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 <iostream>
#include <bits/stdc++.h>
#define MaxN 100000
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pii;
const ll INF = 1e15 + 7;
int n, m, s, t, U, V;
ll DistST[MaxN+5], RevDistST[MaxN+5], DistUV[MaxN+5][2];
vector<pii> g[MaxN+5];
struct PQNode {
ll d;
int used, u;
bool operator > (const PQNode& other) const {
return (d > other.d);
}
};
void ReadData() {
int u, v;
ll w;
for (int i=1; i<=m; i++) {
cin >> u >> v >> w;
g[u].push_back(pii(v, w));
g[v].push_back(pii(u, w));
}
}
void Init() {
for (int i=1; i<=n; i++)
DistST[i] = RevDistST[i] = DistUV[i][0] = DistUV[i][1] = INF;
}
void DijkstraST(int src, ll dist[MaxN+5]) {
priority_queue<pii, vector<pii>, greater<pii>> pq;
dist[src] = 0;
pq.push(pii(dist[src], src));
while (!pq.empty()) {
pii tmp = pq.top();
pq.pop();
ll d = tmp.first;
int u = tmp.second;
if (d > dist[u])
continue;
for (pii tmpe: g[u]) {
int v = tmpe.first;
ll w = tmpe.second;
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
pq.push(pii(dist[v], v));
}
}
}
}
bool IsInST(int u, int v, ll w) {
return ((DistST[u] + w + RevDistST[v]) == DistST[t]);
}
void DijkstraUV(int src) {
priority_queue<PQNode, vector<PQNode>, greater<PQNode>> pq;
DistUV[src][0] = DistUV[src][1] = 0;
pq.push({DistUV[src][0], 0, src});
pq.push({DistUV[src][1], 1, src});
while (!pq.empty()) {
PQNode tmp = pq.top();
pq.pop();
ll d = tmp.d;
int used = tmp.used, u = tmp.u;
if (d > DistUV[u][used])
continue;
for (pii tmpe: g[u]) {
int v = tmpe.first;
ll w = tmpe.second;
if (used == 0) {
if (IsInST(u, v, w)) {
if (DistUV[v][1] > DistUV[u][0]) {
DistUV[v][1] = DistUV[u][0];
pq.push({DistUV[v][1], 1, v});
}
}
else {
if (DistUV[v][0] > DistUV[u][0] + w) {
DistUV[v][0] = DistUV[u][0] + w;
pq.push({DistUV[v][0], 0, v});
}
}
}
else {
if (IsInST(u, v, w)) {
if (DistUV[v][1] > DistUV[u][1]) {
DistUV[v][1] = DistUV[u][1];
pq.push({DistUV[v][1], 1, v});
}
}
else {
if (DistUV[v][0] > DistUV[u][1] + w) {
DistUV[v][0] = DistUV[u][1] + w;
pq.push({DistUV[v][0], 0, v});
}
}
}
}
}
}
ll Solution() {
Init();
DijkstraST(s, DistST);
DijkstraST(t, RevDistST);
DijkstraUV(U);
ll ans = min(DistUV[V][0], DistUV[V][1]);
return ans;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m >> s >> t >> U >> V;
ReadData();
cout << Solution();
return 0;
}
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