Submission #223610

#	Time	Username	Problem	Language	Result	Execution time	Memory
223610		DavidDamian	Roller Coaster Railroad (IOI16_railroad)	C++11	100 / 100	203 ms	26076 KiB

railroad

#include "railroad.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
///Disjoint Sets
///Sweep Line
///Set the balance always to 0, connecting special sections
int link[200005];
int setSize[200005];
int Find(int u)
{
    if(link[u]==u) return u;
    else return link[u]=Find(link[u]);
}
bool same(int u,int v)
{
    return Find(u)==Find(v);
}
void unite(int u,int v)
{
    u=Find(u);
    v=Find(v);
    if(u==v) return;
    if(setSize[v]>setSize[u]) swap(u,v);
    setSize[u]+=setSize[v];
    link[v]=u;
}
void initDSU(int n)
{
    for(int i=1;i<=n;i++){
        setSize[i]=1;
        link[i]=i;
    }
}
struct event
{
    int T;
    int op;
    int id; //Which special section
    bool operator<(const event& a)
    {
        if(T<a.T) return true;
        else{
            if(T==a.T){
                if(op<a.op) return true;
                else return false;
            }
            else return false;
        }
    }
};
struct segment
{
    ll length;
    int a,b; //ID where it starts and ends
    bool operator<(const segment& s)
    {
        return length<s.length;
    }
};
vector<event> timeline;
vector<segment> remaining; //Not taken because its balance was 0
long long plan_roller_coaster(vector<int> s, vector<int> t) {
    int n=s.size();
    ll cost=0;
    initDSU(n);
    for(int i=0;i<n;i++){
        event e={s[i],+1,i+1};
        timeline.push_back(e);
        e={t[i],-1,i+1};
        timeline.push_back(e);
    }
    sort(timeline.begin(),timeline.end());
    //Lines to the right are +1
    //Lines to the left are -1
    ll balance=-1; //Because there is a line that goes from inf to 1
    for(int i=0;i<2*n-1;i++){
        balance+=timeline[i].op;
        if(balance<0){
            unite(timeline[i].id,timeline[i+1].id); //Add a track from left to right (free) and connect i with i+1
        }
        else if(balance>0){
            cost+=(ll)(timeline[i+1].T-timeline[i].T)*balance; //We need to slow down the train so we add "balance" tracks
            //With length: distance between that two events
            unite(timeline[i].id,timeline[i+1].id);
        }
        else if(balance==0){
            segment s;
            s.length=(timeline[i+1].T-timeline[i].T);
            s.a=timeline[i].id;
            s.b=timeline[i+1].id;
            remaining.push_back(s);
        }
    }
    sort(remaining.begin(),remaining.end());
    set<int> R; //Roots
    for(int i=1;i<=n;i++){
        R.insert(Find(i));
    }
    int roots=R.size();
    int i=0;
    while(roots>1){ //Not fully connected
        int a=remaining[i].a;
        int b=remaining[i].b;
        if(!same(a,b)){
            unite(a,b);
            cost+=remaining[i].length;
            roots--;
        }
        i++;
    }
    return cost;
}

• Subtask 1: 11 / 11
• Subtask 2: 23 / 23
• Subtask 3: 30 / 30
• Subtask 4: 36 / 36