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;
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, m, t, l;
cin >> n >> m >> t >> l;
vector<vector<pair<int, int>>> g(n);
for (int i = 0; i < m; i++) {
int x, y, z;
cin >> x >> y >> z;
--x; --y;
g[x].emplace_back(y, z);
g[y].emplace_back(x, z);
}
vector<int> seq(l);
for (int i = 0; i < l; i++) {
cin >> seq[i];
--seq[i];
}
{
int p, x;
cin >> p >> x;
--p; --x;
seq[p] = x;
}
vector<int> deg(n);
for (int i = 0; i < n; i++) {
deg[i] = (int) g[i].size();
}
vector<vector<int>> idx(n, vector<int>(n));
for (int i = 0; i < n; i++) {
for (int j = 0; j < deg[i]; j++) {
idx[i][g[i][j].first] = j;
}
}
const long long inf = (long long) 1e18;
vector<vector<vector<vector<long long>>>> dist(n, vector<vector<vector<long long>>>(n));
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
if (i == j) {
continue;
}
dist[i][j].resize(deg[i]);
for (int k = 0; k < deg[i]; k++) {
dist[i][j][k] = vector<long long>(deg[j], inf);
}
}
}
vector<vector<long long>> d(n);
for (int i = 0; i < n; i++) {
d[i].resize(deg[i]);
}
vector<int> ia(n), ib(n);
set<tuple<long long, int, int>> st;
for (int ver = 0; ver < n; ver++) {
for (int e = 0; e < deg[ver]; e++) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < deg[i]; j++) {
d[i][j] = inf;
}
ia[i] = -1;
ib[i] = -1;
}
int to = g[ver][e].first;
int w = g[ver][e].second;
d[to][idx[to][ver]] = w;
st.clear();
st.emplace(d[to][idx[to][ver]], to, idx[to][ver]);
ia[to] = idx[to][ver];
auto Update = [&](int x, int y, long long z) {
if (ia[x] == y || ib[x] == y) {
st.erase(st.find({d[x][y], x, y}));
}
d[x][y] = z;
if (ia[x] == y) {
return;
}
if (ib[x] == y) {
if (d[x][y] < d[x][ia[x]]) {
swap(ia[x], ib[x]);
}
return;
}
if (ia[x] == -1) {
ia[x] = y;
st.emplace(d[x][y], x, y);
return;
}
if (ib[x] == -1) {
if (d[x][y] < d[x][ia[x]]) {
swap(ia[x], ib[x]);
ia[x] = y;
} else {
ib[x] = y;
}
st.emplace(d[x][y], x, y);
return;
}
if (d[x][y] >= d[x][ia[x]] && d[x][y] < d[x][ib[x]]) {
st.erase(st.find({d[x][ib[x]], x, ib[x]}));
ib[x] = y;
st.emplace(d[x][y], x, y);
return;
}
if (d[x][y] < d[x][ia[x]]) {
st.erase(st.find({d[x][ib[x]], x, ib[x]}));
swap(ia[x], ib[x]);
ia[x] = y;
st.emplace(d[x][y], x, y);
}
};
while (!st.empty()) {
auto it = st.begin();
int v = get<1>(*it);
int lst = get<2>(*it);
st.erase(it);
for (int i = 0; i < deg[v]; i++) {
if (i == lst) {
continue;
}
int to = g[v][i].first;
int w = g[v][i].second;
if (d[to][idx[to][v]] > d[v][lst] + w) {
Update(to, idx[to][v], d[v][lst] + w);
assert((int) st.size() <= 2 * n);
}
}
}
for (int i = ver + 1; i < n; i++) {
if (i == ver) {
continue;
}
for (int j = 0; j < deg[i]; j++) {
dist[ver][i][e][j] = d[i][j];
}
}
}
}
vector<vector<vector<vector<int>>>> good(n, vector<vector<vector<int>>>(n));
for (int from = 0; from < n; from++) {
for (int to = 0; to < n; to++) {
if (from == to) {
continue;
}
good[from][to].resize(deg[from]);
for (int i = 0; i < deg[from]; i++) {
if (from < to) {
int x = -1, y = -1;
for (int j = 0; j < deg[to]; j++) {
if (x == -1 || dist[from][to][i][j] < dist[from][to][i][x]) {
y = x;
x = j;
} else if (y == -1 || dist[from][to][i][j] < dist[from][to][i][y]) {
y = j;
}
}
if (x != -1) {
good[from][to][i].push_back(x);
}
if (y != -1) {
good[from][to][i].push_back(y);
}
} else {
int x = -1, y = -1;
for (int j = 0; j < deg[to]; j++) {
if (x == -1 || dist[to][from][j][i] < dist[to][from][x][i]) {
y = x;
x = j;
} else if (y == -1 || dist[to][from][j][i] < dist[to][from][y][i]) {
y = j;
}
}
if (x != -1) {
good[from][to][i].push_back(x);
}
if (y != -1) {
good[from][to][i].push_back(y);
}
}
}
}
}
vector<long long> dp(n, inf);
for (int i = 0; i < deg[seq[0]]; i++) {
for (int j = 0; j < deg[seq[1]]; j++) {
if (seq[0] <= seq[1]) {
dp[j] = min(dp[j], dist[seq[0]][seq[1]][i][j]);
} else {
dp[j] = min(dp[j], dist[seq[1]][seq[0]][j][i]);
}
}
}
vector<long long> new_dp(n);
vector<long long> val(n);
for (int p = 2; p < l; p++) {
for (int i = 0; i < deg[seq[p]]; i++) {
new_dp[i] = inf;
}
for (int i = 0; i < deg[seq[p - 1]]; i++) {
val[i] = inf;
}
{
long long mn = inf;
for (int i = 0; i < deg[seq[p - 1]]; i++) {
val[i] = min(val[i], mn);
mn = min(mn, dp[i]);
}
}
{
long long mn = inf;
for (int i = deg[seq[p - 1]] - 1; i >= 0; i--) {
val[i] = min(val[i], mn);
mn = min(mn, dp[i]);
}
}
for (int i = 0; i < deg[seq[p - 1]]; i++) {
if (val[i] != inf) {
for (int j : good[seq[p - 1]][seq[p]][i]) {
if (seq[p - 1] <= seq[p]) {
new_dp[j] = min(new_dp[j], val[i] + dist[seq[p - 1]][seq[p]][i][j]);
} else {
new_dp[j] = min(new_dp[j], val[i] + dist[seq[p]][seq[p - 1]][j][i]);
}
}
}
}
for (int i = 0; i < deg[seq[p]]; i++) {
dp[i] = new_dp[i];
}
}
long long res = inf;
for (int i = 0; i < deg[seq.back()]; i++) {
res = min(res, dp[i]);
}
cout << (res == inf ? -1 : res) << '\n';
return 0;
}
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