct Modulo { long long value; Modulo() { value = 0; } Modulo(long long v) { v %= 998244353ll; if (v < 0) { v += 998244353ll; } value = v; } Modulo operator+(Modulo x) { return Modulo(value + x.value); } Modulo operator-(Modulo x) { return Modulo(value - x.value); } Modulo operator*(Modulo x) { return Modulo(value * x.value); } Modulo operator/(Modulo x) { return Modulo(value * bigmod(x.value, 998244353ll - 2)); } Modulo operator+(long long x) { return Modulo(value + x); } Modulo operator-(long long x) { return Modulo(value - x); } Modulo operator*(long long x) { return Modulo(value * x); } Modulo operator/(long long x) { return Modulo(value * bigmod(x, 998244353ll - 2)); } bool operator==(long long x) { return value == x; } bool operator!=(long long x) { return value != x; } bool operator==(Modulo x) { return value == x.value; } bool operator!=(Modulo x) { return value != x.value; } void print() { printf("%lld\n", value); } }; Modulo ONE = Modulo(1); Modulo ZERO = Modulo(0); Modulo dp[2009][2009]; int cnt[2009]; char str[2009]; int main() { int n, i; scanf("%s", str + 1); n = strlen(str + 1); for (i = 1; i <= n; i++) { cnt[i] = cnt[i - 1] + (str[i] == '?'); } for (int len = 2; len <= n; len++) { for (int l = 1, r = len; r <= n; l++, r++) { if (str[l] != '(') { dp[l][r] = dp[l][r] + dp[l + 1][r]; } if (str[r] != ')') { dp[l][r] = dp[l][r] + dp[l][r - 1]; } if (str[l] != '(' && str[r] != ')') { dp[l][r] = dp[l][r] - dp[l + 1][r - 1]; } if (str[l] != ')' && str[r] != '(') { dp[l][r] = dp[l][r] + dp[l + 1][r - 1] + bigmod(2, cnt[r - 1] - cnt[l]); } } } Modulo ans = dp[1][n]; ans.print(); return 0; }
#include <bits/stdc++.h> using namespace std; char v[2010]; long long sp[2010], p[2010], dp[2010][2010]; int n, i, j, lg; long long get_value(int i, int j) { long long nr = sp[j] - sp[i - 1]; return p[nr]; } int main() { cin >> v + 1; n = strlen(v + 1); for (i = 1; i <= n; i++) { sp[i] = sp[i - 1]; if (v[i] == '?') sp[i]++; } p[0] = 1; for (i = 1; i <= n; i++) p[i] = (1LL * 2 * p[i - 1]) % 998244353; for (i = 1; i < n; i++) { if (v[i] == '(') { if (v[i + 1] == ')' || v[i + 1] == '?') dp[i][i + 1] = 1; else dp[i][i + 1] = 0; } else { if (v[i] == ')') dp[i][i + 1] = 0; else { if (v[i + 1] == '?' || v[i + 1] == ')') dp[i][i + 1] = 1; else dp[i][i + 1] = 0; } } } for (lg = 2; lg < n; lg++) { for (i = 1; i + lg <= n; i++) { j = i + lg; if (v[i] == ')' || v[i] == '?') dp[i][j] = (dp[i][j] + dp[i + 1][j]) % 998244353; if (v[j] == '(' || v[j] == '?') dp[i][j] = (dp[i][j] + dp[i][j - 1]) % 998244353; if ((v[i] == ')' || v[i] == '?') && (v[j] == '(' || v[j] == '?')) { dp[i][j] = (dp[i][j] - dp[i + 1][j - 1]) % 998244353; if (dp[i][j] < 0) dp[i][j] += 998244353; } int ok = 1; if (v[i] == ')' || v[j] == '(') ok = 0; if (ok) { dp[i][j] = (dp[i][j] + dp[i + 1][j - 1]) % 998244353; dp[i][j] = (dp[i][j] + get_value(i + 1, j - 1)) % 998244353; } } } cout << dp[1][n]; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using pii = pair<int, int>; void min_self(int& a, int b) { if (a > b) a = b; } void max_self(int& a, int b) { if (a < b) a = b; } const int mod = 998244353; int mult(int a, int b) { return (int)(((ll)a * b) % mod); } int add_self(int& a, int b) { a += b; if (a >= mod) a -= mod; } int sub_self(int& a, int b) { a -= b; if (a < 0) a += mod; } int power(int a, int k) { int answer = 1; while (k >= 1) { if (k & 1) { answer = mult(answer, a); } a = mult(a, a); k >>= 1; } return answer; } int inverse(int a) { return power(a, mod - 2); } void solve() { string s; cin >> s; const int n = (int)s.size(); vector<vector<int> > dp(n, vector<int>(n)); vector<int> count(n + 1); for (int i = 0; i < n; i++) { count[i + 1] = count[i] + (s[i] == '?'); } for (int len = 2; len <= n; len++) { for (int i = 0; i <= n - len; i++) { int j = i + len - 1; if (s[i] != '(') { add_self(dp[i][j], dp[i + 1][j]); } if (s[j] != ')') { add_self(dp[i][j], dp[i][j - 1]); } if (s[i] != '(' && s[j] != ')') { sub_self(dp[i][j], dp[i + 1][j - 1]); } if (s[i] != ')' && s[j] != '(') { int p = power(2, count[j] - count[i + 1]); add_self(p, dp[i + 1][j - 1]); add_self(dp[i][j], p); } } } printf("%d\n", dp[0][n - 1]); } int main() { int t; t = 1; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; long long mod = 998244353; long long **num_of_substrs; long long **dp; void compute_substrs(string s, int n) { for (int i = 0; i < n; i++) { long long ans = 1; for (int j = i; j < n; j++) { if (s[j] == '?') ans = (ans * 2) % mod; num_of_substrs[i][j] = ans; } } } long long dp_func(int i, int j, string &s) { if (i == j) return 0; if (i + 1 == j) { if (s[i] == ')' || s[j] == '(') return 0; return 1; } if (dp[i][j] != -1) return dp[i][j]; if (s[i] == ')') return dp[i][j] = dp_func(i + 1, j, s); if (s[j] == '(') return dp[i][j] = dp_func(i, j - 1, s); if (s[i] == '(' && s[j] == ')') { return dp[i][j] = (dp_func(i + 1, j - 1, s) + num_of_substrs[i + 1][j - 1]) % mod; } if (s[i] == '(' && s[j] == '?') { return dp[i][j] = (dp_func(i + 1, j - 1, s) + num_of_substrs[i + 1][j - 1] + dp_func(i, j - 1, s)) % mod; } if (s[i] == '?' && s[j] == ')') { return dp[i][j] = (dp_func(i + 1, j - 1, s) + num_of_substrs[i + 1][j - 1] + dp_func(i + 1, j, s)) % mod; } return dp[i][j] = (dp_func(i + 1, j, s) + dp_func(i, j - 1, s) + num_of_substrs[i + 1][j - 1]) % mod; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); ; string s; cin >> s; int n = s.length(); num_of_substrs = new long long *[n]; dp = new long long *[n]; for (int i = 0; i < n; i++) { num_of_substrs[i] = new long long[n]; dp[i] = new long long[n]; for (int j = 0; j < n; j++) dp[i][j] = -1; } compute_substrs(s, n); cout << dp_func(0, n - 1, s); }
#include <bits/stdc++.h> using ll = long long; const int mod = 998244353; int n, p[2005], p2[2005]; ll d[2005][2005]; char a[2005]; inline int conv(char c) { return c == '(' ? 0 : (c == '?' ? 1 : 2); } int main() { scanf("%s", a + 1); n = strlen(a + 1); for (int i = 1; i <= n; i++) p[i] = p[i - 1] + (a[i] == '?'); p2[0] = 1; for (int i = 1; i <= n; i++) p2[i] = p2[i - 1] * 2 % mod; for (int l = n - 1; l >= 1; l--) for (int r = l + 1; r <= n; r++) { int type = conv(a[l]) * 3 + conv(a[r]), k = p[r - 1] - p[l]; ll &f = d[l][r]; switch (type) { case 0: f = d[l][r - 1]; break; case 1: f = d[l][r - 1] + d[l + 1][r - 1] + p2[k]; break; case 2: f = d[l + 1][r - 1] + p2[k]; break; case 3: f = d[l][r - 1]; break; case 4: f = d[l][r - 1] + d[l + 1][r] + p2[k]; break; case 5: f = d[l + 1][r] + d[l + 1][r - 1] + p2[k]; break; case 6: f = d[l + 1][r - 1]; break; case 7: f = d[l + 1][r]; break; case 8: f = d[l + 1][r]; break; } f = ((f % mod) + mod) % mod; } printf("%lld", d[1][n]); return 0; }
