oj.uz

답안 #47868

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
47868 2018-05-08T09:45:34 Z Extazy Building Bridges (CEOI17_building) C++17
100 / 100
 223 ms 20912 KB 
#include <bits/stdc++.h>
#define endl '\n'
 
using namespace std;
 
const int N = 100007;
const double EPS = 0.0000001;

struct dynamic_convex_hull_trick {
  struct line {
    long long a,b;
    
    line(){}
    line(long long x, long long y): a(x), b(y) {}
 
    bool operator <(const line &x) const {
      return a==x.a ? b<x.b : a<x.a;
    }
  };
 
  struct cross_t {
    double x;
    line l;

    cross_t(){}
    cross_t(double a, line b): x(a), l(b) {}

    bool operator <(const cross_t &a) const {
      return fabs(x-a.x)<=EPS ? false : x<a.x;
    }
  };

  set < line > s;
  set < cross_t > cross_set;

  long long eval(line l, long long x) {
    return l.a*x+l.b;
  }
 
  double cross_x(line l1, line l2) {
    return (double)(l2.b-l1.b)/(double)(l1.a-l2.a);
  }

  void erase_line(set < line >::iterator it) {
    if(it!=s.begin()) {
      cross_set.erase(cross_t(cross_x(*it,*prev(it)),*it));
    }
    if(next(it)!=s.end()) {
      cross_set.erase(cross_t(cross_x(*next(it),*it),*next(it)));
    }
    if(it!=s.begin() && next(it)!=s.end()) {
      cross_set.insert(cross_t(cross_x(*next(it),*prev(it)),*next(it)));
    }
    s.erase(it);
  }

  void erase_line2(set < line >::iterator it) {
    if(prev(it)!=s.begin()) {
      cross_set.erase(cross_t(cross_x(*it,*prev(prev(it))),*it));
    }
    if(next(it)!=s.end()) {
      cross_set.erase(cross_t(cross_x(*next(it),*it),*next(it)));
    }
    if(prev(it)!=s.begin() && next(it)!=s.end()) {
      cross_set.insert(cross_t(cross_x(*next(it),*prev(prev(it))),*next(it)));
    }
    s.erase(it);
  }

  void insert_line(set < line >::iterator it) {
    if(it!=s.begin() && next(it)!=s.end()) {
      cross_set.erase(cross_t(cross_x(*next(it),*prev(it)),*next(it)));
    }
    if(it!=s.begin()) {
      cross_set.insert(cross_t(cross_x(*it,*prev(it)),*it));
    }
    if(next(it)!=s.end()) {
      cross_set.insert(cross_t(cross_x(*next(it),*it),*next(it)));
    }
  }

  void add_line(line l) {
    if(s.find(l)!=s.end()) return;
 
    set < line >::iterator it=s.insert(l).first,it1,it2;

    if(it!=s.begin()) {
      it1=prev(it);
      if(it1->a==it->a) {
        s.erase(it);
        return;
      }
    }

    if(it!=s.end()) {
      it2=next(it);
      if(it->a==it2->a) {
        erase_line2(it2);
      }
    }

    insert_line(it);

    if(it!=s.begin() && it!=s.end()) {
      it1=prev(it);
      it2=next(it);
 
      if(it2!=s.end()) {
        if(cross_x(*it2,*it1)>=cross_x(*it,*it1)) {
          erase_line(it);
          return;
        }
      }
    }
 
    while(it!=s.begin()) {
      it1=prev(it);
      if(it1==s.begin()) break;
      it2=prev(it1);
 
      if(cross_x(*it2,*it)>=cross_x(*it2,*it1)) {
        erase_line(it1);
        it=s.find(l);
      }
      else {
        break;
      }
    }
 
    while(it!=s.end()) {
      it1=next(it);
      if(it1==s.end()) break;
      it2=next(it1);
      if(it2==s.end()) break;
 
      if(cross_x(*it2,*it)>=cross_x(*it1,*it)) {
        erase_line(it1);
        it=s.find(l);
      }
      else {
        break;
      }
    }
  }
 
  long long get(long long x) {
    long long ans=eval(*s.begin(),x);

    set < cross_t >::iterator it=cross_set.lower_bound(cross_t(x,line(0,0)));
    if(it!=cross_set.end()) {
      ans=min(ans,eval(it->l,x));
      if(next(it)!=cross_set.end()) ans=min(ans,eval(next(it)->l,x));
    }
    if(it!=cross_set.begin()) {
      ans=min(ans,eval(prev(it)->l,x));
    }

    return ans;
  }
};
 
int n,h[N],w[N];
long long s[N];
dynamic_convex_hull_trick cht;
long long dp[N];
 
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int i;
 
  scanf("%d", &n);
  for(i=1;i<=n;i++) {
    scanf("%d", &h[i]);
  }
  for(i=1;i<=n;i++) {
    scanf("%d", &w[i]);
    s[i]=s[i-1]+w[i];
  }
 
  dp[n]=0;
  for(i=n-1;i>=1;i--) {
    cht.add_line(dynamic_convex_hull_trick::line(-2ll*h[i+1],s[i]+h[i+1]*1ll*h[i+1]+dp[i+1]));
    dp[i]=h[i]*1ll*h[i]-s[i]+cht.get(h[i]);
  }

  printf("%lld\n", dp[1]);
 
  return 0;
}

Compilation message

building.cpp: In function 'int main()':
building.cpp:172:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d", &n);
   ~~~~~^~~~~~~~~~
building.cpp:174:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d", &h[i]);
     ~~~~~^~~~~~~~~~~~~
building.cpp:177:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d", &w[i]);
     ~~~~~^~~~~~~~~~~~~

Subtask #1
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 488 KB Output is correct
3 Correct 2 ms 488 KB Output is correct
4 Correct 3 ms 488 KB Output is correct
5 Correct 3 ms 512 KB Output is correct

Subtask #2
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 185 ms 2944 KB Output is correct
2 Correct 185 ms 2944 KB Output is correct
3 Correct 223 ms 2944 KB Output is correct
4 Correct 179 ms 3012 KB Output is correct
5 Correct 142 ms 5244 KB Output is correct

Subtask #3
40.0 / 40.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 488 KB Output is correct
3 Correct 2 ms 488 KB Output is correct
4 Correct 3 ms 488 KB Output is correct
5 Correct 3 ms 512 KB Output is correct
6 Correct 185 ms 2944 KB Output is correct
7 Correct 185 ms 2944 KB Output is correct
8 Correct 223 ms 2944 KB Output is correct
9 Correct 179 ms 3012 KB Output is correct
10 Correct 142 ms 5244 KB Output is correct
11 Correct 182 ms 5244 KB Output is correct
12 Correct 192 ms 5244 KB Output is correct
13 Correct 139 ms 6224 KB Output is correct
14 Correct 189 ms 7556 KB Output is correct
15 Correct 179 ms 20912 KB Output is correct
16 Correct 141 ms 20912 KB Output is correct
17 Correct 26 ms 20912 KB Output is correct
18 Correct 35 ms 20912 KB Output is correct