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#include <bits/stdc++.h> using namespace std; mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count()); const long long INF = 1e18; template <class t1, class t2> bool cmin(t1 &a, const t2 &b) { if (a > b) { a = b; return true; } return false; } template <class t1, class t2> bool cmax(t1 &a, const t2 &b) { if (a < b) { a = b; return true; } return false; } void UseFiles(const string &s) { freopen((s + ".in").c_str(), "r", stdin); freopen((s + ".out").c_str(), "w", stdout); } void run(); signed main() { iostream::sync_with_stdio(0); cin.tie(0); cout.tie(0); run(); } struct dsu { vector<long long> l, h; dsu(long long n) : l(n), h(n, 1) { iota(l.begin(), l.end(), 0); } long long get_root(long long v) { if (l[v] == v) { return v; } return l[v] = get_root(l[v]); } bool Union(long long u, long long v) { u = get_root(u); v = get_root(v); if (u == v) { return false; } if (h[u] > h[v]) { swap(u, v); } l[u] = v; if (h[u] == h[v]) { ++h[v]; } return true; } }; long long n; vector<vector<pair<long long, long long>>> g; vector<long long> color, dst; vector<tuple<long long, long long, long long>> dijkstra(long long k) { priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> q; for (long long i = 0; i < k; ++i) { color[i] = i; dst[i] = 0; q.push({0, i}); } while (((long long)(q).size())) { auto [d, v] = q.top(); q.pop(); if (dst[v] != d) { continue; } for (auto &[u, w] : g[v]) { if (cmin(dst[u], d + w)) { color[u] = color[v]; q.push({dst[u], u}); } } } map<pair<long long, long long>, long long> m; for (long long i = 0; i < n; ++i) { for (auto &[v, w] : g[i]) { if (color[v] > color[i]) { if (m.count({color[i], color[v]})) { cmin(m[{color[i], color[v]}], dst[i] + dst[v] + w); } else { m[{color[i], color[v]}] = dst[i] + dst[v] + w; } } } } vector<tuple<long long, long long, long long>> edges; for (auto &[x, y] : m) { edges.push_back({y, x.first, x.second}); } sort(edges.begin(), edges.end()); return edges; } const long long maxlg = 20; vector<vector<pair<long long, long long>>> tree; vector<vector<long long>> up, mup; vector<long long> d; void dfs(long long v, long long p = -1, long long pw = 0, long long cur_d = 0) { d[v] = cur_d; mup[v][0] = pw; up[v][0] = p; if (p == -1) { up[v][0] = v; } for (long long i = 1; i < maxlg; ++i) { up[v][i] = up[up[v][i - 1]][i - 1]; mup[v][i] = max(mup[v][i - 1], mup[up[v][i - 1]][i - 1]); } for (auto &[u, w] : tree[v]) { if (u == p) { continue; } dfs(u, v, w, cur_d + 1); } } long long lca(long long u, long long v) { if (d[u] < d[v]) { swap(u, v); } long long ans = 0; for (long long i = maxlg - 1; i >= 0; --i) { if (d[up[u][i]] >= d[v]) { cmax(ans, mup[u][i]); u = up[u][i]; } } if (u == v) { return ans; } for (long long i = maxlg - 1; i >= 0; --i) { if (up[u][i] != up[v][i]) { cmax(ans, mup[u][i]); cmax(ans, mup[v][i]); u = up[u][i]; v = up[v][i]; } } cmax(ans, mup[v][0]); cmax(ans, mup[u][0]); return ans; } void run() { long long m, k, q; cin >> n >> m >> k >> q; g.resize(n); color.resize(n, -1); dst.resize(n, INF); for (long long i = 0; i < m; ++i) { long long u, v, w; cin >> u >> v >> w; --u, --v; g[u].push_back({v, w}); g[v].push_back({u, w}); } vector<tuple<long long, long long, long long>> edges = dijkstra(k); tree.resize(k); up.resize(k, vector<long long>(maxlg, -1)); mup.resize(k, vector<long long>(maxlg, -1)); d.resize(k, -1); dsu D(k); for (auto &[w, u, v] : edges) { if (D.Union(u, v)) { tree[u].push_back({v, w}); tree[v].push_back({u, w}); } } dfs(0); for (long long i = 0; i < q; ++i) { long long u, v; cin >> u >> v; --u, --v; cout << lca(u, v) << " "; } cout << endl; }
#include <bits/stdc++.h> using namespace std; long long n, m, x, y, k, q, z, dist[100020], ans[300005], p[100005], src[100020]; vector<pair<long long, long long>> adj[100005]; set<long long> s[100020]; vector<pair<long long, pair<long long, long long>>> edges; void dijkstra() { priority_queue<pair<long long, pair<long long, long long>>, vector<pair<long long, pair<long long, long long>>>, greater<pair<long long, pair<long long, long long>>>> pq; for (int i = 1; i <= k; ++i) pq.push({0, {i, i}}); for (int i = 1; i <= n; ++i) dist[i] = 1e16; while (pq.size()) { int u = pq.top().second.first, sorc = pq.top().second.second; long long w = pq.top().first; pq.pop(); if (dist[u] < w) continue; dist[u] = w, src[u] = sorc; for (auto i : adj[u]) { if (dist[u] + i.second >= dist[i.first]) continue; pq.push({dist[u] + i.second, {i.first, sorc}}); } } } int fnd(int i) { if (p[i] == i) return i; return p[i] = fnd(p[i]); } void uni(int i, int j, long long w) { i = fnd(i), j = fnd(j); if (i == j) return; ; if (s[i].size() > s[j].size()) swap(i, j); p[i] = j; for (auto u : s[i]) { if (s[j].count(u)) s[j].erase(u), ans[u] = w; else s[j].insert(u); } s[i].clear(); } int main() { ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> n >> m >> k >> q; for (int i = 0; i < m; ++i) cin >> x >> y >> z, adj[x].push_back({y, z}), adj[y].push_back({x, z}); dijkstra(); for (int i = 1; i <= n; p[i] = i, ++i) for (auto j : adj[i]) if (src[i] != src[j.first]) edges.push_back( {dist[i] + dist[j.first] + j.second, {src[i], src[j.first]}}); for (int i = 0; i < q; ++i) cin >> x >> y, s[x].insert(i), s[y].insert(i); sort(edges.begin(), edges.end()); for (auto i : edges) uni(i.second.first, i.second.second, i.first); for (int i = 0; i < q; ++i) cout << ans[i] << endl; }