#include <bits/stdc++.h> using namespace std; const long long mod = 998244353; const int N = 200000 + 7; string s; long long dp[2007][2007]; long long pow2[2007]; int nq[2007]; long long solve(int l, int r) { if (l >= r) return 0; if (dp[l][r] != -1) return dp[l][r]; long long numq = pow2[nq[r - 1] - nq[l]]; if (s[l] == '(' && s[r] == ')') { dp[l][r] = solve(l + 1, r - 1) + numq; } else if (s[r] == '(') { dp[l][r] = solve(l, r - 1); } else if (s[l] == ')') { dp[l][r] = solve(l + 1, r); } else if (s[l] == '?' && s[r] == '?') { dp[l][r] = solve(l + 1, r) + numq + solve(l, r - 1); } else if (s[l] == '?') { dp[l][r] = solve(l + 1, r) + solve(l + 1, r - 1) + numq; } else if (s[r] == '?') { dp[l][r] = solve(l + 1, r - 1) + numq + solve(l, r - 1); } dp[l][r] %= mod; return dp[l][r]; } int main() { std::ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); pow2[0] = 1; for (int i = 1; i < 2007; i++) { pow2[i] = (pow2[i - 1] * 2) % mod; } for (int i = 0; i < 2007; i++) { for (int j = 0; j < 2007; j++) dp[i][j] = -1; } cin >> s; int n = s.length(); if (s[0] == '?') nq[0] = 1; for (int i = 1; i < n; i++) { nq[i] = nq[i - 1]; if (s[i] == '?') nq[i]++; } cout << solve(0, n - 1) << "\n"; return 0; }
#include <bits/stdc++.h> #pragma warning(disable : 4996) const long long MOD = 998244353; using namespace std; long long mpow(long long x, long long n) { long long ans = 1; while (n != 0) { if (n & 1) ans = ans * x % MOD; x = x * x % MOD; n = n >> 1; } return ans; } long long minv(long long x) { return mpow(x, MOD - 2); } char str[2005]; long long a0[2005][2005]; long long a1[2005][2005]; int main(int argc, char* argv[]) { scanf("%s", str); int n = strlen(str); int i, j; a0[0][0] = 1; for (i = 0; i < n; i++) { for (j = 0; j <= i; j++) { if (a0[i][j]) { if (str[i] != ')') a0[i + 1][j + 1] = (a0[i + 1][j + 1] + a0[i][j]) % MOD; if (str[i] != '(') a0[i + 1][j] = (a0[i + 1][j] + a0[i][j]) % MOD; } } } a1[0][0] = 1; for (i = 0; i < n; i++) { for (j = 0; j <= i; j++) { if (a1[i][j]) { if (str[n - 1 - i] != '(') a1[i + 1][j + 1] = (a1[i + 1][j + 1] + a1[i][j]) % MOD; if (str[n - 1 - i] != ')') a1[i + 1][j] = (a1[i + 1][j] + a1[i][j]) % MOD; } } } long long ans = 0; for (i = 0; i < n; i++) { int k; for (k = 1; k <= n / 2; k++) { long long tmp = a0[i][k] * a1[n - 1 - i][k] % MOD; if (tmp) { if (str[i] != ')') { ans = (ans + tmp * k) % MOD; } if (str[i] != '(') { ans = (ans + tmp * k) % MOD; } } } } for (i = 0; i < n - 1; i++) { if (str[i] != '(' && str[i + 1] != ')') { int k; for (k = 0; k <= n / 2; k++) { long long tmp = a0[i][k] * a1[n - 2 - i][k] % MOD; if (tmp) { ans = (ans - tmp * k % MOD + MOD) % MOD; } } } if (str[i] != ')' && str[i + 1] != '(') { int k; for (k = 0; k <= n / 2; k++) { long long tmp = a0[i][k] * a1[n - 2 - i][k] % MOD; if (tmp) { ans = (ans + tmp * (k + 1)) % MOD; } } } } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> void out(T x) { cout << x << endl; exit(0); } const long long mod = 998244353; const int maxn = 2013; int n; string s; long long dpLeft[maxn][maxn]; long long dpRight[maxn][maxn]; void add(long long& x, long long y) { x %= mod; y %= mod; x += y; x %= mod; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> s; n = s.length(); dpLeft[0][0] = 1; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { if (dpLeft[i][j] == 0) continue; if (s[i] == '(') { add(dpLeft[i + 1][j + 1], dpLeft[i][j]); } else if (s[i] == ')') { add(dpLeft[i + 1][j], dpLeft[i][j]); } else { assert(s[i] == '?'); add(dpLeft[i + 1][j + 1], dpLeft[i][j]); add(dpLeft[i + 1][j], dpLeft[i][j]); } } } dpRight[n + 1][0] = 1; for (int i = n; i > 0; i--) { for (int j = 0; j < n; j++) { if (dpRight[i + 1][j] == 0) continue; if (s[i - 1] == ')') { add(dpRight[i][j + 1], dpRight[i + 1][j]); } else if (s[i - 1] == '(') { add(dpRight[i][j], dpRight[i + 1][j]); } else { assert(s[i - 1] == '?'); add(dpRight[i][j + 1], dpRight[i + 1][j]); add(dpRight[i][j], dpRight[i + 1][j]); } } } long long res = 0; for (int i = 1; i <= n - 1; i++) { for (long long j = 0; j <= n; j++) { add(res, j * dpLeft[i][j] % mod * dpRight[i + 1][j] % mod); } } res %= mod; res += mod; res %= mod; cout << res << endl; return 0; }
#include <bits/stdc++.h> using namespace std; inline long long Getint() { char ch = getchar(); long long x = 0, fh = 1; while (ch < '0' || ch > '9') { if (ch == '-') fh = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { (x *= 10) += ch ^ 48; ch = getchar(); } return x * fh; } const long long mod = 998244353; const int N = 2005; int n, su[N]; char s[N]; bool vis[N][N][3][3]; int f[N][N][3][3], pw[N]; inline int Getsu(int l, int r) { if (r < l) return 0; return su[r] - su[l - 1]; } inline long long Dfs(int l, int r, int l1, int l2) { if (r <= l) return 0; else if (vis[l][r][l1][l2]) return f[l][r][l1][l2]; long long Ans = 0; vis[l][r][l1][l2] = 1; int li = l1 == 2 ? 0 : l1, ri = l1 == 2 ? 1 : l1; int lj = l2 == 2 ? 0 : l2, rj = l2 == 2 ? 1 : l2; for (int i = li; i <= ri; i++) for (int j = lj; j <= rj; j++) { if (i == 1 && j == 0) Ans += Dfs(l + 1, r - 1, s[l + 1], s[r - 1]); else if (i == 1) Ans += Dfs(l + 1, r, l + 1 == r ? j : s[l + 1], j); else if (j == 0) Ans += Dfs(l, r - 1, i, r - 1 == l ? i : s[r - 1]); else Ans += Dfs(l + 1, r - 1, s[l + 1], s[r - 1]) + pw[Getsu(l + 1, r - 1)]; } return f[l][r][l1][l2] = Ans % mod; } int main() { scanf("%s", s + 1); n = strlen(s + 1); pw[0] = 1; for (int i = 1; i <= N - 1; i++) pw[i] = pw[i - 1] * 2ll % mod; for (int i = 1; i <= n; i++) su[i] = su[i - 1] + (s[i] == '?'); for (int i = 1; i <= n; i++) s[i] = (s[i] == '(' ? 0 : (s[i] == ')' ? 