This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define FOR(i,s,e) for(int i = s; i <= (int)e; ++i)
#define DEC(i,s,e) for(int i = s; i >= (int)e; --i)
#define IAMSPEED ios_base::sync_with_stdio(false); cin.tie(0);
#ifdef LOCAL
#define db(x) cerr << #x << "=" << x << "\n"
#define db2(x, y) cerr << #x << "=" << x << " , " << #y << "=" << y << "\n"
#define db3(a,b,c) cerr<<#a<<"="<<a<<","<<#b<<"="<<b<<","<<#c<<"="<<c<<"\n"
#define dbv(v) cerr << #v << ":"; for (auto ite : v) cerr << ite << ' '; cerr <<"\n"
#define dbvp(v) cerr << #v << ":"; for (auto ite : v) cerr << "{" << ite.f << ',' << ite.s << "} "; cerr << "\n"
#define dba(a,ss,ee) cerr << #a << ":"; FOR(ite,ss,ee) cerr << a[ite] << ' '; cerr << "\n"
#define reach cerr << "LINE: " << __LINE__ << "\n";
#else
#define reach
#define db(x)
#define db2(x,y)
#define db3(a,b,c)
#define dbv(v)
#define dbvp(v)
#define dba(a,ss,ee)
#endif
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define pb push_back
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define f first
#define s second
#define g0(x) get<0>(x)
#define g1(x) get<1>(x)
#define g2(x) get<2>(x)
#define g3(x) get<3>(x)
typedef pair <int, int> pi;
typedef tuple<int,int,int> ti3;
typedef tuple<int,int,int,int> ti4;
int rand(int a, int b) { return a + rng() % (b-a+1); }
const int MOD = 1e9 + 7;
const int inf = (int)1e9 + 500;
const long long oo = (long long)1e18 + 500;
template <typename T> bool chmax(T& a, const T b) { return a<b ? a = b, 1 : 0; }
template <typename T> bool chmin(T& a, const T b) { return a>b ? a = b, 1 : 0; }
const int MAXN = 200005;
int n,m;
struct edge{
int a,b,c,p;
};
edge E[MAXN];
vector<pi> V[MAXN];
map<int,int> dist[MAXN][2];
map<int,vector<pi>> T[MAXN];
map<int,int> S[MAXN];
struct state {
int node;
bool a;// should this be the one left??
int color; // what colour is the edge that came in?
bool operator<(const state& o) const { return node < o.node; }
};
typedef pair<int,state> pis ;
int32_t main()
{
IAMSPEED
cin >> n >> m;
FOR(i,1,m) {
cin >> E[i].a >> E[i].b >> E[i].c >> E[i].p;
V[E[i].a].pb({E[i].b,i});
V[E[i].b].pb({E[i].a,i});
}
FOR(i,1,n) {
for(auto v:V[i]){
S[i][E[v.s].c]+=E[v.s].p;
T[i][E[v.s].c].pb(v);
}
}
std::priority_queue<pis,vector<pis>,greater<pis>> pq;
dist[1][0][0]=0;
dist[1][1][0]=0;
pq.push(make_pair(0, state({1, 0, 0})));
pq.push(make_pair(0, state({1, 1, 0})));
while(pq.size()) { // color is jsut the color you CAME INTO THE NODE with
pis c=pq.top(); pq.pop();
state ss=c.s;
int d=c.f;
int node=ss.node, z=ss.a;
int color=ss.color;
if(dist[node][z][color] != d)continue;
if(z){
if(T[node][color].size()<=1)continue;
for(auto v:T[node][color]){ // adj list of this color
if(v.f == node)continue;
int sum=S[node][E[v.s].c]; // take everything
int nx=v.f;
int nd=d + sum - E[v.s].p; // sum - Px (-Pparent is already done at previous node)
auto it=dist[nx][0].find(color);
if(it == dist[nx][0].end() || it->s>nd) {
if(it!=dist[nx][0].end())it->s=nd;
else dist[nx][0][color]=nd;
pq.push(make_pair(nd, state({nx, 0, color}))); // don't make the other node choose everything
}
}
} else {
for(auto v:V[node]) {
int nx=v.f;
int nd=d;
int thiscolor=E[v.s].c;
bool changed=0;
if(T[node][thiscolor].size()>1) {
nd += E[v.s].p;
changed=1;
}
auto it1=dist[nx][0].find(thiscolor);
if(it1 == dist[nx][0].end() || it1->s>min(nd, d + S[node][E[v.s].c] - E[v.s].p)) {
if(it1!=dist[nx][0].end()) it1->s=min(nd, d + S[node][E[v.s].c] - E[v.s].p);
else dist[nx][0][thiscolor]=min(nd, d + S[node][E[v.s].c] - E[v.s].p);
pq.push(make_pair(min(nd, d + S[node][E[v.s].c] - E[v.s].p), state({nx, 0, thiscolor}))); // don't make the other node choose everything
}
if(changed){
auto it2=dist[nx][1].find(thiscolor);
if(it2 == dist[nx][1].end() || it2->s>nd-E[v.s].p) {
if(it2!=dist[nx][1].end())it2->s=nd-E[v.s].p;
else dist[nx][1][thiscolor]=nd-E[v.s].p;
pq.push(make_pair(nd-E[v.s].p, state({nx, 1, thiscolor})));//yes you must choose everything to get this compensation
}
}
}
}
}
int ans = oo;
for(auto i:dist[n][0]) {
chmin(ans, i.s);
}
if(ans==oo)cout<<-1;
else cout << ans;
}
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