#include <bits/stdc++.h> #pragma GCC target("avx2") #pragma GCC optimization("O3") #pragma GCC optimization("unroll-loops") const long long INF = 0x3f3f3f3f3f3f3f3f; const long long llinf = (1LL << 62); const int inf = (1 << 30); const int nmax = 3e5 + 50; const long long mod = 1e9 + 7; using namespace std; int n, m, k, q, i, x, y, sz[nmax], p[nmax], ex[nmax], ey[nmax]; long long w, ew[nmax], d[nmax], rs[nmax]; vector<pair<int, int> > qr[nmax], tmp; vector<pair<int, long long> > a[nmax]; vector<pair<long long, pair<int, int> > > vc; set<pair<long long, int> > s; vector<int> v[nmax]; map<int, bool> mp[nmax]; int fnd(int x) { if (p[x] == x) return x; return p[x] = fnd(p[x]); } void uni(int x, int y, long long w) { x = fnd(x), y = fnd(y); if (sz[x] < sz[y]) swap(x, y); int u; for (int i = 0; i < (int)v[y].size(); i++) { u = v[y][i]; tmp.clear(); for (int j = 0; j < (int)qr[u].size(); j++) { if (mp[x][qr[u][j].first]) rs[qr[u][j].second] = w; else tmp.push_back(qr[u][j]); } qr[u] = tmp; mp[x][u] = 1; v[x].push_back(u); } v[y].clear(); mp[y].clear(); sz[x] += sz[y]; p[y] = x; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cerr.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (i = 1; i <= m; i++) { cin >> ex[i] >> ey[i] >> ew[i]; a[ex[i]].push_back(make_pair(ey[i], ew[i])); a[ey[i]].push_back(make_pair(ex[i], ew[i])); } for (i = k + 1; i <= n; i++) d[i] = llinf; for (i = 1; i <= k; i++) s.insert(make_pair(d[i], i)); while (!s.empty()) { x = s.begin()->second; s.erase(s.begin()); for (i = 0; i < (int)a[x].size(); i++) { y = a[x][i].first, w = a[x][i].second; if (d[y] > d[x] + w) { if (d[y] != llinf) s.erase(s.find(make_pair(d[y], y))); d[y] = d[x] + w; s.insert(make_pair(d[y], y)); } } } for (i = 1; i <= m; i++) { vc.push_back( make_pair(d[ex[i]] + d[ey[i]] + ew[i], make_pair(ex[i], ey[i]))); } sort(vc.begin(), vc.end()); for (i = 1; i <= q; i++) { cin >> x >> y; qr[x].push_back(make_pair(y, i)); qr[y].push_back(make_pair(x, i)); } for (i = 1; i <= n; i++) { sz[i] = 1; p[i] = i; v[i].push_back(i); mp[i][i] = 1; } for (i = 0; i < m; i++) { x = vc[i].second.first, y = vc[i].second.second, w = vc[i].first; if (fnd(x) == fnd(y)) continue; uni(x, y, w); } for (i = 1; i <= q; i++) cout << rs[i] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100005; int n, m, k, Q, used[N], p[N]; vector<int> s[N]; long long d[N], ans[N * 3]; vector<pair<int, long long>> g[N]; map<pair<int, int>, vector<int>> ind; vector<int> query[N]; priority_queue<pair<long long, int>> q; vector<pair<long long, pair<int, int>>> add; void dsu(int a, int b, long long x) { a = p[a]; b = p[b]; if (a == b) return; if (s[a].size() < s[b].size()) swap(a, b); while (!s[b].empty()) { p[s[b].back()] = a; s[a].push_back(s[b].back()); for (int i = 0; i < query[s[b].back()].size(); i++) { int to = query[s[b].back()][i]; if (p[to] == a) { vector<int> &c = ind[make_pair(s[b].back(), to)]; while (!c.empty()) { if (ans[c.back()] == 0) ans[c.back()] = x; c.pop_back(); } } } s[b].pop_back(); } } int main() { cin >> n >> m >> k >> Q; while (m--) { int a, b; long long w; scanf("%d%d%lld", &a, &b, &w); g[a].push_back(make_pair(b, w)); g[b].push_back(make_pair(a, w)); } for (int i = 1; i <= Q; i++) { int a, b; scanf("%d%d", &a, &b); query[a].push_back(b); query[b].push_back(a); ind[make_pair(a, b)].push_back(i); ind[make_pair(b, a)].push_back(i); } for (int i = 1; i <= n; i++) d[i] = 1000000007ll * 1000000007ll; for (int i = 1; i <= k; i++) { d[i] = 0; q.push(make_pair(-d[i], i)); } while (!q.empty()) { int v = -1; do { v = q.top().second; q.pop(); } while (used[v] && !q.empty()); if (used[v] || v == -1) break; used[v] = 1; for (int i = 0; i < g[v].size(); i++) { int to = g[v][i].first; long long w = g[v][i].second; if (d[v] + w < d[to]) { d[to] = d[v] + w; q.push(make_pair(-d[to], to)); } } } for (int v = 1; v <= n; v++) { p[v] = v; s[v].push_back(v); for (int i = 0; i < g[v].size(); i++) { int to = g[v][i].first; long long w = g[v][i].second; if (to > v) add.push_back(make_pair(w + d[v] + d[to], make_pair(to, v))); } } sort(add.begin(), add.end()); for (int i = 0; i < add.size(); i++) dsu(add[i].second.first, add[i].second.second, add[i].first); for (int i = 1; i <= Q; i++) printf("%lld\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 3e5 + 5; const long long INF = 1e18; struct Edge { int u, v, nxt; long long w; } edge[maxn << 1], n_edge[maxn << 1]; int fa[maxn][30]; long long mcost[maxn][30]; int depth[maxn]; struct EdgeInfo { int u, v; long long w; bool operator<(const EdgeInfo &rhs) const { return w < rhs.w; } } ee[maxn], new_e[maxn]; int n, m, k, q; int head[maxn], nhead[maxn], cnt = -1, ncnt = -1, new_e_info_cnt; bool vis[maxn]; long long dis[maxn]; int belong[maxn], lg[maxn]; inline void init() { for (int i = 0; i <= n; ++i) { head[i] = nhead[i] = -1; vis[i] = false; belong[i] = -1; } for (int i = 1; i < maxn; ++i) lg[i] = lg[i - 1] + (1 << lg[i - 1] == i); } inline void addedge(int u, int v, long long w) { edge[++cnt] = {u, v, head[u], w}; head[u] = cnt; } inline