Submission #528417

#	Time	Username	Problem	Language	Result	Execution time	Memory
528417		cig32	Building Bridges (CEOI17_building)	C++17	100 / 100	111 ms	12864 KiB

building

#include "bits/stdc++.h"
using namespace std;
mt19937_64 rng((int)std::chrono::steady_clock::now().time_since_epoch().count());
const int MAXN = 5e5 + 10;
const int MOD = 1e9 + 7;
#define int long long
 
int rnd(int x, int y) {
  int u = uniform_int_distribution<int>(x, y)(rng); return u;
}
const int is_query = -(1ll<<62);
struct Line {
  int m, b;
  mutable function<const Line*()> succ;
  bool operator<(const Line& rhs) const {
    if (rhs.b != is_query) return m < rhs.m;
    const Line* s = succ();
    if (!s) return 0;
    int x = rhs.m;
    return b - s->b < (s->m - m) * x;
  }
};
struct dynamic_hull : public multiset<Line> { // wiint maintain upper hull for maximum
  bool bad(iterator y) {
    auto z = next(y);
    if (y == begin()) {
        if (z == end()) return 0;
        return y->m == z->m && y->b <= z->b;
    }
    auto x = prev(y);
    if (z == end()) return y->m == x->m && y->b <= x->b;
    return (x->b - y->b)*(z->m - y->m) >= (y->b - z->b)*(y->m - x->m);
  }
  void insert_line(int m, int b) {
    auto y = insert({ m, b });
    y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
    if (bad(y)) { erase(y); return; }
    while (next(y) != end() && bad(next(y))) erase(next(y));
    while (y != begin() && bad(prev(y))) erase(prev(y));
  }
  int eval(int x) {
    auto l = *lower_bound((Line) { x, is_query });
    return l.m * x + l.b;
  }
};


void solve(int tc) {
  int n;
  cin >> n;
  int h[n+1];
  int ps[n+1];
  ps[0] = 0;
  for(int i=1; i<=n; i++) {
    cin >> h[i];
  }
  for(int i=1; i<=n; i++) {
    cin >> ps[i];
    ps[i] += ps[i-1];
  }
  int dp[n+1];
  dp[1] = 0;
  dynamic_hull cht;
  cht.insert_line(-h[1], -h[1] * h[1] + ps[1]);
  for(int i=2; i<=n; i++) {
    dp[i] = -cht.eval(-2 * h[i]) + h[i] * h[i] + ps[i-1];
    cht.insert_line(-h[i], -h[i] * h[i] + ps[i] - dp[i]);
  }
  cout << dp[n] << "\n";
}
 
int32_t main(){
  ios::sync_with_stdio(0); cin.tie(0);
  int t = 1;// cin >> t;
  for(int i=1; i<=t; i++) solve(i);
} 
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/

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