#931751 (C++14) No.1961 Clear Brackets

提出ソース

結果

問題	No.1961 Clear Brackets
ユーザー	👑 hos.lyric
提出日時	2023-11-25 23:23:40
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	107 ms / 2,000 ms
コード長	8,704 bytes
コンパイル時間	1,659 ms
コンパイル使用メモリ	125,596 KB
実行使用メモリ	26,668 KB
最終ジャッジ日時	2024-09-26 11:22:15
合計ジャッジ時間	6,071 ms
ジャッジサーバーID （参考情報）	judge4 / judge1

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	2 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	3 ms 5,376 KB
testcase_14	AC	94 ms 26,540 KB
testcase_15	AC	97 ms 26,412 KB
testcase_16	AC	83 ms 26,408 KB
testcase_17	AC	96 ms 26,532 KB
testcase_18	AC	95 ms 26,540 KB
testcase_19	AC	77 ms 26,540 KB
testcase_20	AC	102 ms 26,664 KB
testcase_21	AC	79 ms 26,600 KB
testcase_22	AC	83 ms 26,668 KB
testcase_23	AC	96 ms 26,540 KB
testcase_24	AC	57 ms 26,540 KB
testcase_25	AC	96 ms 26,584 KB
testcase_26	AC	87 ms 26,536 KB
testcase_27	AC	85 ms 26,540 KB
testcase_28	AC	67 ms 26,532 KB
testcase_29	AC	107 ms 26,536 KB
testcase_30	AC	91 ms 26,532 KB
testcase_31	AC	69 ms 26,532 KB
testcase_32	AC	93 ms 26,532 KB
testcase_33	AC	79 ms 26,540 KB
testcase_34	AC	91 ms 26,540 KB
testcase_35	AC	85 ms 26,536 KB
testcase_36	AC	96 ms 26,536 KB
testcase_37	AC	99 ms 26,540 KB
testcase_38	AC	105 ms 26,664 KB
testcase_39	AC	94 ms 26,660 KB
testcase_40	AC	99 ms 26,536 KB
testcase_41	AC	93 ms 26,536 KB
testcase_42	AC	95 ms 26,532 KB
testcase_43	AC	91 ms 26,540 KB
testcase_44	AC	92 ms 26,540 KB

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ソースコード

raw source code

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


// T: monoid representing information of an interval.
//   T()  should return the identity.
//   T(S s)  should represent a single element of the array.
//   T::pull(const T &l, const T &r)  should pull two intervals.
template <class T> struct SegmentTreePoint {
  int logN, n;
  vector<T> ts;
  SegmentTreePoint() : logN(0), n(0) {}
  explicit SegmentTreePoint(int n_) {
    for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
    ts.resize(n << 1);
  }
  template <class S> explicit SegmentTreePoint(const vector<S> &ss) {
    const int n_ = ss.size();
    for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
    ts.resize(n << 1);
    for (int i = 0; i < n_; ++i) at(i) = T(ss[i]);
    build();
  }
  T &at(int i) {
    return ts[n + i];
  }
  void build() {
    for (int u = n; --u; ) pull(u);
  }

  inline void pull(int u) {
    ts[u].pull(ts[u << 1], ts[u << 1 | 1]);
  }

  // Changes the value of point a to s.
  template <class S> void change(int a, const S &s) {
    assert(0 <= a); assert(a < n);
    ts[a += n] = T(s);
    for (; a >>= 1; ) pull(a);
  }

  // Applies T::f(args...) to point a.
  template <class F, class... Args>
  void ch(int a, F f, Args &&... args) {
    assert(0 <= a); assert(a < n);
    (ts[a += n].*f)(args...);
    for (; a >>= 1; ) pull(a);
  }