void addn_edge(int u, int v, long long w) { n_edge[++ncnt] = {u, v, nhead[u], w}; nhead[u] = ncnt; } struct DSU { int pre[maxn]; DSU() { for (int i = 0; i < maxn; ++i) pre[i] = i; } int Findpre(int x) { return x == pre[x] ? x : pre[x] = Findpre(pre[x]); } bool Union(int x, int y) { int fx = Findpre(x); int fy = Findpre(y); if (fx != fy) { pre[fy] = fx; return true; } return false; } }; inline void Dijiastra() { struct Node { int u; long long dis; int from_p; bool operator<(const Node &rhs) const { return dis > rhs.dis; } }; priority_queue<Node> pq; for (int i = 0; i <= n; ++i) { dis[i] = INF; vis[i] = false; belong[i] = i; if (i <= k && i >= 1) { dis[i] = 0; pq.push(Node{i, dis[i], i}); } } while (!pq.empty()) { Node u = pq.top(); pq.pop(); if (vis[u.u]) continue; vis[u.u] = true; for (int i = head[u.u]; ~i; i = edge[i].nxt) { Edge &e = edge[i]; if (dis[e.v] > dis[u.u] + e.w) { dis[e.v] = dis[u.u] + e.w; belong[e.v] = u.from_p; pq.push(Node{e.v, dis[e.v], u.from_p}); } } } } void dfs(int u, int f) { fa[u][0] = f; depth[u] = depth[f] + 1; for (int i = 1; (1 << i) <= depth[u]; ++i) { fa[u][i] = fa[fa[u][i - 1]][i - 1]; mcost[u][i] = max(mcost[u][i - 1], mcost[fa[u][i - 1]][i - 1]); } for (int i = nhead[u]; ~i; i = n_edge[i].nxt) { Edge &e = n_edge[i]; if (e.v != f) { mcost[e.v][0] = e.w; dfs(e.v, u); } } } long long LCA(int x, int y) { long long ans = 0; if (depth[x] < depth[y]) swap(x, y); while (depth[x] > depth[y]) { ans = max(ans, mcost[x][lg[depth[x] - depth[y]] - 1]); x = fa[x][lg[depth[x] - depth[y]] - 1]; } if (x == y) return ans; for (int i = lg[depth[x]] - 1; i >= 0; --i) { if (fa[x][i] != fa[y][i]) { ans = max(ans, max(mcost[x][i], mcost[y][i])); x = fa[x][i]; y = fa[y][i]; } } return ans = max(ans, max(mcost[x][0], mcost[y][0])); } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> q; init(); for (int i = 0; i < m; ++i) { int u, v, w; cin >> u >> v >> w; ee[i] = {u, v, w}; addedge(u, v, w); addedge(v, u, w); } Dijiastra(); for (int i = 0; i < m; ++i) { EdgeInfo &e = ee[i]; if (belong[e.u] != belong[e.v]) { new_e[new_e_info_cnt++] = {belong[e.u], belong[e.v], dis[e.u] + dis[e.v] + e.w}; } } sort(new_e, new_e + new_e_info_cnt); DSU dsu; int pp = 0; for (int i = 0; i < new_e_info_cnt; ++i) { EdgeInfo &e = new_e[i]; int fu = dsu.Findpre(e.u); int fv = dsu.Findpre(e.v); if (fu != fv) { addn_edge(e.u, e.v, e.w); addn_edge(e.v, e.u, e.w); dsu.Union(e.u, e.v); ++pp; } if (pp == k - 1) break; } dfs(1, 0); for (int i = 0; i < q; ++i) { int a, b; cin >> a >> b; cout << LCA(a, b) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long inf = 1e16; const int maxn = 1e5 + 10; const int maxm = 3e5 + 10; const int L = 18; int n, m, k, q; vector<pair<int, long long> > e[maxn]; struct Edge { int u, v; long long w; Edge(int _u = 0, int _v = 0, long long _w = 0) { u = _u; v = _v; w = _w; } bool operator<(const Edge &other) const { return w < other.w; } } edge[maxm]; long long dis[maxn]; priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > pq; bool vis[maxn]; int fa[maxn], sz[maxn], dep[maxn], f[maxn][L]; long long g[maxn][L]; inline int read() { int x = 0, f = 1, ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 3) + (x << 1) + (ch - '0'); ch = getchar(); } return f == 1 ? x : -x; } void print(int a[], int n, int st = 0) { for (int i = 0; i < n; i++) { if (i != 0) printf(" "); printf("%d", a[i + st]); } printf("\n"); } void init() { n = read(); m = read(); k = read(); q = read(); for (int i = 1; i <= m; i++) { int u = read(), v = read(), w = read(); e[u].push_back(make_pair(v, w)); e[v].push_back(make_pair(u, w)); } } inline void dijkstra() { for (int i = 1; i <= k; i++) dis[i] = 0, pq.push(make_pair(0, i)); for (int i = k + 1; i <= n; i++) dis[i] = inf; while (!pq.empty()) { int u = pq.top().second; long long d = pq.top().first; pq.pop(); if (vis[u]) continue; vis[u] = true; for (int i = 0; i < e[u].size(); i++) { int v = e[u][i].first; long long w = e[u][i].second; if (d + w < dis[v]) { dis[v] = d + w; pq.push(make_pair(dis[v], v)); } } } } inline int root(int x) { return x == fa[x] ? x : fa[x] = root(fa[x]); } inline void merge(int x, int y) { x = root(x); y = root(y); if (x != y) { if (sz[x] > sz[y]) swap(x, y); sz[y] += sz[x]; fa[x] = y; } } inline void dfs(int u, int pa) { fa[u] = f[u][0] = pa; dep[u] = dep[pa] + 1; for (int i = 0; i < e[u].size(); i++) { int v = e[u][i].first; long long w = e[u][i].second; if (v == pa) continue; dfs(v, u); g[v][0] = w; } } inline int getlca(int u, int v) { if (dep[u] < dep[v]) swap(u, v); for (int diff = dep[u] - dep[v], i = 0; i < L; i++) if ((diff >> i) & 1) u = f[u][i]; if (u == v) return u; for (int i = L - 1; i >= 0; i--) if (f[u][i] != f[v][i]) u = f[u][i], v = f[v][i]; return f[u][0]; } inline long long lift(int u, int len) { if (len <= 0) return 0; long long ret = 0; for (int i = 0; i < L; i++) if ((len >> i) & 1) ret = max(ret, g[u][i]), u = f[u][i]; return ret; } void doit() { dijkstra(); m = 0; for (int u = 1; u <= n; u++) for (int i = 0; i < e[u].size(); i++) { int v = e[u][i].first; if (v < u) continue; edge[++m] = Edge(u, v, dis[u] + dis[v] + e[u][i].second); } sort(edge + 1, edge + m + 1); for (int i = 1; i <= n; i++) e[i].clear(); for (int i = 1; i <= n; i++) fa[i] = i, sz[i] = 1; for (int i = 1; i <= m; i++) if (root(edge[i].u) != root(edge[i].v)) { merge(edge[i].u, edge[i].v); e[edge[i].u].push_back(make_pair(edge[i].v, edge[i].w)); e[edge[i].v].push_back(make_pair(edge[i].u, edge[i].w)); } dfs(1, 0); for (int j = 1; j < L; j++) for (int i = 1; i <= n; i++) f[i][j] = f[f[i][j - 1]][j - 1], g[i][j] = max(g[i][j - 1], g[f[i][j - 1]][j - 1]); while (q--) { int x = read(), y = read(), lca = getlca(x, y); long long ans = max(lift(x, dep[x] - dep[lca]), lift(y, dep[y] - dep[lca])); printf("%lld\n", ans); } } int main() { init(); doit(); return 0; }
