제출 #840503

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
840503		jonathanirvings	봉쇄 시간 (IOI23_closing)	C++17	100 / 100	533 ms	45832 KiB

closing

#include "closing.h"

#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder

#endif  // ATCODER_INTERNAL_TYPE_TRAITS_HPP

#ifndef ATCODER_FENWICKTREE_HPP
#define ATCODER_FENWICKTREE_HPP 1

#include <cassert>
#include <vector>

namespace atcoder {

// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
    using U = internal::to_unsigned_t<T>;

  public:
    fenwick_tree() : _n(0) {}
    explicit fenwick_tree(int n) : _n(n), data(n) {}

    void add(int p, T x) {
        assert(0 <= p && p < _n);
        p++;
        while (p <= _n) {
            data[p - 1] += U(x);
            p += p & -p;
        }
    }

    T sum(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        return sum(r) - sum(l);
    }

  private:
    int _n;
    std::vector<U> data;

    U sum(int r) {
        U s = 0;
        while (r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

}  // namespace atcoder

#endif  // ATCODER_FENWICKTREE_HPP

#include <bits/stdc++.h>
using namespace std;

vector<vector<pair<int, int>>> adj;

struct SumCntFenwickTree {
  SumCntFenwickTree(vector<pair<long long, int>> num)
    : _bit_cnt(num.size()), _bit_sum(num.size()) {
    for (auto [a, _] : num) {
      _num.push_back(a);
    }
  }

  void Add(int x) {
    _bit_cnt.add(x, 1);
    _bit_sum.add(x, _num[x]);
  }

  void Remove(int x) {
    _bit_cnt.add(x, -1);
    _bit_sum.add(x, -_num[x]);
  }

  int Cnt(int x) {
    return _bit_cnt.sum(0, x);    
  }

  long long Sum(int x) {
    return _bit_sum.sum(0, x);
  }

  vector<long long> _num;
  atcoder::fenwick_tree<int> _bit_cnt;
  atcoder::fenwick_tree<long long> _bit_sum;
};

void fill_distance(int u, int from, vector<long long>& distance) {
  for (auto [v, w] : adj[u]) {
    if (v != from) {
      distance[v] = distance[u] + w;
      fill_distance(v, u, distance);
    }
  }
}

int non_intersecting(
    int N, long long K,
    const vector<long long>& fromX, const vector<long long>& fromY) {
  vector<long long> smaller(N);
  for (int i = 0; i < N; ++i) {
    smaller[i] = min(fromX[i], fromY[i]);
  }
  sort(smaller.begin(), smaller.end());
  for (int i = 0; i < N; ++i) {
    if (smaller[i] <= K) {
      K -= smaller[i];
    } else {
      return i;
    }
  }
  return N;
}

int max_score(int N, int X, int Y, long long K,
              std::vector<int> U, std::vector<int> V, std::vector<int> W) {
  adj.clear();
  adj.resize(N);
  for (int i = 0; i < N - 1; ++i) {
    adj[U[i]].emplace_back(V[i], W[i]);
    adj[V[i]].emplace_back(U[i], W[i]);
  }
  vector<long long> fromX(N), fromY(N);
  fill_distance(X, -1, fromX);
  fill_distance(Y, -1, fromY);
  vector<bool> is_in_path(N);
  vector<int> in_path;
  for (int i = 0; i < N; ++i) {
    is_in_path[i] = fromX[i] + fromY[i] == fromX[Y];
    if (is_in_path[i]) {
      in_path.push_back(i);
    }
  }

  int answer = non_intersecting(N, K, fromX, fromY);
  for (int u : in_path) {
    K -= min(fromX[u], fromY[u]);
  }
  if (K >= 0) {
    vector<int> order(N);
    iota(order.begin(), order.end(), 0);
    sort(order.begin(), order.end(), [&] (int a, int b) {
      return make_pair(max(fromX[a], fromY[a]) - min(fromX[a], fromY[a]), a)
          < make_pair(max(fromX[b], fromY[b]) - min(fromX[b], fromY[b]), b);
    });