1 : 2)); cout << Dfs(1, n, s[1], s[n]) << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 998244353; const int maxn = 2e3 + 100; string s; long long dp[maxn][maxn] = {0}; int num[maxn] = {0}; long long qmod(long long a, long long b) { long long ans = 1; while (b) { if (b & 1) ans = ans * a % mod; b >>= 1; a = a * a % mod; } return ans; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> s; int len = s.length(); for (int i = 1; i <= len; ++i) { num[i] = num[i - 1]; if (s[i - 1] == '?') { ++num[i]; } } for (int i = 1; i <= len; ++i) { for (int j = 0; j + i < len; ++j) { int l = j, r = i + j; if (s[l] != '(') { dp[l][r] = (dp[l][r] + dp[l + 1][r]) % mod; } if (s[r] != ')') { dp[l][r] = (dp[l][r] + dp[l][r - 1]) % mod; } if (s[l] != '(' && s[r] != ')') { dp[l][r] = (dp[l][r] - dp[l + 1][r - 1] + mod) % mod; } if (s[l] != ')' && s[r] != '(') { dp[l][r] = (dp[l][r] + dp[l + 1][r - 1] + qmod(2, num[r] - num[l + 1])) % mod; } } } cout << dp[0][len - 1] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int Max = 2e3 + 5; const int Mod = 998244353; int n, dp[Max][Max]; string s; int cnt[Max][Max]; int sum(int i, int j) { if (i > j) return 1; if (cnt[i][j]) return cnt[i][j]; return cnt[i][j] = (s[i] == '?' ? 2 : 1) * sum(i + 1, j) % Mod; } int Try(int l, int r) { if (l >= r) return 0; int& ret = dp[l][r]; if (~ret) return ret; ret = 0; if ((s[l] == '(' || s[l] == '?') && (s[r] == ')' || s[r] == '?')) ret = (Try(l + 1, r - 1) + sum(l + 1, r - 1)) % Mod; bool b1 = false, b2 = false; if (s[l] != '(') ret = (ret + Try(l + 1, r)) % Mod, b1 = true; if (s[r] != ')') ret = (ret + Try(l, r - 1)) % Mod, b2 = true; if (b1 && b2) ret = (ret - Try(l + 1, r - 1) + Mod) % Mod; return ret; } int main() { cin >> s; memset(dp, -1, sizeof(dp)); n = s.size(); cout << Try(0, n - 1) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; using LL = long long; namespace _buff { const size_t BUFF = 1 << 19; char ibuf[BUFF], *ib = ibuf, *ie = ibuf; char getc() { if (ib == ie) { ib = ibuf; ie = ibuf + fread(ibuf, 1, BUFF, stdin); } return ib == ie ? -1 : *ib++; } } // namespace _buff LL read() { using namespace _buff; LL ret = 0; bool pos = true; char c = getc(); for (; (c < '0' || c > '9') && c != '-'; c = getc()) { assert(~c); } if (c == '-') { pos = false; c = getc(); } for (; c >= '0' && c <= '9'; c = getc()) { ret = (ret << 3) + (ret << 1) + (c ^ 48); } return pos ? ret : -ret; } const size_t N = 2e3 + 5; const int MOD = 998244353; void iadd(int &dp, int val) { dp += val; if (dp >= MOD) { dp -= MOD; } } char s[N]; int f[N][N][2], g[N][N]; int main() { scanf("%s", s + 1); int n = strlen(s + 1); f[0][0][0] = 1; for (int i = 1; i <= n; ++i) { if (s[i] == '(' || s[i] == '?') { for (int j = 1; j <= i; ++j) { iadd(f[i][j][1], f[i - 1][j - 1][0]); iadd(f[i][j][1], f[i - 1][j - 1][1]); } } if (s[i] == ')' || s[i] == '?') { for (int j = 0; j <= i; ++j) { iadd(f[i][j][0], f[i - 1][j][0]); iadd(f[i][j][0], f[i - 1][j][1]); } } } g[n + 1][0] = 1; for (int i = n; i >= 1; --i) { if (s[i] == ')' || s[i] == '?') { for (int j = 1; j <= n; ++j) { iadd(g[i][j], g[i + 1][j - 1]); } } if (s[i] == '(' || s[i] == '?') { for (int j = 0; j <= n; ++j) { iadd(g[i][j], g[i + 1][j]); } } } for (int i = 1; i <= n; ++i) { for (int j = n; j >= 1; --j) { iadd(g[i][j - 1], g[i][j]); } } int ans = 0; for (int i = 1; i <= n; ++i) { for (int j = 1; j <= i; ++j) { ans = (ans + (LL)f[i][j][1] * g[i + 1][j]) % MOD; } } cout << ans; return 0; }
