Submission #35839

#	Time	Username	Problem	Language	Result	Execution time	Memory
35839		funcsr	Building Bridges (CEOI17_building)	C++14	100 / 100	666 ms	23176 KiB

building

#include <iostream>
#include <vector>
#include <queue>
#include <string>
#include <set>
#include <cassert>
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(xs) xs.begin(), xs.end()
#define INF (1LL<<60)
#define _1 first
#define _2 second
using namespace std;
typedef pair<int, long long> P;

P operator -(const P &a, const P &b) { return P(a._1-b._1, a._2-b._2); }
inline long long det(P a, P b) { return 1LL*a._1*b._2 - 1LL*a._2*b._1; }

int N;
int H[100000], W[100000];
long long dp[1000001];
long long f[1000001];
set<int> ps;
inline P get(int x) { return P(x, f[x]); }

bool is_all_convex() {
  vector<P> xs;
  for (int x : ps) xs.push_back(P(x, f[x]));
  rep(i, (int)xs.size()-2) {
    if (det(xs[i+1]-xs[i], xs[i+2]-xs[i]) <= 0) return false;
  }
  return true;
}

inline auto lower(int x) { return ps.lower_bound(x); }

void update(int x, long long y) {
  if (dp[x] <= y) return;
  if (dp[x] < INF) {
    auto it = ps.find(x);
    if (it != ps.end()) ps.erase(it);
  }
  P p = P(x, y+1LL*x*x);
  dp[x] = y;
  f[x] = p._2;
  //cout<<"cur: ";for (P p : ps) cout<<"("<<p._1<<","<<p._2<<"),"; cout<<"\n";
  //cout<<"cur: ";for (P p : ps) cout<<"("<<p._1<<","<<p._2<<"),"; cout<<"\n";
  while (true) {
    auto right = lower(x);
    if (right == ps.end()) break;
    P r = get(*right);
    if (p._2 >= r._2) return; // erase p
    else {
      right++;
      if (right == ps.end()) break;
      P k = get(*right);
      if (det(r-p, k-r) > 0) break;
      ps.erase(--right);
    }
  }

  while (true) {
    auto left = lower(x);
    if (left == ps.begin()) break;
    left--;
    P l = get(*left);
    if (l._2 >= p._2) ps.erase(left);
    else {
      if (left == ps.begin()) break;
      left--;
      P k = get(*left);
      if (det(l-k, p-l) > 0) break;
      ps.erase(++left);
    }
  }
  auto right = lower(x);
  if (right != ps.begin() && right != ps.end()) {
    P r = get(*right);
    P l = get(*(--right));
    if (det(p-l, r-p) <= 0) return;
  }
  ps.insert(x);
}

signed main() {
  cin >> N;
  rep(i, N) cin >> H[i];
  long long sum = 0;
  rep(i, N) {
    cin >> W[i];
    sum += W[i];
    W[i] = -W[i];
  }
  rep(h, 1000001) dp[h] = INF, f[h] = INF;
  update(H[0], W[0]);
  for (int i=1; i<N-1; i++) {
    long long m = INF;
    int h = H[i];
    if (ps.size() <= 2) {
      for (int x : ps) m = min(m, f[x] - 2LL*x*h);
    }
    else {
      int lo = *ps.begin(), hi = *(--ps.end());
      while (hi - lo > 1) {
        int mid = (lo + hi) / 2;
        auto l = lower(mid), r = ++lower(mid);
        if (r == ps.end() || det(get(*r)-get(*l), P(1, 2LL*h)) <= 0) hi = mid;
        else lo = mid;
      }
      auto it = lower(lo);
      rep(_, 2) {
        if (it == ps.end()) break;
        int x = *it;
        m = min(m, f[x] - 2LL*x*h);
        it++;
      }
    }
    update(H[i], m+1LL*H[i]*H[i]+W[i]);
  }
  long long m = INF;
  rep(h, 1000001) m = min(m, dp[h] + 1LL*(h-H[N-1])*(h-H[N-1]));
  cout << sum + m + W[N-1] << "\n";
  return 0;
}

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40