    vector<pair<long long, int>> cost_one, cost_two;
    for (int i = 0; i < N; ++i) {
      if (is_in_path[i]) {
        cost_one.emplace_back(
            max(fromX[i], fromY[i]) - min(fromX[i], fromY[i]), i);
      } else {
        cost_two.emplace_back(max(fromX[i], fromY[i]), i);
        cost_one.emplace_back(min(fromX[i], fromY[i]), i);
      }
    }
    sort(cost_one.begin(), cost_one.end());
    sort(cost_two.begin(), cost_two.end());
    
    vector<int> ix_cost_one(N), ix_cost_two(N);
    for (int i = 0; i < N; ++i) {
      ix_cost_one[cost_one[i].second] = i;
      if (i < static_cast<int>(cost_two.size())) {
        ix_cost_two[cost_two[i].second] = i;
      }
    }

    SumCntFenwickTree bit_cost_one(cost_one);
    SumCntFenwickTree bit_cost_two(cost_two);
    for (int i = 0; i < N; ++i) {
      if (!is_in_path[i]) {
        bit_cost_one.Add(ix_cost_one[i]);
      }
    }

    for (int i = 0; i < N; ++i) {
      int u = order[i];
      if (is_in_path[u]) {
        bit_cost_one.Add(ix_cost_one[u]);
      } else {
        bit_cost_one.Remove(ix_cost_one[u]);
        bit_cost_two.Add(ix_cost_two[u]);
      }

      auto check = [&] (int mid) {
        int lowest_cannot_take = lower_bound(
            cost_one.begin(),
            cost_one.end(), 
            make_pair((cost_two[mid].first + 1) >> 1, 0)) - cost_one.begin();
        return bit_cost_two.Sum(mid + 1)
             + bit_cost_one.Sum(lowest_cannot_take) <= K;
      };

      int take_until_two = -1;
      {
        int lo = 0;
        int hi = static_cast<int>(cost_two.size()) - 1;
        while (lo <= hi) {
          int mid = (lo + hi) >> 1;
          if (check(mid)) {
            take_until_two = mid;
            lo = mid + 1;
          } else {
            hi = mid - 1;
          }
        }
      }

      int take_until_one = -1;
      if (false) {
        while (take_until_one + 1 < N &&
               bit_cost_two.Sum(take_until_two + 1)
                  + bit_cost_one.Sum(take_until_one + 2) <= K)
          ++take_until_one;
      } else {
        int lo = 0;
        int hi = N - 1;
        while (lo <= hi) {
          int mid = (lo + hi) >> 1;
          if (bit_cost_two.Sum(take_until_two + 1)
              + bit_cost_one.Sum(mid + 1) <= K) {
            take_until_one = mid;
            lo = mid + 1;
          } else {
            hi = mid - 1;
          }
        }
      }
      answer = max(answer, static_cast<int>(in_path.size())
                         + 2 * bit_cost_two.Cnt(take_until_two + 1)
                         + bit_cost_one.Cnt(take_until_one + 1));

      if (take_until_one >= 0) {
        long long target_cost = bit_cost_one.Sum(take_until_one + 1);
        {
          take_until_one = -1;
          int lo = 0;
          int hi = N - 1;
          while (lo <= hi) {
            int mid = (lo + hi) >> 1;
            if (bit_cost_one.Sum(mid + 1) < target_cost) {
              take_until_one = mid;
              lo = mid + 1;
            } else {
              hi = mid - 1;
            }
          }
        }
        int lo = 0;
        int hi = static_cast<int>(cost_two.size()) - 1;
        while (lo <= hi) {
          int mid = (lo + hi) >> 1;
          if (bit_cost_two.Sum(mid + 1)
              + bit_cost_one.Sum(take_until_one + 1) <= K) {
            take_until_two = mid;
            lo = mid + 1;
          } else {
            hi = mid - 1;
          }
        }
        answer = max(answer, static_cast<int>(in_path.size())
                         + 2 * bit_cost_two.Cnt(take_until_two + 1)
                         + bit_cost_one.Cnt(take_until_one + 1));
      }
    }
  }
  return answer;
}

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