#include <bits/stdc++.h> using namespace std; struct Edge { int u, v; long long w; } e[300010]; struct Query { int a, b; long long ans; Query() { ans = -1; } } q[300010]; struct data { int u; long long s; data(){}; data(int a, long long b) { u = a, s = b; } bool operator<(const data &a) const { return s > a.s; } }; int n, m, k, Q; int fa[100010]; int cnt, head[100010], nxt[300010 << 1], to[300010 << 1], w[300010 << 1]; long long dis[100010]; vector<int> g[100010]; priority_queue<data> que; void adde(int u, int v, int wi) { to[++cnt] = v; w[cnt] = wi; nxt[cnt] = head[u]; head[u] = cnt; } void dijkstra() { memset(dis, 127, sizeof(dis)); for (int i = 1; i <= k; i++) que.push(data(i, 0)), dis[i] = 0; while (!que.empty()) { data now = que.top(); que.pop(); for (int i = head[now.u]; i; i = nxt[i]) { int v = to[i]; if (dis[now.u] + w[i] <= dis[v]) { dis[v] = dis[now.u] + w[i]; que.push(data(v, dis[v])); } } } } bool cmp(Edge a, Edge b) { return a.w < b.w; } int find(int x) { return x == fa[x] ? x : (fa[x] = find(fa[x])); } int main() { scanf("%d%d%d%d", &n, &m, &k, &Q); for (int i = 1; i <= m; i++) { scanf("%d%d%lld", &e[i].u, &e[i].v, &e[i].w); adde(e[i].u, e[i].v, e[i].w), adde(e[i].v, e[i].u, e[i].w); } for (int i = 1; i <= Q; i++) { scanf("%d%d", &q[i].a, &q[i].b); g[q[i].a].push_back(i), g[q[i].b].push_back(i); } dijkstra(); for (int i = 1; i <= m; i++) e[i].w = e[i].w + dis[e[i].u] + dis[e[i].v]; sort(e + 1, e + m + 1, cmp); for (int i = 1; i <= n; i++) fa[i] = i; for (int i = 1; i <= m; i++) { int a = find(e[i].u), b = find(e[i].v); if (a != b) { if (g[b].size() < g[a].size()) swap(a, b); fa[a] = b; for (int j = 0, size = g[a].size(); j < size; j++) { int x = find(q[g[a][j]].a), y = find(q[g[a][j]].b); if (x == y) { if (q[g[a][j]].ans == -1) q[g[a][j]].ans = e[i].w; } else g[b].push_back(g[a][j]); } } } for (int i = 1; i <= Q; i++) printf("%lld\n", q[i].ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 3e5 + 10; const long long INF = 0x3f3f3f3f3f3f; struct Edge { int from, to; long long cost; Edge(int u, int v, long long cost) : from(u), to(v), cost(cost) {} }; vector<int> G[maxn]; vector<Edge> edges; void add_edges(int u, int v, long long cost) { edges.push_back(Edge(u, v, cost)); edges.push_back(Edge(v, u, cost)); int sz = edges.size(); G[u].push_back(sz - 2); G[v].push_back(sz - 1); } int vis[maxn]; long long dis[maxn]; int belong[maxn]; int n, m, k, q; struct HeapNode { int u; long long d; HeapNode(int _u, long long _d) : u(_u), d(_d) {} bool operator<(const HeapNode &rhs) const { return d > rhs.d; } }; void Dijkstra() { memset(vis, 0, sizeof(vis)); for (int i = 0; i <= n; i++) { dis[i] = INF; } priority_queue<HeapNode> Q; for (int i = 1; i <= k; i++) { Q.push(HeapNode(i, 0)); dis[i] = 0; belong[i] = i; } while (Q.size()) { HeapNode x = Q.top(); Q.pop(); int u = x.u; if (vis[u]) continue; vis[u] = 1; for (int i = 0; i < G[u].size(); i++) { Edge &e = edges[G[u][i]]; if (dis[e.to] > dis[u] + e.cost) { dis[e.to] = dis[u] + e.cost; belong[e.to] = belong[u]; Q.push(HeapNode(e.to, dis[e.to])); } } } } namespace MST { vector<int> g[maxn]; vector<Edge> E; const int POW = 20; long long dis[maxn][POW + 2]; int fa[maxn][POW + 2]; int dep[maxn]; void add_edges(int u, int v, long long cost) { E.push_back(Edge(u, v, cost)); E.push_back(Edge(v, u, cost)); int sz = E.size(); g[u].push_back(sz - 2); g[v].push_back(sz - 1); } void dfs(int u, int f) { for (int i = 0; i < g[u].size(); i++) { Edge &e = E[g[u][i]]; int v = e.to; if (v == f) continue; dep[v] = dep[u] + 1; fa[v][0] = u; dis[v][0] = e.cost; dfs(v, u); } } void initLCA() { fa[1][0] = -1; dep[1] = 0; dfs(1, -1); for (int k = 0; k < POW; k++) { for (int v = 1; v <= n; v++) { if (fa[v][k] < 0) fa[v][k + 1] = -1; else fa[v][k + 1] = fa[fa[v][k]][k], dis[v][k + 1] = max(dis[v][k], dis[fa[v][k]][k]); } } } long long query(int u, int v) { if (dep[u] > dep[v]) swap(u, v); long long re = -1; for (int k = 0; k < POW; k++) { if ((dep[v] - dep[u]) >> k & 1) re = max(re, dis[v][k]), v = fa[v][k]; } if (u == v) return re; for (int k = POW - 1; k >= 0; k--) { if (fa[u][k] != fa[v][k]) { re = max(re, dis[v][k]), re = max(re, dis[u][k]); u = fa[u][k], v = fa[v][k]; } } re = max(re, dis[u][0]); re = max(re, dis[v][0]); return re; } } // namespace MST namespace Graph { int tot; struct EEdge { int from, to; long long cost; } edges[(signed)6e5 + 10]; int fa[maxn]; int find_set(int x) { return fa[x] == x ? fa[x] : fa[x] = find_set(fa[x]); } void add_edges(int u, int v, long long cost) { edges[tot].from = u; edges[tot].to = v; edges[tot].cost = cost; tot++; } int cmp(const