  // Calculates the product for [a, b).
  T get(int a, int b) {
    assert(0 <= a); assert(a <= b); assert(b <= n);
    if (a == b) return T();
    a += n; b += n;
    T prodL, prodR, t;
    for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
      if (aa & 1) { t.pull(prodL, ts[aa++]); prodL = t; }
      if (bb & 1) { t.pull(ts[--bb], prodR); prodR = t; }
    }
    t.pull(prodL, prodR);
    return t;
  }

  // Calculates T::f(args...) of a monoid type for [a, b).
  //   op(-, -)  should calculate the product.
  //   e()  should return the identity.
  template <class Op, class E, class F, class... Args>
#if __cplusplus >= 201402L
  auto
#else
  decltype((std::declval<T>().*F())())
#endif
  get(int a, int b, Op op, E e, F f, Args &&... args) {
    assert(0 <= a); assert(a <= b); assert(b <= n);
    if (a == b) return e();
    a += n; b += n;
    auto prodL = e(), prodR = e();
    for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
      if (aa & 1) prodL = op(prodL, (ts[aa++].*f)(args...));
      if (bb & 1) prodR = op((ts[--bb].*f)(args...), prodR);
    }
    return op(prodL, prodR);
  }

  // Find min b s.t. T::f(args...) returns true,
  // when called for the partition of [a, b) from left to right.
  //   Returns n + 1 if there is no such b.
  template <class F, class... Args>
  int findRight(int a, F f, Args &&... args) {
    assert(0 <= a); assert(a <= n);
    if ((T().*f)(args...)) return a;
    if (a == n) return n + 1;
    a += n;
    for (; ; a >>= 1) if (a & 1) {
      if ((ts[a].*f)(args...)) {
        for (; a < n; ) {
          if (!(ts[a <<= 1].*f)(args...)) ++a;
        }
        return a - n + 1;
      }
      ++a;
      if (!(a & (a - 1))) return n + 1;
    }
  }

  // Find max a s.t. T::f(args...) returns true,
  // when called for the partition of [a, b) from right to left.
  //   Returns -1 if there is no such a.
  template <class F, class... Args>
  int findLeft(int b, F f, Args &&... args) {
    assert(0 <= b); assert(b <= n);
    if ((T().*f)(args...)) return b;
    if (b == 0) return -1;
    b += n;
    for (; ; b >>= 1) if ((b & 1) || b == 2) {
      if ((ts[b - 1].*f)(args...)) {
        for (; b <= n; ) {
          if (!(ts[(b <<= 1) - 1].*f)(args...)) --b;
        }
        return b - n - 1;
      }
      --b;
      if (!(b & (b - 1))) return -1;
    }
  }
};

////////////////////////////////////////////////////////////////////////////////

constexpr int INF = 1001001001;

struct NodeMin {
  int mn;
  NodeMin() : mn(+INF) {}
  NodeMin(int val) : mn(val) {}
  void pull(const NodeMin &l, const NodeMin &r) {
    mn = min(l.mn, r.mn);
  }
  void ch(int val) {
    mn = val;
  }
  void chmin(int val) {
    if (mn > val) mn = val;
  }
  bool test(int tar) const {
    return (mn <= tar);
  }
};
struct NodeMax {
  int mx;
  NodeMax() : mx(-INF) {}
  NodeMax(int val) : mx(val) {}
  void pull(const NodeMax &l, const NodeMax &r) {
    mx = max(l.mx, r.mx);
  }
  void ch(int val) {
    mx = val;
  }
  void chmax(int val) {
    if (mx < val) mx = val;
  }
  bool test(int tar) const {
    return (mx >= tar);
  }
};

////////////////////////////////////////////////////////////////////////////////


int N;
char S[200'010];

int main() {
  for (; ~scanf("%d", &N); ) {
    scanf("%s", S);
    
    vector<int> F(N + 1), G(N + 1);
    {
      vector<int> is(2 * (N + 1) + 1, N + 1);
      int d = N + 1;
      for (int i = N; i >= 0; --i) {
        if (i < N) {
          d = (S[i] == ')') ? (d + 1) : (d - 1);
        }
        F[i] = is[d - 1] - 1;
        is[d] = i;
      }
    }
    {
      vector<int> is(2 * (N + 1) + 1, -1);
      int d = N + 1;
      for (int i = 0; i <= N; ++i) {
        G[i] = is[d - 1] + 1;
        is[d] = i;
        if (i < N) {
          d = (S[i] == '(') ? (d + 1) : (d - 1);
        }
      }
    }
// cerr<<"F = "<<F<<endl;
// cerr<<"G = "<<G<<endl;
    
