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 pii pair<int,int>
#define fi first
#define se second
const int N = 1e5 + 5;
const int inf = 1e18;
int dist[N],n,m,d[N];
vector<int>g[N],cost[N],adj[N];
void bfs(int s) {
for (int i = 1; i <= n; i++) d[i] = inf;
queue<int>q;
q.push(s);
d[s] = 0;
while (!q.empty()) {
int u = q.front();
q.pop();
for (auto v: adj[u]) {
if (d[v] != inf) continue;
d[v] = d[u] + 1;
q.push(v);
}
}
}
void dijkstra(int s) {
priority_queue<pii,vector<pii>,greater<pii>>q;
for (int i = 1; i <= n; i++) dist[i] = inf;
q.push({0,s});
dist[s] = 0;
while (!q.empty()) {
int u = q.top().se,c = q.top().fi;
q.pop();
if (dist[u] != c) continue;
//minimum path match with maximum cost
for (int i = 0; i < (int)g[u].size(); i++) {
int v = g[u][i],c = cost[u][i];
if (dist[v] > dist[u] + c) {
dist[v] = dist[u] + c;
q.push({dist[v],v});
}
}
}
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n >> m;
for (int i = 1; i <= m; i++) {
int u,v,c;
cin >> u >> v >> c;
g[u].push_back(v);
adj[v].push_back(u);
cost[u].push_back(c);
}
for (int i = 1; i <= n; i++)
sort(cost[i].begin(),cost[i].end(),greater<int>());
bfs(n);
for (int i = 1; i <= n; i++) {
sort(g[i].begin(),g[i].end(),[&](int &a,int &b) {
return d[a] < d[b];
});
}
dijkstra(1);
cout << dist[n] << "\n";
}
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