EEdge a, const EEdge b) { return a.cost < b.cost; } void kruskal() { sort(edges, edges + tot, cmp); for (int i = 0; i < tot; i++) { EEdge &e = edges[i]; int fx = find_set(e.from), fy = find_set(e.to); if (fx != fy) { if (fx > fy) { fa[fy] = fx; } else { fa[fx] = fy; } MST::add_edges(e.from, e.to, e.cost); } } } } // namespace Graph signed main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 1; i <= m; i++) { int u, v; long long cost; scanf("%d%d%I64d", &u, &v, &cost); add_edges(u, v, cost); } Dijkstra(); for (int u = 1; u <= n; u++) { for (int i = 0; i < G[u].size(); i++) { Edge &e = edges[G[u][i]]; if (belong[u] != belong[e.to]) { Graph::add_edges(belong[u], belong[e.to], dis[u] + dis[e.to] + e.cost); } } } for (int i = 1; i <= n; i++) Graph::fa[i] = i; Graph::kruskal(); MST::initLCA(); while (q--) { int x, y; scanf("%d%d", &x, &y); printf("%I64d\n", MST::query(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100005; const int MAXM = 300005; const long long INF = 0x3f3f3f3f3f3f3f3f; template <typename T> inline void read(T &AKNOI) { T x = 0, flag = 1; char ch = getchar(); while (!isdigit(ch)) { if (ch == '-') flag = -1; ch = getchar(); } while (isdigit(ch)) { x = x * 10 + ch - '0'; ch = getchar(); } AKNOI = flag * x; } template <typename T> inline void cmax(T &x, T y) { if (x < y) x = y; } int n, m, k, Q; int vis[MAXN], from[MAXN], fa[MAXN], siz[MAXN]; long long dis[MAXN], fw[MAXN]; priority_queue<pair<long long, int> > q; struct Edge { int v, w, nxt; } g[MAXM << 1]; int first[MAXN], eCnt; inline void AddEdge(int u, int v, int w) { g[++eCnt].v = v; g[eCnt].w = w; g[eCnt].nxt = first[u]; first[u] = eCnt; } struct Edge2 { int u, v; long long w; bool operator<(const Edge2 &rhs) const { return w < rhs.w; } } e[MAXM]; void Dijkstra() { memset(dis, 0x3f, sizeof(dis)); memset(vis, 0, sizeof(vis)); for (int i = 1; i <= k; ++i) { dis[i] = 0; from[i] = i; q.push(make_pair(0, i)); } while (!q.empty()) { int u = q.top().second; q.pop(); if (vis[u]) continue; vis[u] = 1; for (int i = first[u]; i; i = g[i].nxt) { int v = g[i].v; if (dis[v] > dis[u] + g[i].w) { dis[v] = dis[u] + g[i].w; from[v] = from[u]; q.push(make_pair(-dis[v], v)); } } } } int getf(int u) { while (fa[u] != u) u = fa[u]; return u; } void Build() { for (int i = 2; i <= eCnt; i += 2) { e[i >> 1].u = from[g[i].v]; e[i >> 1].v = from[g[i - 1].v]; e[i >> 1].w = dis[g[i].v] + dis[g[i - 1].v] + g[i].w; } sort(e + 1, e + m + 1); for (int i = 1; i <= n; ++i) { fa[i] = i; siz[i] = 1; } for (int i = 1; i <= m; ++i) { int u = getf(e[i].u), v = getf(e[i].v); if (u == v) continue; if (siz[u] > siz[v]) swap(u, v); siz[v] += siz[u]; fa[u] = v; fw[u] = e[i].w; } } long long Query(int u, int v) { long long ret = 0; while (u ^ v) { if (siz[u] > siz[v]) swap(u, v); cmax(ret, fw[u]); u = fa[u]; } return ret; } void init() { read(n); read(m); read(k); read(Q); for (int i = 1; i <= m; ++i) { int u, v, w; read(u); read(v); read(w); AddEdge(u, v, w); AddEdge(v, u, w); } } void solve() { Dijkstra(); Build(); while (Q--) { int x, y; read(x); read(y); printf("%lld\n", Query(x, y)); } } int main() { init(); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const long long inf = 1e18; const int maxn = 1e6 + 10; int n, m, k, qnum, st[maxn], to[maxn], nt[maxn], topt, fa[maxn]; int ffa[21][100010], lg[maxn], dep[maxn]; long long dis[maxn], w[maxn], ma[21][100010]; bool f[maxn]; struct da { int first, to; long long v; } a[maxn]; priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > q; inline void add(int x, int y, long long z) { to[++topt] = y; nt[topt] = st[x]; st[x] = topt; w[topt] = z; } void dij() { for (int i = 1; i <= n; i++) dis[i] = inf; for (int i = 1; i <= k; i++) dis[i] = 0, q.push(make_pair(0, i)); while (!q.empty()) { int x = q.top().second; q.pop(); if (f[x]) continue; else f[x] = 1; int p = st[x]; while (p) { if (dis[to[p]] > dis[x] + w[p]) { dis[to[p]] = dis[x] + w[p]; q.push(make_pair(dis[to[p]], to[p])); } p = nt[p]; } } } inline bool cmp(da aa, da bb) { return aa.v < bb.v; } int getf(int x) { if (fa[x] == x) return x; fa[x] = getf(fa[x]); return fa[x]; } void dfs(int x, int d, long long vv) { f[x] = 1; dep[x] = d; ma[0][x] = vv; int p = st[x]; while (p) { if (!f[to[p]]) dfs(to[p], d + 1, w[p]), ffa[0][to[p]] = x; p = nt[p]; } } inline void init() { for (int i = 1; i <= n; i++) lg[i] = lg[i - 1] + ((1 << (lg[i - 1] + 1)) == i); for (int j = 1; (1 << j) <= n; j++) for (int i = 1; i <= n; i++) ffa[j][i] = ffa[j - 1][ffa[j - 1][i]]; for (int j = 1; (1 << j) <= n; j++) for (int i = 1; i <= n; i++) ma[j][i] = max(ma[j - 1][i], ma[j - 1][ffa[j - 1][i]]); } long long solve(int x, int y) { long long ans = 0; if (dep[x] < dep[y]) swap(x, y); while (dep[x] > dep[y]) { ans = max(ans, ma[lg[dep[x] - dep[y]]][x]); x = ffa[lg[dep[x] - dep[y]]][x]; } if (x == y) return ans; for (register int i = lg[dep[x]]; i >= 0; i--) if (ffa[i][x] != ffa[i][y]) { ans = max(ans, ma[i][x]); ans = max(ans, ma[i][y]); x = ffa[i][x]; y = ffa[i][y]; } ans = max(ans, ma[0][x]); ans = max(ans, ma[0][y]); return ans; } int main() { scanf("%d%d%d%d", &n, &m, &k, &qnum); for (int i = 1; i <= m; i++) { scanf("%d%d%lld", &a[i].first, &a[i].to, &a[i].v); add(a[i].first, a[i].to, a[i].v); add(a[i].to, a[i].first, a[i].v); } dij(); for (int i = 1; i <= m; i++) a[i].v = a[i].v + dis[a[i].first] + dis[a[i].to]; sort(a + 1, a + m + 1, cmp); topt = 0; for (int i = 1; i <= n; i++) st[i] = 0, fa[i] = i; for (int i = 1; i <= m; i++) { if (getf(a[i].first) == getf(a[i].to)) continue; fa[getf(a[i].first)] = getf(a[i].to); add(a[i].first, a[i].to, a[i].v); add(a[i].to, a[i].first, a[i].v); } for (int i = 1; i <= n; i++) f[i] = 0; dfs(1, 1, 0); init(); for (int i = 1; i <= qnum; i++) { int xx, yy; scanf("%d%d", &xx, &yy); printf("%lld\n", solve(xx, yy)); } return 0; }
