結果

問題 No.3148 Min-Cost Destruction of Parentheses
ユーザー noya2
提出日時 2025-05-16 23:12:28
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 61 ms / 4,000 ms
コード長 10,434 bytes
コンパイル時間 3,758 ms
コンパイル使用メモリ 301,272 KB
実行使用メモリ 15,976 KB
最終ジャッジ日時 2025-05-16 23:12:35
合計ジャッジ時間 5,084 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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 # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/misc/O1onTree.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/misc/O1onTree.hpp"
#include <bit>
#include <concepts>

namespace noya2 {

// root is vertex 0, par[i] < i
// bool comp(int u, int v), comp(u, v) ? [u, ...] < [v, ...] : [u, ...] >= [v, ...]
// void merge(int u, int v), [p, ...] ++ [v, ...]  -- merge(p, v) -->  [p, ......]
template<bool get_order = true>
std::conditional_t<get_order, std::vector<int>, void> O1onTree(int n, const std::vector<int> &par, auto comp, auto merge){
    if (n == 1){
        if constexpr (get_order){
            return {0};
        }
        else {
            return ;
        }
    }
    assert(ssize(par) == n);
    for (int i = 0; i < n; i++){
        assert(par[i] < i);
    }
    // dsu without weighted union heuristic
    std::vector<int> uf(n, -1);
    // leader is the highest vertex among the connected component
    auto leader = [&](int a){
        auto dfs = [&](auto sfs, int v){
            if (uf[v] < 0) return v;
            return uf[v] = sfs(sfs,uf[v]);
        };
        return dfs(dfs,a);
    };
    // updatable priority_queue using segtree
    int sz = std::bit_ceil<uint32_t>(n);
    std::vector<int> seg(sz);
    std::vector<bool> done(sz, true);
    auto op = [&](int a, int b){
        if (done[b]) return a;
        if (done[a]) return b;
        return comp(a, b) ? a : b;
    };
    // definition of op is updated
    auto update = [&](int i){
        i += sz;
        i >>= 1;
        // segtree leaf i always contains i
        seg[i] = op(i * 2 - sz, i * 2 + 1 - sz);
        while (i > 1){
            i >>= 1;
            seg[i] = op(seg[i * 2], seg[i * 2 + 1]);
        }
    };
    for (int i = 1; i < n; i++){
        done[i] = false;
    }
    for (int i = sz - 1; i >= sz / 2; i--){
        seg[i] = op(i * 2 - sz, i * 2 + 1 - sz);
    }
    for (int i = sz / 2 - 1; i >= 1; i--){
        seg[i] = op(seg[i * 2], seg[i * 2 + 1]);
    }
    std::vector<int> poped_time(n);
    poped_time[0] = 0;
    for (int i = 1; i < n; i++){
        int c = seg[1];
        int p = leader(par[c]);
        done[c] = true;
        merge(p, c);
        uf[c] = p;
        update(c);
        update(p);
        poped_time[c] = i;
    }
    if constexpr (!get_order){
        return ;
    }
    // topological sort of vertex by comparison of poped_time
    std::vector<std::vector<int>> childs(n);
    for (int v = 1; v < n; v++){
        childs[par[v]].emplace_back(v);
    }
    std::priority_queue<long long, std::vector<long long>, std::greater<long long>> tvs;
    auto val = [&](int v) -> long long {
        return ((long long)(poped_time[v]) << 32) | v;
    };
    tvs.push(0);
    std::vector<int> order; order.reserve(n);
    const long long mask = (1LL << 32) - 1;
    while (!tvs.empty()){
        int v = tvs.top() & mask; tvs.pop();
        order.emplace_back(v);
        for (int c : childs[v]){
            tvs.push(val(c));
        }
    }
    if constexpr (get_order){
        return order;
    }
}

// root is vertex 0, par[i] < i
template<typename T, bool get_order = true>
requires requires (T x, T y){
    x < y;
    {T::op(x, y)} -> std::same_as<T>;
}
std::conditional_t<get_order, std::vector<int>, T> O1onTree(int n, const std::vector<int> &par, std::vector<T> a){
    assert(ssize(par) == n);
    for (int i = 0; i < n; i++){
        assert(par[i] < i);
    }
    std::vector<int> uf(n, -1);
    auto leader = [&](int aa){
        auto dfs = [&](auto sfs, int v){
            if (uf[v] < 0) return v;
            return uf[v] = sfs(sfs,uf[v]);
        };
        return dfs(dfs,aa);
    };
    using dat = std::pair<T, long long>;
    std::priority_queue<dat, std::vector<dat>, std::greater<dat>> pque;
    for (int i = 1; i < n; i++){
        pque.push({a[i], i});
    }
    const long long mask = (1LL << 32) - 1;
    const int time_max = (1 << 30);
    std::vector<int> latest(n,0);
    std::vector<int> poped_time(n);
    poped_time[0] = 0;
    int idx = 1;
    while (!pque.empty()){
        auto [xc, tc] = pque.top(); pque.pop();
        if (latest[tc & mask] > (tc >> 32)) continue;
        int c = (tc & mask);
        latest[c] = time_max;
        int p = leader(par[c]);
        uf[c] = p;
        a[p] = T::op(a[p], xc);
        if (p != 0){
            latest[p]++;
            pque.push({a[p], ((long long)(latest[p]) << 32) | p});
        }
        poped_time[c] = idx++;
    }
    if constexpr (!get_order){
        return a[0];
    }
    std::vector<std::vector<int>> childs(n);
    for (int v = 1; v < n; v++){
        childs[par[v]].emplace_back(v);
    }
    std::priority_queue<long long, std::vector<long long>, std::greater<long long>> tvs;
    auto val = [&](int v) -> long long {
        return ((long long)(poped_time[v]) << 32) | v;
    };
    tvs.push(0);
    std::vector<int> order; order.reserve(n);
    while (!tvs.empty()){
        int v = tvs.top() & mask; tvs.pop();
        order.emplace_back(v);
        for (int c : childs[v]){
            tvs.push(val(c));
        }
    }
    if constexpr (get_order){
        return order;
    }
}

} // namespace noya2
#line 4 "c.cpp"

struct S {
    ll ans, sum, cnt;
    static S op(S a, S b){
        S c;
        c.ans = a.ans + b.ans + a.cnt * b.sum;
        c.sum = a.sum + b.sum;
        c.cnt = a.cnt + b.cnt;
        return c;
    }
    friend bool operator<(S a, S b){
        return op(a,b).ans < op(b,a).ans;
    }
};

void solve(){
    int n; in(n);
    string s; in(s);
    vector<ll> a(n); in(a);
    a.insert(a.begin(),0);
    s = "(" + s + ")";
    stack<int> st;
    vector<int> par(n+1);
    par[0] = -1;
    for (int id = 0; auto c : s){
        if (c == '('){
            st.push(id);
            id++;
        }
        else {
            int v = st.top(); st.pop();
            if (!st.empty()){
                par[v] = st.top();
            }
        }
    }
    vector<S> b(n+1);
    rep(i,n+1){
        b[i].ans = 0;
        b[i].cnt = 1;
        b[i].sum = a[i];
    }
    out(O1onTree<S,false>(n+1,par,b).ans);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
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