#include <iostream>
#include <algorithm>
#include <utility>
#include <vector>
#include <stack>
#include <map>
#include <queue>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <cstring>
#include <cmath>
#include <functional>
#include <cassert>
#include <iomanip>
#include <numeric>
#include <bitset>
#include <sstream>
#include <chrono>
#include <random>
#define ff first
#define ss second
#define PB push_back
#define sz(x) int(x.size())
#define rsz resize
#define fch(xxx, yyy) for (auto xxx : yyy) // abusive notation
#define all(x) (x).begin(),(x).end()
#define eps 1e-9
// more abusive notation (use at your own risk):
// #define int ll
using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;
// debugging
void __print(int x) {std::cerr << x;}
void __print(ll x) {std::cerr << x;} /* remember to uncomment this when not using THE MACRO */
void __print(unsigned x) {std::cerr << x;}
void __print(ull x) {std::cerr << x;}
void __print(float x) {std::cerr << x;}
void __print(double x) {std::cerr << x;}
void __print(ld x) {std::cerr << x;}
void __print(char x) {std::cerr << '\'' << x << '\'';}
void __print(const char *x) {std::cerr << '\"' << x << '\"';}
void __print(const string& x) {std::cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V> void __print(const pair<T, V> &x) {std::cerr << '{'; __print(x.ff); std::cerr << ", "; __print(x.ss); std::cerr << '}';}
template<typename T> void __print(const T& x) {int f = 0; std::cerr << '{'; for (auto &i: x) std::cerr << (f++ ? ", " : ""), __print(i); std::cerr << "}";}
void _print() {std::cerr << "]\n";}
template <typename T, typename... V> void _print(T t, V... v) {__print(t); if (sizeof...(v)) std::cerr << ", "; _print(v...);}
void println() {std::cerr << ">--------------------<" << endl;}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
// templates
template <class T> bool ckmin(T &a, const T &b) {return b<a ? a = b, 1 : 0;}
template <class T> bool ckmax(T &a, const T &b) {return b>a ? a = b, 1 : 0;}
template <class T> using gr = greater<T>;
template <class T> using vc = vector<T>;
template <class T> using p_q = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vc<T>, gr<T>>;
template <class T1, class T2> using pr = pair<T1, T2>;
mt19937_64 rng_ll(chrono::steady_clock::now().time_since_epoch().count());
int rng(int M) {return (int)(rng_ll()%M);} /*returns any random number in [0, M) */
// const variables
constexpr int INF = (int)2e9;
constexpr int MOD = 998244353;
constexpr long double EPS = (ld)1e-11, PI = 3.1415926535;
constexpr ll LL_INF = (ll)3e18;
constexpr int mod = (int)1e9 + 7;
constexpr ll inverse = 500000004LL; // inverse of 2 modulo 1e9 + 7
void setIO(const string& str) {// fast input/output
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
if (str.empty()) return;
freopen((str + ".in").c_str(), "r", stdin);
freopen((str + ".out").c_str(), "w", stdout);
}
int N, M;
vc<vc<pii>> adj;
vc<map<int, vc<pii>>> adj_;
vc<map<int, ll>> sum;
vi C, P;
vll pd;
vc<map<int, ll>> dp;
signed main() { // TIME YOURSELF !!!
setIO("");
cin >> N >> M;
adj.rsz(N+1), pd.rsz(N+1, LL_INF), dp.rsz(N+1), sum.rsz(N+1), adj_.rsz(N+1);
for (int i = 0; i < M; ++i) {
int a, b, c, p;
cin >> a >> b >> c >> p;
adj[a].PB({b, i});
adj[b].PB({a, i});
adj_[a][c].PB({b, i});
adj_[b][c].PB({a, i});
sum[a][c] += p;
sum[b][c] += p;
P.PB(p);
C.PB(c);
}
pqg<pr<ll, pii>> pq;
pd[1] = 0;
pq.push({pd[1], {1, -1}});
while (!pq.empty()) {
pii state = pq.top().ss;
ll d = pq.top().ff;
pq.pop();
if (state.ss == -1 && d != pd[state.ff]) continue;
if (state.ss != -1 && d != dp[state.ff][state.ss]) continue;
if (state.ss == -1) {
fch(to, adj[state.ff]) {
int u = to.ff;
int c = C[to.ss];
ll p_w = P[to.ss], c_w = sum[state.ff][c] - p_w;
// if (state.ss == -1) {
if (ckmin(pd[u], pd[state.ff] + min(p_w, c_w))) {
pq.push({pd[u], {u, -1}});
}
if (dp[u].count(c) == 0 || dp[u][c] > pd[state.ff]) { // either it doesn't exist, or it is too large
dp[u][c] = pd[state.ff];
pq.push({dp[u][c], {u, c}});
}
// }
// else {
// if (c != state.ss) continue; // this will cause TLE because we will continually go through the vertices over and over again
// if (ckmin(pd[u], dp[state.ff][state.ss] + c_w)) {
// pq.push({pd[u], {u, -1}});
// }
// }
}
} else {
fch(to, adj_[state.ff][state.ss]) {
int u = to.ff;
int c = C[to.ss];
ll p_w = P[to.ss], c_w = sum[state.ff][c] - p_w;
if (ckmin(pd[u], dp[state.ff][state.ss] + c_w)) {
pq.push({pd[u], {u, -1}});
}
}
}
}
cout << (pd[N] == LL_INF ? -1 : pd[N]);
return 0;
}
// TLE -> TRY NOT USING DEFINE INT LONG LONG
// CE -> CHECK LINE 45
// 5000 * 5000 size matrices are kinda big (potential mle)
// Do something, start simpler
컴파일 시 표준 에러 (stderr) 메시지
Main.cpp: In function 'void setIO(const string&)':
Main.cpp:89:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
89 | freopen((str + ".in").c_str(), "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:90:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
90 | freopen((str + ".out").c_str(), "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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