#include <bits/stdc++.h> using namespace std; inline int read() { char c = getchar(); int x = 0, f = 1; while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); } return x * f; } const int maxn = 1e5 + 10; const long long inf = (long long)1e15; int n, m, k, q; struct enode { int v, nxt; long long w; } edge[maxn * 6]; struct dnode { int u, v; long long w; } a[maxn * 3]; bool cmp(dnode& a, dnode& b) { return a.w < b.w; } int head[maxn], tot; void add(int u, int v, long long w) { edge[++tot].v = v; edge[tot].w = w; edge[tot].nxt = head[u]; head[u] = tot; } long long dis[maxn]; int fro[maxn]; bool vis[maxn]; void dijkstra() { priority_queue<pair<long long, int> > pq; for (int i = 1; i <= k; ++i) { dis[i] = 0; fro[i] = i; pq.push(make_pair(0, i)); } for (int i = k + 1; i <= n; ++i) dis[i] = inf; while (!pq.empty()) { int u = pq.top().second; pq.pop(); if (vis[u]) continue; vis[u] = true; for (int i = head[u]; i; i = edge[i].nxt) { int v = edge[i].v, w = edge[i].w; if (dis[u] + w < dis[v]) { dis[v] = dis[u] + w; fro[v] = fro[u]; pq.push(make_pair(-dis[v], v)); } } } } int fa[maxn]; int sz[maxn]; long long val[maxn]; int find(int x) { if (x == fa[x]) return x; return find(fa[x]); } long long query(int u, int v) { long long ans = 0; while (u != v) { if (sz[u] > sz[v]) swap(u, v); ans = max(ans, val[u]); u = fa[u]; } return ans; } int main() { n = read(), m = read(), k = read(), q = read(); for (int i = 0; i < m; ++i) { int u = read(), v = read(); long long w; scanf("%lld", &w); add(u, v, w); add(v, u, w); } dijkstra(); for (int i = 1; i <= m; ++i) { a[i].u = fro[edge[i * 2 - 1].v]; a[i].v = fro[edge[i * 2].v]; a[i].w = dis[edge[i * 2 - 1].v] + dis[edge[i * 2].v] + edge[i * 2].w; } sort(a + 1, a + 1 + m, cmp); for (int i = 1; i <= n; ++i) { sz[i] = 1; fa[i] = i; } for (int i = 1; i <= m; ++i) { int u = find(a[i].u), v = find(a[i].v); if (u == v) continue; if (sz[u] > sz[v]) swap(u, v); fa[u] = fa[v]; sz[v] += sz[u]; val[u] = a[i].w; } while (q--) { int u = read(), v = read(); printf("%lld\n", query(u, v)); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long LL_INF = (long long)2e18 + 5; struct edge { int node = -1; long long weight = LL_INF; edge() {} edge(int _node, long long _weight) : node(_node), weight(_weight) {} }; struct dijkstra_state { long long dist; int node; dijkstra_state() {} dijkstra_state(long long _dist, int _node) : dist(_dist), node(_node) {} bool operator<(const dijkstra_state &other) const { return dist > other.dist; } }; int N, M, K, Q; vector<vector<edge>> adj; vector<long long> dist; void dijkstra_check(priority_queue<dijkstra_state> &pq, int node, long long current_dist) { if (current_dist < dist[node]) { dist[node] = current_dist; pq.emplace(current_dist, node); } } void dijkstra() { dist.assign(N, LL_INF); priority_queue<dijkstra_state> pq; for (int source = 0; source < K; source++) dijkstra_check(pq, source, 0); while (!pq.empty()) { dijkstra_state top = pq.top(); pq.pop(); if (top.dist > dist[top.node]) continue; for (edge &e : adj[top.node]) dijkstra_check(pq, e.node, top.dist + e.weight); } } struct ab_edge { int a, b; long long weight; bool operator<(const ab_edge &other) const { return weight < other.weight; } }; vector<ab_edge> edges; void compute_real_weights() { for (int i = 0; i < N; i++) for (edge &e : adj[i]) { e.weight += dist[i] + dist[e.node]; edges.push_back({i, e.node, e.weight}); } } vector<vector<pair<int, int>>> queries; vector<long long> answers; vector<vector<int>> groups; vector<int> owner; void merge_and_solve(int a, int b, long long weight) { a = owner[a]; b = owner[b]; if (a == b) return; if (groups[a].size() > groups[b].size()) swap(a, b); for (int x : groups[a]) for (pair<int, int> &query : queries[x]) if (owner[query.first] == b) { assert(answers[query.second] < 0); answers[query.second] = weight; } for (int x : groups[a]) { owner[x] = b; groups[b].push_back(x); } groups[a].clear(); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cin >> N >> M >> K >> Q; adj.assign(N, {}); for (int i = 0; i < M; i++) { int u, v, weight; cin >> u >> v >> weight; u--; v--; adj[u].emplace_back(v, weight); adj[v].emplace_back(u, weight); } dijkstra(); compute_real_weights(); queries.assign(N, {}); answers.assign(Q, -1); for (int q = 0; q < Q; q++) { int a, b; cin >> a >> b; a--; b--; queries[a].emplace_back(b, q); queries[b].emplace_back(a, q); } groups.assign(N, {}); owner.resize(N); for (int i = 0; i < N; i++) { owner[i] = i; groups[i] = {i}; } sort(edges.begin(), edges.end()); for (ab_edge &e : edges) merge_and_solve(e.a, e.b, e.weight); for (int q = 0; q < Q; q++) cout << answers[q] << '\n'; }
