Submission #1112363

#	Time	Username	Problem	Language	Result	Execution time	Memory
1112363		Aviansh	Building Bridges (CEOI17_building)	C++17	100 / 100	122 ms	51528 KiB

building

#include <bits/stdc++.h>

using namespace std;

long long inf = 2e18;

struct line{
    long long m;
    long long c;
    double val(double x){
        return m*x+c;
    }
    int left=-1;
    int right=-1;
};

struct liChaoTree{
    line *st;
    line def;
    int cr = 0;
    liChaoTree(int nodes){
        def.m=0;
        def.c=LLONG_MAX;
        st=new line[nodes];
        fill(st,st+nodes,def);
    }
    void addLine(line lin, long long l=0, long long r=1e9+5, int ind=0){
        long long mid = (l+r)/2;
        if(st[ind].val(l)<=lin.val(l)&&st[ind].val(r)<=lin.val(r)){
            return;
        }
        lin.left=st[ind].left;
        lin.right=st[ind].right;
        if(st[ind].val(mid)>lin.val(mid)){
            swap(lin,st[ind]);
        }
        if(l==r)
            return;
        else if(st[ind].val(l)>lin.val(l)){
            if(lin.left==-1){
                cr++;
                st[ind].left=cr;
            }
            addLine(lin,l,mid,st[ind].left);
        }
        else{
            if(lin.right==-1){
                cr++;
                st[ind].right=cr;
            }
            addLine(lin,mid+1,r,st[ind].right);
        }
    }
    double query(long long x, long long l=0, long long r=1e9+5, int ind=0){
        if(l==r&&r==x){
            return st[ind].val(x);
        }
        if(x<l||x>r){
            return def.val(x);
        }
        long long mid = (l+r)/2;
        double ans1 = 2e18;
        if(st[ind].left!=-1){
            ans1=query(x,l,mid,st[ind].left);
        }

        double ans2 = 2e18;
        if(st[ind].right!=-1){
            ans2=query(x,mid+1,r,st[ind].right);
        }
        return min({st[ind].val(x),ans1,ans2});
    }
};


signed main(){
    //ios::sync_with_stdio(0);
    //cin.tie(0);
    long long n;
    cin >> n;
    long long arr[n];
    for(long long &i : arr){
        cin >> i;
    }
    long long w[n];
    for(long long &i : w){
        cin >> i;
    }
    long long dp[n];
    dp[0]=0;
    dp[1]=arr[0]*arr[0]+arr[1]*arr[1]-2*arr[0]*arr[1];
    long long pref[n];
    pref[0]=w[0];
    for(int i = 1;i<n;i++){
        pref[i]=pref[i-1]+w[i];
    }
    liChaoTree lct(2e6+50);
    line l1,l2;
    l1.m=-2*arr[0];
    l2.m=-2*arr[1];
    l1.c=dp[0]-pref[0]+arr[0]*arr[0];
    l2.c=dp[1]-pref[1]+arr[1]*arr[1];
    //cout << "adding: \n";
    lct.addLine(l1);
    lct.addLine(l2);
    for(long long i = 2;i<n;i++){
        dp[i]=inf;
        //cout << dp[i] << " " << lct.query(arr[i]) << "\n";
        dp[i]=lct.query(arr[i]);
        dp[i]+=pref[i-1]+arr[i]*arr[i];
        line t;
        t.m=-2*arr[i];
        t.c=dp[i]-pref[i]+arr[i]*arr[i];
        lct.addLine(t);
    }
    cout << dp[n-1];
    return 0;
}

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40