#include <bits/stdc++.h> using namespace std; long long dp[2000 + 5][2000 + 5]; long long ques[2000 + 5]; long long mod = 998244353; long long poww(long long a, long long b) { long long tmp = 1; while (b) { if (b & 1) tmp = (tmp * a) % mod; a = (a * a) % mod; b >>= 1; } return tmp; } int main(void) { string str; cin >> str; str = " " + str; int n = str.size() - 1; for (int i = 1; i <= n; i++) { ques[i] = ques[i - 1] + (str[i] == '?'); } for (int len = 2; len <= n; len++) { for (int i = 1; i + len - 1 <= n; i++) { int j = i + len - 1; if (str[i] != '(') dp[i][j] = (dp[i][j] + dp[i + 1][j]) % mod; if (str[j] != ')') dp[i][j] = (dp[i][j] + dp[i][j - 1]) % mod; if (str[i] != '(' && str[j] != ')') dp[i][j] = (dp[i][j] - dp[i + 1][j - 1] + mod) % mod; if (str[i] != ')' && str[j] != '(') { dp[i][j] = ((dp[i][j] + dp[i + 1][j - 1]) % mod + poww(2, ques[j - 1] - ques[i])) % mod; } } } cout << dp[1][n] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; long long mod = 998244353; long long fast_exp(long long a, long long b) { if (b == 0) return 1; else { long long res = 1; res = fast_exp(a, b / 2); res = (res * res) % mod; if (b % 2 == 1) res = (res * a) % mod; return res; } } const long long N = 1e5 + 10; long long nCr[2500][2500]; long long vis[2500][2500] = {}; long long binom(long long n, long long r) { if (r < 0 || r > n) return 0; if (vis[n][r]) return nCr[n][r]; if (r == 0 || n == r) return 1; else { vis[n][r] = 1; nCr[n][r] = (binom(n - 1, r - 1) + binom(n - 1, r)) % mod; return nCr[n][r]; } } int main() { string s; cin >> s; long long n = s.size(); long long prefop[n], prefq[n], sufcl[n], sufq[n]; long long op = 0, q = 0, cl = 0; for (long long i = 0; i < n; i++) { if (s[i] == '(') op++; if (s[i] == '?') q++; prefop[i] = op; prefq[i] = q; } q = 0; for (long long i = n - 1; i >= 0; i--) { if (s[i] == ')') cl++; if (s[i] == '?') q++; sufcl[i] = cl; sufq[i] = q; } long long ans = 0; for (long long i = 1; i < n; i++) { long long lop = prefop[i - 1], lq = prefq[i - 1], rq = sufq[i], rcl = sufcl[i]; for (long long k = 0; k < n; k++) { long long rk = lop + k - rcl; ans = (ans + ((((lop + k) * binom(lq, k)) % mod) * binom(rq, rk)) % mod) % mod; } } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; template <int MOD> class ModInt { long long x; public: ModInt(long long v = 0) : x(v % MOD) { if (x < 0) x += MOD; } ModInt& operator+=(const ModInt& r) { x += r.x; if (x >= MOD) x -= MOD; return *this; } ModInt& operator-=(const ModInt& r) { x -= r.x; if (x < 0) x += MOD; return *this; } ModInt& operator*=(const ModInt& r) { x = (x * r.x) % MOD; return *this; } ModInt& operator/=(const ModInt& r) { *this *= r.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt& r) const { return ModInt(*this) += r; } ModInt operator-(const ModInt& r) const { return ModInt(*this) -= r; } ModInt operator*(const ModInt& r) const { return ModInt(*this) *= r; } ModInt operator/(const ModInt& r) const { return ModInt(*this) /= r; } bool operator==(const ModInt& r) const { return x == r.x; } bool operator!