oj.uz

Submission #221884

# Submission time Handle Problem Language Result Execution time Memory
221884 2020-04-11T12:54:18 Z MKopchev Building Bridges (CEOI17_building) C++14
100 / 100
 151 ms 40408 KB 
#include<bits/stdc++.h>
using namespace std;
const int nmax=2e5+42;

const int MX=4*2*nmax;

int n;

long long h[nmax],w[nmax],pref[nmax];

long long dp[nmax];

set<long long> coeffs;

long long x_mult[nmax],pointer=0;

pair<long long,long long> tree[MX];

long long eval(pair<long long,long long> line,long long x)
{
    return x*line.first+line.second;
}
long long query(int node,int l,int r,int x)
{
    if(l==r)return eval(tree[node],x);

    long long ret=eval(tree[node],x);

    int av=(l+r)/2;

    if(x<=x_mult[av])return min(query(node*2,l,av,x),ret);

    return min(query(node*2+1,av+1,r,x),ret);
}

void add_line(int node,int l,int r,pair<long long,long long> current_line)
{
    //cout<<"add line "<<node<<" "<<l<<" "<<r<<" "<<current_line.first<<" "<<current_line.second<<endl;

    if(eval(tree[node],x_mult[l])<=eval(current_line,x_mult[l])&&eval(tree[node],x_mult[r])<=eval(current_line,x_mult[r]))return;//tree[node] is better than current_line

    if(eval(tree[node],x_mult[l])>=eval(current_line,x_mult[l])&&eval(tree[node],x_mult[r])>=eval(current_line,x_mult[r]))//current_line is better than tree[node]
    {
        tree[node]=current_line;
        return;
    }

    //now l!=r
    int av=(l+r)/2;

    //tree[node] is better in [x[l],x[av]]
    if(eval(tree[node],x_mult[l])<=eval(current_line,x_mult[l])&&eval(tree[node],x_mult[av])<=eval(current_line,x_mult[av])){add_line(node*2+1,av+1,r,current_line);return;}

    //current is better in [x[l],x[av]]
    if(eval(tree[node],x_mult[l])>=eval(current_line,x_mult[l])&&eval(tree[node],x_mult[av])>=eval(current_line,x_mult[av])){add_line(node*2+1,av+1,r,tree[node]);tree[node]=current_line;return;}

    //tree[node] is better in [x[av+1],x[r]]
    if(eval(tree[node],x_mult[av+1])<=eval(current_line,x_mult[av+1])&&eval(tree[node],x_mult[r])<=eval(current_line,x_mult[r])){add_line(node*2,l,av,current_line);return;}

    //current is better in [x[av+1],x[r]]
    if(eval(tree[node],x_mult[av+1])>=eval(current_line,x_mult[av+1])&&eval(tree[node],x_mult[r])>=eval(current_line,x_mult[r])){add_line(node*2,l,av,tree[node]);tree[node]=current_line;return;}

    assert(0==1);//should not happen
}
int main()
{
    scanf("%i",&n);

    for(int i=1;i<=n;i++)scanf("%lld",&h[i]);

    for(int i=1;i<=n;i++){coeffs.insert(-2*h[i]);coeffs.insert(h[i]);}

    for(auto k:coeffs)
    {
        pointer++;
        x_mult[pointer]=k;
    }

    for(int i=0;i<MX;i++)tree[i]={0,1e18};

    for(int i=1;i<=n;i++)scanf("%lld",&w[i]);

    for(int i=1;i<=n;i++)pref[i]=pref[i-1]+w[i];

    /*
    cout<<"pointer= "<<pointer<<endl;
    for(int i=1;i<=pointer;i++)cout<<x_mult[i]<<" ";cout<<endl;
    */

    for(int j=1;j<=n;j++)
    {
        dp[j]=h[j]*h[j]+pref[j-1]+query(1,1,pointer,h[j]);

        if(j==1)dp[j]=0;

        add_line(1,1,pointer,{-2*h[j],h[j]*h[j]-pref[j]+dp[j]});

        //cout<<j<<" -> "<<dp[j]<<endl;
    }

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

Compilation message

building.cpp: In function 'int main()':
building.cpp:67:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%i",&n);
     ~~~~~^~~~~~~~~
building.cpp:69:31: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     for(int i=1;i<=n;i++)scanf("%lld",&h[i]);
                          ~~~~~^~~~~~~~~~~~~~
building.cpp:81:31: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     for(int i=1;i<=n;i++)scanf("%lld",&w[i]);
                          ~~~~~^~~~~~~~~~~~~~

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 25600 KB Output is correct
2 Correct 17 ms 25472 KB Output is correct
3 Correct 17 ms 25472 KB Output is correct
4 Correct 17 ms 25472 KB Output is correct
5 Correct 23 ms 25472 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 95 ms 29432 KB Output is correct
2 Correct 95 ms 29436 KB Output is correct
3 Correct 98 ms 29432 KB Output is correct
4 Correct 85 ms 28792 KB Output is correct
5 Correct 114 ms 39416 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 25600 KB Output is correct
2 Correct 17 ms 25472 KB Output is correct
3 Correct 17 ms 25472 KB Output is correct
4 Correct 17 ms 25472 KB Output is correct
5 Correct 23 ms 25472 KB Output is correct
6 Correct 95 ms 29432 KB Output is correct
7 Correct 95 ms 29436 KB Output is correct
8 Correct 98 ms 29432 KB Output is correct
9 Correct 85 ms 28792 KB Output is correct
10 Correct 114 ms 39416 KB Output is correct
11 Correct 146 ms 36600 KB Output is correct
12 Correct 143 ms 36472 KB Output is correct
13 Correct 79 ms 29816 KB Output is correct
14 Correct 151 ms 36600 KB Output is correct
15 Correct 116 ms 40312 KB Output is correct
16 Correct 115 ms 40408 KB Output is correct
17 Correct 47 ms 29560 KB Output is correct
18 Correct 43 ms 29560 KB Output is correct