#include <bits/stdc++.h> using namespace std; pair<pair<int, int>, int> edge[300001]; vector<pair<long long, pair<int, int>>> ne; vector<pair<int, int>> e[100001]; priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq; long long dis[100001]; int color[100001]; bool v[100001]; int fa[100001], tf[100001][17], depth[100001]; long long val[100001]; vector<int> ned[100001]; int find(int x) { return fa[x] == x ? x : fa[x] = find(fa[x]); } void dfs(int x) { for (int i = 1; i < 17; i++) tf[x][i] = tf[tf[x][i - 1]][i - 1]; for (int nex : ned[x]) depth[nex] = depth[x] + 1, dfs(nex); } long long get(int x, int y) { if (depth[x] > depth[y]) swap(x, y); int delta = depth[y] - depth[x]; if (delta) { delta--; for (int i = 0; i < 17; i++) if (delta & (1 << i)) y = tf[y][i]; if (tf[y][0] == x) return val[y]; y = tf[y][0]; } for (int i = 16; i >= 0; i--) if (tf[x][i] != tf[y][i]) x = tf[x][i], y = tf[y][i]; return max(val[x], val[y]); } int main() { int n, m, k, q; scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 1; i <= m; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); edge[i] = make_pair(make_pair(u, v), w); e[u].emplace_back(v, w); e[v].emplace_back(u, w); } for (int i = 1; i <= k; i++) color[i] = i, pq.emplace(0, i); for (int i = k + 1; i <= n; i++) dis[i] = LLONG_MAX; while (!pq.empty()) { long long d = pq.top().first; int x = pq.top().second; pq.pop(); if (v[x]) continue; v[x] = 1; for (auto p : e[x]) { int nex = p.first, w = p.second; if (dis[nex] > d + w) { dis[nex] = d + w; color[nex] = color[x]; pq.emplace(dis[nex], nex); } } } for (int i = 1; i <= k; i++) fa[i] = i; for (int i = 1; i <= m; i++) { int u = edge[i].first.first, v = edge[i].first.second, w = edge[i].second; if (color[u] != color[v]) ne.push_back( make_pair(dis[u] + dis[v] + w, make_pair(color[u], color[v]))); } sort(ne.begin(), ne.end()); for (auto p : ne) { int u = find(p.second.first), v = find(p.second.second); long long w = p.first; if (u == v) continue; fa[u] = tf[u][0] = v; val[u] = w; ned[v].emplace_back(u); } int rt = 1; for (; rt <= k; rt++) if (!tf[rt][0]) break; dfs(rt); if (n == 500) { for (int i = 1; i <= n; i++) if (dis[i] < 0) printf("culprit:%d\n", i); } while (q--) { int x, y; scanf("%d%d", &x, &y); printf("%lld\n", get(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 1e5 + 5, oo = 1e18, LG = 22; long long n, m, k, q, P[N][LG], dep[N], mx[N][LG]; vector<array<long long, 2>> adj[N], tree[N]; array<long long, 2> dist[N]; vector<array<long long, 3>> Edges; void dfs(long long u, long long pre) { for (auto D : tree[u]) { long long v = D[0], w = D[1]; if (v == pre) continue; P[v][0] = u; mx[v][0] = w; dep[v] = dep[u] + 1; dfs(v, u); } } long long query(long long u, long long v) { long long ret = 0; if (dep[u] < dep[v]) swap(u, v); for (long long i = LG - 1; i >= 0; --i) if ((1 << i) <= dep[u] - dep[v]) { ret = max(ret, mx[u][i]); u = P[u][i]; } if (u == v) return ret; for (long long i = LG - 1; i >= 0; --i) if ((1 << i) <= dep[u] && P[u][i] != P[v][i]) { ret = max(ret, mx[u][i]); ret = max(ret, mx[v][i]); u = P[u][i]; v = P[v][i]; } ret = max(ret, mx[u][0]); ret = max(ret, mx[v][0]); return ret; } struct dsu_t { long long n; vector<long long> lab, Rank; dsu_t() {} dsu_t(long long _n) { this->n = _n; lab.assign(n + 5, -1); Rank.assign(n + 5, 1); } long long root(long long x) { return lab[x] == -1 ? x : lab[x] = root(lab[x]); } bool merge(long long u, long long v) { long long x = root(u), y = root(v); if (x == y) return false; if (Rank[x] < Rank[y]) swap(x, y); lab[y] = x; Rank[x] += Rank[y]; return true; } }; signed main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> n >> m >> k >> q; for (long long i = 1; i <= m; ++i) { long long u, v, w; cin >> u >> v >> w; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } priority_queue<array<long long, 3>, vector<array<long long, 3>>, greater<array<long long, 3>>> pq; while (!pq.empty()) pq.pop(); for (long long i = 1; i <= k; ++i) { pq.push({0, i, i}); dist[i] = {0, i}; } for (long long i = k + 1; i <= n; ++i) { dist[i] = {oo, -1}; } while (!pq.empty()) { array<long long, 3> cur = pq.top(); pq.pop(); long long D = cur[0], u = cur[1], beg = cur[2]; if (D > dist[u][0]) continue; for (auto vv : adj[u]) { long long v = vv[0], w = vv[1]; if (D + w < dist[v][0]) { dist[v][0] = D + w; dist[v][1] = beg; pq.push({D + w, v, beg}); } } } for (long long u = 1; u <= n; ++u) { for (auto vv : adj[u]) { long long v = vv[0]; if (dist[v][1] == dist[u][1] || u > v) continue; Edges.push_back( {dist[v][0] + dist[u][0] + vv[1], dist[v][1], dist[u][1]}); } } sort(Edges.begin(), Edges.end()); dsu_t dsu = dsu_t(k); for (auto D : Edges) { long long u = D[1], v = D[2], w = D[0]; if (dsu.merge(u, v)) { tree[u].push_back({v, w}); tree[v].push_back({u, w}); } } dfs(1, -1); for (long long i = 1; i < LG; ++i) { for (long long u = 1; u <= n; ++u) { P[u][i] = P[P[u][i - 1]][i - 1]; mx[u][i] = max(mx[u][i - 1], mx[P[u][i - 1]][i - 1]); } } for (long long i = 1; i <= q; ++i) { long long u, v; cin >> u >> v; cout << query(u, v) << endl; } return 0; }
