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Submission #985484

# Submission time Handle Problem Language Result Execution time Memory
985484 2024-05-18T00:40:38 Z 12345678 Building Bridges (CEOI17_building) C++17
100 / 100
 46 ms 9808 KB 
#include <bits/stdc++.h>

using namespace std;

#define ll long long

const int nx=1e5+5;

ll n, h[nx], w[nx], dp[nx], res, inf=1e18;
bool querymode;

struct line
{
    ll m, c;
    mutable ll p;
    line(ll m=0, ll c=0, ll p=0): m(m), c(c), p(p) {}
    bool operator< (const line &o) const {return querymode?p<o.p:m>o.m;}
};

struct convexhulltrick:multiset<line>
{
    ll div(ll a, ll b)
    {
        if ((a%b)==0||(a^b)>=0) return a/b;
        return a/b-1;
    }
    bool isect(iterator x, iterator y)
    {
        if (y==end()) return x->p=inf, 0;
        if (x->m==y->m) x->p=(x->c>=y->c)?-inf:inf;
        else x->p=div(y->c-x->c, x->m-y->m);
        return x->p>=y->p;
    }
    void add(line k)
    {
        auto x=insert(k), y=next(x);
        while (isect(x, y)) y=erase(y);
        if ((y=x)!=begin()&&isect(--x, y)) isect(x, erase(y));
        while ((y=x)!=begin()&&(--x)->p>=y->p) isect(x, erase(y));
    }
    ll query(ll x)
    {
        querymode=1;
        auto tmp=lower_bound(line(0, 0, x));
        querymode=0;
        return tmp->m*x+tmp->c;
    }
} s;

int main()
{
    cin.tie(NULL)->sync_with_stdio(false);
    cin>>n;
    for (int i=1; i<=n; i++) cin>>h[i];
    for (int i=1; i<=n; i++) cin>>w[i], res+=w[i];
    dp[1]=-w[1];
    s.add(line(h[1], dp[1]+h[1]*h[1], 0));
    for (int i=2; i<=n; i++)
    {
        dp[i]=s.query(-2*h[i])+h[i]*h[i]-w[i];
        s.add(line(h[i], dp[i]+h[i]*h[i], 0));
    }
    cout<<dp[n]+res;
}

/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2392 KB Output is correct
2 Correct 2 ms 2548 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 35 ms 3672 KB Output is correct
2 Correct 34 ms 3652 KB Output is correct
3 Correct 32 ms 3676 KB Output is correct
4 Correct 31 ms 3676 KB Output is correct
5 Correct 26 ms 4836 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2392 KB Output is correct
2 Correct 2 ms 2548 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 35 ms 3672 KB Output is correct
7 Correct 34 ms 3652 KB Output is correct
8 Correct 32 ms 3676 KB Output is correct
9 Correct 31 ms 3676 KB Output is correct
10 Correct 26 ms 4836 KB Output is correct
11 Correct 30 ms 4156 KB Output is correct
12 Correct 31 ms 3676 KB Output is correct
13 Correct 25 ms 3672 KB Output is correct
14 Correct 32 ms 4156 KB Output is correct
15 Correct 46 ms 9808 KB Output is correct
16 Correct 26 ms 4804 KB Output is correct
17 Correct 17 ms 3848 KB Output is correct
18 Correct 17 ms 3676 KB Output is correct