結果

問題 No.3148 Min-Cost Destruction of Parentheses
ユーザー dyktr_06
提出日時 2025-05-16 23:40:33
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 100 ms / 4,000 ms
コード長 10,788 bytes
コンパイル時間 2,563 ms
コンパイル使用メモリ 216,872 KB
実行使用メモリ 18,396 KB
最終ジャッジ日時 2025-05-16 23:40:39
合計ジャッジ時間 5,497 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 31
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>

using namespace std;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))

typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;

template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);

template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template <typename T>
long long binary_search(long long ok, long long ng, T check){
    while(abs(ok - ng) > 1){
        long long mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

template <typename T>
long double binary_search_real(long double ok, long double ng, T check, int iter = 100){
    for(int i = 0; i < iter; ++i){
        long double mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

template <typename T>
long long trisum(T a, T b){
    long long res = ((b - a + 1) * (a + b)) / 2;
    return res;
}

template <typename T>
T intpow(T x, int n){
    T ret = 1;
    while(n > 0) {
        if(n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}

template <typename T>
T getReminder(T a, T b){
    if(b == 0) return -1;
    if(a >= 0 && b > 0){
        return a % b;
    } else if(a < 0 && b > 0){
        return ((a % b) + b) % b;
    } else if(a >= 0 && b < 0){
        return a % b;
    } else{
        return (abs(b) - abs(a % b)) % b;
    }
}

template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>> &G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }

template <typename T>
struct fraction{
    T p, q; // long long or BigInt
    fraction(T P = 0, T Q = 1) : p(P), q(Q){
        // normalize();
    }
    void normalize(){
        T g = __gcd(p, q);
        p /= g, q /= g;
        if(q < 0) p *= -1, q *= -1;
    }
    inline bool operator==(const fraction &other) const {
        return p * other.q == other.p * q;
    }
    inline bool operator!=(const fraction &other) const {
        return p * other.q != other.p * q;
    }
    inline bool operator<(const fraction &other) const {
        return p * other.q < other.p * q;
    }
    inline bool operator<=(const fraction &other) const {
        return p * other.q <= other.p * q;
    }
    inline bool operator>(const fraction &other) const {
        return p * other.q > other.p * q;
    }
    inline bool operator>=(const fraction &other) const {
        return p * other.q >= other.p * q;
    }
    inline fraction operator+(const fraction &other) const { return fraction(p * other.q + q * other.p, q * other.q); }
    inline fraction operator-(const fraction &other) const { return fraction(p * other.q - q * other.p, q * other.q); }
    inline fraction operator*(const fraction &other) const { return fraction(p * other.p, q * other.q); }
    inline fraction operator/(const fraction &other) const { return fraction(p * other.q, q * other.p); }
    inline fraction &operator+=(const fraction &rhs) noexcept {
        *this = *this + rhs;
        return *this;
    }
    inline fraction &operator-=(const fraction &rhs) noexcept {
        *this = *this - rhs;
        return *this;
    }
    inline fraction &operator*=(const fraction &rhs) noexcept {
        *this = *this * rhs;
        return *this;
    }
    inline fraction &operator/=(const fraction &rhs) noexcept {
        *this = *this / rhs;
        return *this;
    }
    friend inline istream &operator>>(istream &is, fraction &x) noexcept {
        is >> x.p;
        x.q = 1;
        return is;
    }
    friend inline ostream &operator<<(ostream &os, const fraction &x) noexcept { return os << x.p << "/" << x.q; }
};

struct UnionFind{
    vector<int> par;
    vector<int> edg;

    UnionFind(int N) : par(N), edg(N){
        for(int i = 0; i < N; ++i){
            par[i] = -1;
            edg[i] = 0;
        }
    }

    int root(int x){
        if(par[x] < 0) return x;
        return par[x] = root(par[x]);
    }

    int unite(int x, int y){
        int rx = root(x);
        int ry = root(y);
        if(rx == ry){
            edg[rx]++;
            return rx;
        }
        if(-par[rx] < -par[ry]) swap(rx, ry);
        par[rx] = par[rx] + par[ry];
        par[ry] = rx;
        edg[rx] += edg[ry] + 1;
        return rx;
    }

    bool same(int x, int y){
        int rx = root(x);
        int ry = root(y);
        return rx == ry;
    }

    long long size(int x){
        return -par[root(x)];
    }

    long long edge(int x){
        return edg[root(x)];
    }
};

template <typename T>
struct PriorityQueue{
    priority_queue<T> q, removed_q;

    PriorityQueue(){ }

    void normalize(){
        while(!q.empty() && !removed_q.empty()){
            if(q.top() == removed_q.top()){
                q.pop();
                removed_q.pop();
            } else{
                break;
            }
        }
    }

    void push(const T &x){
        q.push(x);
    }

    void erase(const T &x){
        removed_q.push(x);
    }

    size_t size(){
        return q.size() - removed_q.size();
    }

    bool empty(){
        return (size() == 0);
    }

    T top(){
        normalize();
        assert(!q.empty());
        return q.top();
    }
};

ll zeroOneOnTree(vll &p, vll &zero, vll &one){
    ll n = p.size();
    UnionFind uf(n);
    PriorityQueue<pair<fraction<ll>, ll>> pq;
    vll inv(n);
    vector<fraction<ll>> fv(n);
    rep(i, n){
        fv[i] = {zero[i], one[i]};
        if(i >= 1) pq.push({fv[i], i});
    }
    while(pq.size()){
        auto [f, idx] = pq.top();
        pq.erase(pq.top());
        ll r = uf.root(idx);
        ll par = uf.root(p[r]);
        ll nxt = uf.unite(r, par);
        p[nxt] = p[par];
        inv[nxt] += fv[par].q * fv[r].p;
        pair<fraction<ll>, ll> prv = {fv[par], par};
        ll from = par;
        if(nxt == par) from = r;
        inv[nxt] += inv[from];
        fv[nxt].p += fv[from].p;
        fv[nxt].q += fv[from].q;
        if(p[nxt] != -1){
            pq.erase(prv);
            pq.push({fv[nxt], nxt});
        }
    }
    return inv[uf.root(0)];
}

ll T;

void input(){
    in(T);
}

void solve(){
    ll n; in(n);
    string s; in(s);
    vll a(n + 1);
    rep(i, 1, n + 1) in(a[i]);

    vll close(n * 2);
    {
        vll v;
        rep(i, n * 2){
            if(s[i] == ')'){
                close[v.back()] = i;
                v.pop_back();
            }
            if(s[i] == '(') v.push_back(i);
        }
    }

    ll idx = 0;
    vector<P> e;
    auto dfs = [&](auto self, ll l, ll r, ll prv){
        if(l >= r) return;
        ll cur = l;
        while(cur < r){
            ll nxt = idx++;
            self(self, cur + 1, close[cur], nxt);
            e.emplace_back(prv, nxt);
            cur = close[cur] + 1;
        }
    };
    dfs(dfs, 0, n * 2, idx++);

    vll par(idx, -1);
    for(auto [a, b] : e){
        par[b] = a;
    }

    vll zero(idx), one(idx);
    rep(i, 1, idx){
        zero[i] = a[i];
        one[i] = 1;
    }
    // out(par);
    // out(zero);
    // out(one);
    out(zeroOneOnTree(par, zero, one) + sum(a));
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);

    T = 1;
    // input();
    while(T--) solve();
}
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