    /*
      o? - o? - o? - o? + o? + o?
      0: down
      1: up
      2: down, o
      3: up, o
      
      i < j
      2 | j - i
      F[i] >= j
      i >= G[j]
    */
    vector<pair<int, int>> fis(N + 1);
    for (int i = 0; i <= N; ++i) {
      fis[i] = make_pair(F[i], i);
    }
    sort(fis.begin(), fis.end());
    int pos = 0;
    vector<int> on(N + 1, 1);
    
    vector<vector<int>> dp(N + 1, vector<int>(4, -INF));
    SegmentTreePoint<NodeMax> segs[2][2];
    for (int u = 0; u < 2; ++u) for (int h = 0; h < 2; ++h) {
      segs[u][h] = SegmentTreePoint<NodeMax>(N + 1);
    }
    for (int u = 0; u < 2; ++u) {
      dp[0][u] = 0;
      segs[u][0].change(0, 0);
    }
    for (int j = 1; j <= N; ++j) {
      {
        const int i = j - 1;
        if (S[i] == '?' || S[i] == ')') {
          for (int u = 0; u < 4; u += 2) {
            chmax(dp[i + 1][0], dp[i][u]);
          }
        }
        if (S[i] == '?' || S[i] == '(') {
          for (int u = 0; u < 4; ++u) {
            chmax(dp[i + 1][1], dp[i][u]);
          }
        }
      }
      for (; pos < N + 1 && fis[pos].first < j; ++pos) {
        const int i = fis[pos].second;
        on[i] = 0;
        for (int u = 0; u < 2; ++u) {
          segs[u][i & 1].change(i, -INF);
        }
      }
      for (int u = 0; u < 2; ++u) {
        chmax(dp[j][u + 2], segs[u][j & 1].get(G[j], j).mx + 1);
      }
      if (on[j]) {
        for (int u = 0; u < 2; ++u) {
          segs[u][j & 1].change(j, dp[j][u]);
        }
      }
    }
    const int ans = *max_element(dp[N].begin(), dp[N].end());
    printf("%d\n", ans);
    
#ifdef LOCAL
vector<vector<int>>brt(N+1,vector<int>(4,-INF));
brt[0][0]=0;
brt[0][1]=0;
for(int i=0;i<N;++i){
 if(S[i]=='?'||S[i]==')'){
  chmax(brt[i+1][0],brt[i][0]);
  chmax(brt[i+1][0],brt[i][2]);
 }
 if(S[i]=='?'||S[i]=='('){
  chmax(brt[i+1][1],brt[i][0]);
  chmax(brt[i+1][1],brt[i][1]);
  chmax(brt[i+1][1],brt[i][2]);
  chmax(brt[i+1][1],brt[i][3]);
 }
 for(int j=i+1;j<=N;++j)if((j-i)%2==0&&F[i]>=j&&i>=G[j]){
  chmax(brt[j][2],brt[i][0]+1);
  chmax(brt[j][3],brt[i][1]+1);
 }
}
// for(int i=0;i<=N;++i)cerr<<"brt["<<i<<"] = "<<brt[i]<<endl;
// for(int i=0;i<=N;++i)cerr<<"dp["<<i<<"] = "<<dp[i]<<endl;
for(int i=0;i<=N;++i)for(int u=0;u<4;++u)assert(max(brt[i][u],-1)==max(dp[i][u],-1));
#endif
  }
  return 0;
}

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結果

テストケース

ソースコード