// moreflags=grader.cpp
#include "railroad.h"
// 16
// is this cheating?...
// again, I should have solved this problem earlier.
#include<algorithm>
#include<numeric>
#if not LOCAL
#define NDEBUG 1
#endif
#include<cassert>
struct Dsu{
std::vector<int> data;
Dsu(int number): data(number){
while(number--) data[number]=number;
}
void join(int first, int sec){
first=root(first); sec=root(sec);
data[first]=sec;
}
int root(int node){
return data[node]!=node? data[node]=root(data[node]): node;
}
};
long long plan_roller_coaster(std::vector<int> s, std::vector<int> t) {
std::vector<int> values; values.reserve(s.size()+t.size());
for(auto it: s) values.push_back(it);
for(auto it: t) values.push_back(it);
std::sort(begin(values), end(values));
values.resize(std::unique(begin(values), end(values))-values.begin());
std::vector<int> degree(values.size());
Dsu dsu((int)values.size());
for(int i=0; i<(int)s.size(); ++i){
auto const a=int(std::lower_bound(begin(values), end(values), s[i])-begin(values));
auto const b=int(std::lower_bound(begin(values), end(values), t[i])-begin(values));
degree[a]++;
degree[b]--;
dsu.join(a, b);
}
degree[0]--; // add a huge edge downward
dsu.join(0, (int)values.size()-1);
std::partial_sum(begin(degree), end(degree), degree.begin());
degree.pop_back();
struct Edge{int len, first, sec;};
std::vector<Edge> pending;
int64_t result{};
for(int index=0; index<(int)degree.size(); ++index){
auto const edgeLen=values[index+1]-values[index];
if(degree[index]>0)
result+=int64_t(edgeLen)*degree[index];
if(degree[index]!=0)
dsu.join(index, index+1);
else if(dsu.root(index)!=dsu.root(index+1))
pending.push_back({edgeLen, index, index+1});
}
std::sort(begin(pending), end(pending),[&](Edge first, Edge sec){return first.len<sec.len;});
for(auto [len, first, sec]: pending) if(dsu.root(first)!=dsu.root(sec)){
dsu.join(first, sec);
result+=len;
}
for(int i=0; i<(int)dsu.data.size(); ++i)
assert(dsu.root(i)==dsu.root(0));
return result;
}
