magicalPillar.cpp

#include <bits/stdc++.h>
using namespace std;

// macros
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<ll, ll> lll;
typedef tuple<ll, ll, ll> llll;
typedef tuple<int, int, int> iii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<ll> vll;
typedef vector<lll> vlll;
#define REP(a,b,c) for(int a=int(b); a<int(c); a++)
#define RE(a,c) REP(a,0,c)
#define RE1(a,c) REP(a,1,c+1)
#define REI(a,b,c) REP(a,b,c+1)
#define REV(a,b,c) for(int a=int(c-1); a>=int(b); a--)
#define FOR(a,b) for(auto& a : b)
#define all(a) a.begin(), a.end()
#define INF 1e18
#define EPS 1e-9
#define pb push_back
#define popb pop_back
#define fi first
#define se second
#define sz size()
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

// input
template<class T> void IN(T& x) {cin >> x;}
template<class H, class... T> void IN(H& h, T&... t) {IN(h); IN(t...); }

// output
template<class T1, class T2> void OUT(const pair<T1,T2>& x);
template<class T> void OUT(const vector<T>& x);
template<class T> void OUT(const T& x) {cout << x;}
template<class H, class... T> void OUT(const H& h, const T&... t) {OUT(h); OUT(t...); }
template<class T1, class T2> void OUT(const pair<T1,T2>& x) {OUT(x.fi,' ',x.se);}
template<class T> void OUT(const vector<T>& x) {RE(i,x.size()) OUT(i==0?"":" ",x[i]);}
template<class... T> void OUTL(const T&... t) {OUT(t..., "\n"); }
template<class H> void OUTLS(const H& h) {OUTL(h); }
template<class H, class... T> void OUTLS(const H& h, const T&... t) {OUT(h,' '); OUTLS(t...); }

void program();
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    program();
}


//===================//
//   begin program   //
//===================//

const int MX = 5e5;

int n;
ll xs, ys, xf, yf;
ll X[MX], Y[MX], R[MX], C[MX];
vlll adj[MX];
ll dist[MX];

void program() {
    IN(n,xs,ys,xf,yf);
    RE(i,n) IN(X[i], Y[i], R[i], C[i]);
    X[n]=xs, Y[n]=ys, R[n]=0, C[n]=INF; n++;
    X[n]=xf, Y[n]=yf, R[n]=0, C[n]=0  ; n++;

    // horizontal graph
    {
        priority_queue<llll> pq;
        RE(i,n) {
            pq.push({Y[i]+R[i],2,i});
            pq.push({Y[i]-R[i],1,i});
        }

        ll inside = 0, last = 0;
        while(!pq.empty()) {
            ll y, typ, i;
            tie(y,typ,i) = pq.top(); pq.pop();
            if(typ == 2) {
                // create
                if(inside) {
                    adj[i   ].pb({last,0});
                    adj[last].pb({i   ,0});
                }
                inside++;
                last = i;
            } else {
                // destroy
                inside--;
            }
        }
    }

    // vertical graph
    {
        priority_queue<llll> pq;
        RE(i,n) {
            pq.push({X[i]+R[i],2,i});
            pq.push({X[i]-R[i],1,i});
        }

        ll inside = 0, last = 0;
        while(!pq.empty()) {
            ll x, typ, i;
            tie(x,typ,i) = pq.top(); pq.pop();
            if(typ == 2) {
                // create
                if(inside) {
                    adj[i   +n].pb({last+n,0});
                    adj[last+n].pb({i   +n,0});
                }
                inside++;
                last = i;
            } else {
                // destroy
                inside--;
            }
        }
    }

    RE(i,n) {
        adj[i  ].pb({i+n, C[i]});
        adj[i+n].pb({i  , C[i]});
    }

    // dijkstra
    RE(i,n*2) dist[i] = INF;
    priority_queue<lll,vlll,greater<lll>> pq;
    pq.push({0,n-2}); dist[n-2] = 0;
    while(!pq.empty()) {
        lll p = pq.top(); pq.pop();
        if(dist[p.se] != p.fi) continue;
        if(p.se == n-1) break;
        FOR(v,adj[p.se]) {
            if(p.fi+v.se < dist[v.fi]) {
                dist[v.fi] = p.fi+v.se;
                pq.push({dist[v.fi], v.fi});
            }
        }
    }

    if(dist[n-1] == INF) dist[n-1] = -1;

    OUTL(dist[n-1]);
}