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Submission #37484

# Submission time Handle Problem Language Result Execution time Memory
37484 2017-12-26T02:41:36 Z MatheusLealV Building Bridges (CEOI17_building) C++14
100 / 100
 303 ms 10784 KB 
// Building bridges - CEOI 2017
// Complexidade O(N*sqrt(N))

#include <bits/stdc++.h>
#define inf 2000000000000000000LL
#define N 100050
#define f first
#define s second
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pii;

vector<pii> lines;

ll h[N], sum[N], n, dp[N], raiz;

struct Convex_Hull
{
    vector<pii> lines;

    double intersect(pii r, pii s)
    {
      return ((double)(r.s - s.s))/((double)(s.f - r.f));
    }

    bool bad(pii A, pii B, pii C)
    {
      return intersect(A, C) <= intersect(B, A);
    }

    void addline(pii line, bool flag)
    {
      if(flag)
      {
          while(lines.size() >= 2 && bad(lines[lines.size() - 2], lines[lines.size() - 1], line) ) lines.pop_back();

          if(lines.size() == 1 && lines[0].f == line.f) lines.pop_back();

          lines.push_back(line);
      }

      else
      {
        lines.push_back(line);

        for(int i = lines.size() - 1; i >= 0; i--)
        {
           if(i != 0 && lines[i - 1] <= lines[i]) swap(lines[i], lines[i - 1]);

           else break;
        }
      }
    }

    ll query_Hull(ll x) 
    {
        int ini = 0, fim = lines.size() - 1, mid, best = -1;

        while(fim >= ini)
        {
            mid = (ini + fim)/2;

            double pos = mid > 0? intersect(lines[mid], lines[mid - 1]) : - inf;

            if(pos <= x) best = mid, ini = mid + 1;

            else fim = mid - 1; 
        }

        return (best == -1 ? inf : lines[best].f*x + lines[best].s);
    }

} oficial, aux, pilha;

void Clear_Stack()
{
  aux.lines.clear();

  int esq = 0, dir = 0;

  while(esq < oficial.lines.size() && dir < pilha.lines.size())
  {
    if(oficial.lines[esq] >= pilha.lines[dir]) aux.addline(oficial.lines[esq], 1), esq ++;

    else aux.addline(pilha.lines[dir], 1), dir ++;
  }

  while(esq < oficial.lines.size()) aux.addline(oficial.lines[esq], 1), esq ++;

  while(dir < pilha.lines.size()) aux.addline(pilha.lines[dir], 1), dir ++;

  oficial.lines = aux.lines, pilha.lines.clear(), aux.lines.clear();
}

int main()
{
  ios::sync_with_stdio(false); cin.tie(0);

  cin>>n;

  raiz = sqrt(n);

  for(int i = 1; i <= n; i++) cin>>h[i];

  for(int i = 1; i <= n; i++) cin>>sum[i], sum[i] += sum[i - 1];

  dp[1] = 0;

  pilha.addline(pii(-2*h[1], h[1]*h[1] - sum[1]), 0);

  for(int i = 2; i <= n; i++)
  {
      ll q = oficial.query_Hull(h[i]);

      for(auto line: pilha.lines) q = min(q, line.f*h[i] + line.s);

      dp[i] = q + h[i]*h[i] + sum[i - 1];

      pilha.addline(pii(-2*h[i], h[i]*h[i] - sum[i] + dp[i]), 0);

      if(pilha.lines.size() >= raiz) Clear_Stack();
  }

  cout<<dp[n]<<"\n";
}

Compilation message

building.cpp: In function 'void Clear_Stack()':
building.cpp:81:13: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(esq < oficial.lines.size() && dir < pilha.lines.size())
             ^
building.cpp:81:43: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(esq < oficial.lines.size() && dir < pilha.lines.size())
                                           ^
building.cpp:88:13: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(esq < oficial.lines.size()) aux.addline(oficial.lines[esq], 1), esq ++;
             ^
building.cpp:90:13: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(dir < pilha.lines.size()) aux.addline(pilha.lines[dir], 1), dir ++;
             ^
building.cpp: In function 'int main()':
building.cpp:121:29: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
       if(pilha.lines.size() >= raiz) Clear_Stack();
                             ^

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 4536 KB Output is correct
2 Correct 0 ms 4536 KB Output is correct
3 Correct 0 ms 4536 KB Output is correct
4 Correct 0 ms 4536 KB Output is correct
5 Correct 0 ms 4536 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 99 ms 4668 KB Output is correct
2 Correct 89 ms 4676 KB Output is correct
3 Correct 83 ms 4692 KB Output is correct
4 Correct 86 ms 4536 KB Output is correct
5 Correct 109 ms 5880 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 4536 KB Output is correct
2 Correct 0 ms 4536 KB Output is correct
3 Correct 0 ms 4536 KB Output is correct
4 Correct 0 ms 4536 KB Output is correct
5 Correct 0 ms 4536 KB Output is correct
6 Correct 99 ms 4668 KB Output is correct
7 Correct 89 ms 4676 KB Output is correct
8 Correct 83 ms 4692 KB Output is correct
9 Correct 86 ms 4536 KB Output is correct
10 Correct 109 ms 5880 KB Output is correct
11 Correct 83 ms 4536 KB Output is correct
12 Correct 76 ms 4676 KB Output is correct
13 Correct 63 ms 4536 KB Output is correct
14 Correct 86 ms 4676 KB Output is correct
15 Correct 303 ms 10784 KB Output is correct
16 Correct 119 ms 5880 KB Output is correct
17 Correct 83 ms 4536 KB Output is correct
18 Correct 79 ms 4536 KB Output is correct