=(const ModInt& r) const { return x != r.x; } ModInt inverse() const { long long a = x, b = MOD, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt<MOD> pow(long long n) const { ModInt ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream& operator<<(ostream& os, const ModInt& x) { return os << x.x; } friend istream& operator>>(istream& is, ModInt& x) { return is >> x.x; } int getMod() { return MOD; } }; using mint = ModInt<998244353>; string S; int main() { cin >> S; int N = S.size(); int M = 0; for (int i = 0; i < (int)N; ++i) M += (S[i] == '?'); vector<int> L(N + 1, 0), R(N + 1, 0); for (int i = 0; i < (int)N; ++i) { L[i + 1] = L[i] + (S[i] != ')'); R[N - i - 1] = R[N - i] + (S[N - i - 1] == ')'); } vector<mint> fact(M + 1), ifact(M + 1); fact[0] = 1; for (int i = 0; i < (int)M; ++i) fact[i + 1] = fact[i] * (i + 1); for (int i = 0; i < (int)M + 1; ++i) ifact[i] = fact[i].inverse(); auto comb = [&](int n, int k) { return fact[n] * ifact[n - k] * ifact[k]; }; vector<mint> SB(M + 2, 0), SQ(M + 1, 0); for (int i = 0; i < (int)M + 1; ++i) SB[i + 1] = SB[i] + comb(M, i); for (int i = 0; i < (int)M; ++i) SQ[i + 1] = SQ[i] + comb(M - 1, i); mint ans = 0; for (int i = 0; i < (int)N; ++i) { if (S[i] == ')') continue; int k = L[i + 1] - R[i + 1]; if (S[i] == '(') ans += SB[M + 1] - SB[min(M + 1, max(k, 0))]; if (S[i] == '?') ans += SQ[M] - SQ[min(M, max(k, 0))]; } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e3 + 50; const long long Mod = 998244353; int n; long long f[maxn][maxn], g[maxn][maxn], dp[maxn][maxn]; char s[maxn]; int main() { cin >> s + 1; n = strlen(s + 1); f[0][0] = 1; for (int i = 1; i <= n; i++) { for (int j = 0; j <= i; j++) { if ((s[i] == '(' || s[i] == '?') && j - 1 >= 0) f[i][j] = (f[i][j] + f[i - 1][j - 1]) % Mod; if (s[i] == ')' || s[i] == '?') f[i][j] = (f[i][j] + f[i - 1][j]) % Mod; } } g[n + 1][0] = 1; for (int i = n; i >= 1; i--) { for (int j = 0; j <= n - i + 1; j++) { if ((s[i] == ')' || s[i] == '?') && j - 1 >= 0) g[i][j] = (g[i][j] + g[i + 1][j - 1]) % Mod; if (s[i] == '(' || s[i] == '?') g[i][j] = (g[i][j] + g[i + 1][j]) % Mod; } } long long ans = 0; for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { ans = (ans + f[i][j] * g[i + 1][j] % Mod * j % Mod) % Mod; } } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using i64 = long long; constexpr int P = 998244353; int power(int a, int b) { int res = 1; for (; b > 0; a = i64(a) * a % P, b /= 2) { if (b % 2 == 1) { res = i64(res) * a % P; } } return res; } int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::string s; std::cin >> s; int n = s.size(); std::vector<int> pr(n + 1); for (int i = 0; i < n; i++) { pr[i + 1] = pr[i] + (s[i] == '?'); } std::vector<std::vector<int>> dp(n, std::vector<int>(n, -1)); std::function<int(int, int)> calc = [&](int l, int r) { if (l >= r) { return 0; } if (~dp[l][r]) { return dp[l][r]; } dp[l][r] = 0; if (s[l] != '(') dp[l][r] = (dp[l][r] + calc(l + 1, r)) % P; if (s[r] != ')') dp[l][r] = (dp[l][r] + calc(l, r - 1)) % P; if (s[l] != '(' && s[r] != ')') dp[l][r] = (dp[l][r] - calc(l + 1, r - 1) + P) % P; if (s[l] != ')' && s[r] != '(') dp[l][r] = ((dp[l][r] + calc(l + 1, r - 1)) % P + power(2, pr[r] - pr[l + 1])) % P; return dp[l][r]; }; std::cout << calc(0, n - 1) << "\n"; return 0; }