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>
#define err(args...) {}
#ifdef DEBUG
#include "_debug.cpp"
#endif
using namespace std;
using ll = long long;
using ld = long double;
template <typename T> using lim = numeric_limits<T>;
template <typename T> istream& operator>>(istream& is, vector<T>& a) { for(T& x : a) { is >> x; } return is; }
template <typename X, typename Y> istream& operator>>(istream& is, pair<X, Y>& p) { return is >> p.first >> p.second; }
template <typename T> struct wedge {
int u, v; T w;
wedge reverse() const { return {v, u, w}; }
friend ostream& operator<<(ostream& os, const wedge& e) {
return os << "{u: " << e.u << ", v: " << e.v << ", w: " << e.w << "}";
}
};
template <bool Directed, typename TEdge, bool Index> struct graph {
using EType = TEdge;
vector<TEdge> edges;
vector<vector<int>> adj;
graph(int n) : adj(n + Index) {}
graph(int n, int m) : graph(n) { edges.reserve(m << not Directed); }
TEdge& operator()(int e) { return edges[e]; }
vector<int>& operator[](int u) { return adj[u]; }
int size() { return adj.size() - Index; }
void append(int u, const TEdge& e) {
adj[u].push_back(edges.size());
edges.push_back(e);
}
void add_edge(const TEdge& e) {
append(e.u, e);
if(not Directed) append(e.v, e.reverse());
}
};
template <bool Directed, typename T, bool Index>
pair<vector<T>, vector<int>> sssp(graph<Directed, wedge<T>, Index>& g, const vector<int>& s) {
vector<int> vis(g.adj.size()), p(g.adj.size(), -1);
vector<T> d(g.adj.size(), lim<T>::max());
priority_queue<pair<T, int>> pq;
for(int u : s) {
pq.push({d[u] = 0, u});
}
while(not pq.empty()) {
int u = pq.top().second; pq.pop();
if(not vis[u]) {
vis[u] = true;
for(int e : g[u]) {
if(not vis[g(e).v] and d[g(e).v] > d[u] + g(e).w) {
pq.push({-(d[g(e).v] = d[u] + g(e).w), g(p[g(e).v] = e).v});
}
}
}
}
return {move(d), move(p)};
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m;
cin >> n >> m;
graph<0, wedge<ll>, 1> g(n, m);
for(int i = 0; i < m; i++) {
int u, v, w;
cin >> u >> v >> w;
g.add_edge({u, v, w});
}
ll max_replace = 0;
ll ans = sssp(g, {1}).first[n];
for(int i = m - 1; i >= 0; i--) {
g.edges[2 * i].w += max_replace;
g.edges[2 * i + 1].w += max_replace;
ans = max(ans, sssp(g, {1}).first[n]);
g.edges[2 * i].w -= max_replace;
g.edges[2 * i + 1].w -= max_replace;
max_replace = max(max_replace, g.edges[2 * i].w);
}
cout << ans << endl;
return 0;
}
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