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Submission #858371

# Submission time Handle Problem Language Result Execution time Memory
858371 2023-10-08T09:14:08 Z Tenis0206 Building Bridges (CEOI17_building) C++11
100 / 100
 53 ms 67320 KB 
#include <bits/stdc++.h>
#define int long long

using namespace std;

const int nmax = 1e5;
const int hmax = 1e6;
const int oo = LLONG_MAX;

int n;
int h[nmax + 5], w[nmax + 5];
int sp[nmax + 5];

int dp[nmax + 5];

pair<int,int> lc[4 * hmax + 5];

int get_val(pair<int,int> f, int x)
{
    if(f.first==oo)
    {
        return oo;
    }
    return f.first * x + f.second;
}

bool is_smaller(pair<int,int> f, pair<int,int> g, int x)
{
    return get_val(f, x) < get_val(g, x);
}

int query(int poz, int nod, int st, int dr)
{
    if(st==dr)
    {
        return get_val(lc[nod], poz);
    }
    int mij = (st + dr) >> 1;
    if(poz <= mij)
    {
        return min(get_val(lc[nod],poz), query(poz,nod*2,st,mij));
    }
    return min(get_val(lc[nod],poz), query(poz,nod*2+1,mij+1,dr));
}

void update(pair<int,int> f, int nod, int st, int dr)
{
    int mij = (st + dr) >> 1;
    bool okst = is_smaller(f, lc[nod], st);
    bool okmij = is_smaller(f, lc[nod], mij);
    if(okmij)
    {
        swap(f,lc[nod]);
    }
    if(st==dr)
    {
        return;
    }
    if(okst!=okmij)
    {
        update(f,nod*2,st,mij);
    }
    else
    {
        update(f,nod*2+1,mij+1,dr);
    }
}

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    #ifdef home
    freopen("nr.in","r",stdin);
    freopen("nr.out","w",stdout);
    #endif // home
    cin>>n;
    for(int i=1;i<=n;i++)
    {
        cin>>h[i];
    }
    for(int i=1;i<=n;i++)
    {
        cin>>w[i];
        sp[i] = sp[i - 1] + w[i];
    }
    for(int i=1;i<=4*hmax;i++)
    {
        lc[i] = {oo,oo};
    }
    dp[1] = 0;
    update({-2 * h[1],dp[1] + 1LL * h[1] * h[1] - sp[1]},1,1,hmax);
    for(int i=2;i<=n;i++)
    {
        dp[i] = query(h[i],1,1,hmax) + 1LL * h[i] * h[i] + sp[i - 1];
        update({-2 * h[i],dp[i] + 1LL * h[i] * h[i] - sp[i]},1,1,hmax);
    }
    cout<<dp[n]<<'\n';
    return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 63068 KB Output is correct
2 Correct 9 ms 62928 KB Output is correct
3 Correct 10 ms 63064 KB Output is correct
4 Correct 9 ms 63068 KB Output is correct
5 Correct 9 ms 63320 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 46 ms 66044 KB Output is correct
2 Correct 53 ms 66012 KB Output is correct
3 Correct 49 ms 66132 KB Output is correct
4 Correct 40 ms 66132 KB Output is correct
5 Correct 38 ms 66128 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 63068 KB Output is correct
2 Correct 9 ms 62928 KB Output is correct
3 Correct 10 ms 63064 KB Output is correct
4 Correct 9 ms 63068 KB Output is correct
5 Correct 9 ms 63320 KB Output is correct
6 Correct 46 ms 66044 KB Output is correct
7 Correct 53 ms 66012 KB Output is correct
8 Correct 49 ms 66132 KB Output is correct
9 Correct 40 ms 66132 KB Output is correct
10 Correct 38 ms 66128 KB Output is correct
11 Correct 49 ms 67320 KB Output is correct
12 Correct 48 ms 67152 KB Output is correct
13 Correct 39 ms 67196 KB Output is correct
14 Correct 49 ms 67152 KB Output is correct
15 Correct 38 ms 66856 KB Output is correct
16 Correct 47 ms 66984 KB Output is correct
17 Correct 35 ms 67152 KB Output is correct
18 Correct 37 ms 67152 KB Output is correct