#include <bits/stdc++.h> const long long INF = 0x3f3f3f3f3f3f3f3fll; class DSU { std::vector<int> fa; public: DSU(int n) : fa(n) { for (int i = 0; i < n; ++i) { fa[i] = i; } } int find(int x) { return fa[x] == x ? x : (fa[x] = find(fa[x])); } bool merge(int x, int y) { x = find(x), y = find(y); if (x == y) { return false; } fa[y] = x; return true; } }; int get_log2(int n) { int res = 1; while ((1 << res) < n) { ++res; } return res; } class tree { const int n, LG; std::vector<std::vector<std::pair<int, long long>>> E; std::vector<int> dep; std::vector<std::vector<int>> fa; std::vector<std::vector<long long>> mx; void dfs(int u) { for (int i = 1; i < LG; ++i) { fa[u][i] = fa[u][i - 1] == -1 ? -1 : fa[fa[u][i - 1]][i - 1]; mx[u][i] = fa[u][i - 1] == -1 ? mx[u][i - 1] : std::max(mx[u][i - 1], mx[fa[u][i - 1]][i - 1]); } for (auto [v, w] : E[u]) { if (v != fa[u][0]) { dep[v] = dep[u] + 1; fa[v][0] = u; mx[v][0] = w; dfs(v); } } } public: tree(int _n) : n(_n), LG(get_log2(n)), E(n), dep(n), fa(n, std::vector<int>(LG, -1)), mx(n, std::vector<long long>(LG, n)) {} void add_edge(int u, int v, long long w) { E[u].emplace_back(v, w); E[v].emplace_back(u, w); } void build() { dep[0] = 0; fa[0][0] = -1; mx[0][0] = 0; dfs(0); } long long query(int u, int v) { if (dep[u] < dep[v]) { std::swap(u, v); } long long ans = 0; for (int i = LG - 1; i >= 0; --i) { if (fa[u][i] != -1 && dep[fa[u][i]] >= dep[v]) { ans = std::max(ans, mx[u][i]); u = fa[u][i]; } } if (u == v) { return ans; } for (int i = LG - 1; i >= 0; --i) { if (fa[u][i] != fa[v][i]) { ans = std::max(ans, std::max(mx[u][i], mx[v][i])); u = fa[u][i], v = fa[v][i]; } } ans = std::max(ans, std::max(mx[u][0], mx[v][0])); return ans; } }; int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(0); int n, m, k, q; std::cin >> n >> m >> k >> q; std::vector<std::vector<std::pair<int, int>>> E(n); for (int i = 0; i < m; ++i) { int u, v, w; std::cin >> u >> v >> w; --u, --v; E[u].emplace_back(v, w); E[v].emplace_back(u, w); } std::vector<long long> dis(n, INF); std::vector<bool> vis(n, false); std::priority_queue<std::pair<long long, int>> Q; for (int i = 0; i < k; ++i) { dis[i] = 0; Q.emplace(0, i); } while (!Q.empty()) { int u = Q.top().second; Q.pop(); if (vis[u]) { continue; } vis[u] = true; for (auto [v, w] : E[u]) { if (dis[v] > dis[u] + w) { dis[v] = dis[u] + w; Q.emplace(-dis[v], v); } } } std::vector<std::tuple<long long, int, int>> edge; for (int u = 0; u < n; ++u) { for (auto [v, w] : E[u]) { if (u < v) { edge.emplace_back(dis[u] + dis[v] + w, u, v); } } } std::sort(edge.begin(), edge.end()); tree T(n); DSU D(n); for (auto [w, u, v] : edge) { if (D.merge(u, v)) { T.add_edge(u, v, w); } } T.build(); while (q--) { int u, v; std::cin >> u >> v; --u, --v; std::cout << T.query(u, v) << "\n"; } }
#include <bits/stdc++.h> using namespace std; int n, m, k, q, vis[100005], cd[100005], etot, fa[100005]; int ffa[100005][24], dep[100005], lg[100005]; long long dis[100005], mma[100005][24]; struct edge { int to; long long w; edge() {} edge(int to, long long w) : to(to), w(w) {} }; struct node { int x, y; long long w; node() {} node(int x, int y, long long w) : x(x), y(y), w(w) {} } ee[1000005]; vector<edge> e[100005], e2[100005]; bool cmp(node a, node b) { return a.w < b.w; } int _find(int x) { return fa[x] == x ? x : fa[x] = _find(fa[x]); } void _merge(int x, int y) { x = _find(x), y = _find(y); fa[x] = y; } void dij() { for (int i = 1; i <= n + 1; i++) dis[i] = 0x3f3f3f3f3f3f3f3fll; dis[n + 1] = 0; priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> q; q.emplace(0, n + 1); while (!q.empty()) { int now = q.top().second; q.pop(); if (vis[now]) continue; vis[now] = 1; for (auto it : e[now]) if (dis[it.to] > dis[now] + it.w) { dis[it.to] = dis[now] + it.w; if (now != n + 1) cd[it.to] = cd[now]; q.emplace(dis[it.to], it.to); } } } void mst() { for (int i = 1; i <= n; i++) fa[i] = i; sort(ee, ee + etot, cmp); for (int i = 0; i < etot; i++) if (_find(ee[i].x) != _find(ee[i].y)) { _merge(ee[i].x, ee[i].y); e2[ee[i].x].emplace_back(ee[i].y, ee[i].w); e2[ee[i].y].emplace_back(ee[i].x, ee[i].w); } } void dfs(int now, int pa, long long dd) { dep[now] = dep[pa] + 1; ffa[now][0] = pa; mma[now][0] = dd; for (int i = 1; (1 << i) <= dep[now]; i++) { ffa[now][i] = ffa[ffa[now][i - 1]][i - 1]; mma[now][i] = max(mma[now][i - 1], mma[ffa[now][i - 1]][i - 1]); } for (auto it : e2[now]) if (it.to != pa) dfs(it.to, now, it.w); } long long lca(int x, int y) { long long ret = 0; if (dep[x] < dep[y]) swap(x, y); while (dep[x] > dep[y]) { ret = max(ret, mma[x][lg[dep[x] - dep[y]] - 1]); x = ffa[x][lg[dep[x] - dep[y]] - 1]; } if (x == y) return ret; for (int i = lg[dep[x]] - 1; i >= 0; i--) if (ffa[x][i] != ffa[y][i]) { ret = max(ret, mma[x][i]); ret = max(ret, mma[y][i]); x = ffa[x][i], y = ffa[y][i]; } return max(ret, max(mma[y][0], mma[x][0])); } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 1; i <= n + 1; i++) lg[i] = lg[i - 1] + (1 << lg[i - 1] == i); for (int i = 1, x, y, w; i <= m; i++) { scanf("%d%d%d", &x, &y, &w); e[x].emplace_back(y, w); e[y].emplace_back(x, w); } for (int i = 1; i <= k; i++) e[n + 1].emplace_back(i, 0), cd[i] = i; dij(); for (int i = 1; i <= n; i++) for (auto it : e[i]) { if (cd[i] != cd[it.to]) ee[etot++] = node(cd[i], cd[it.to], dis[i] + it.w + dis[it.to]); else ee[etot++] = node(i, it.to, it.w); } mst(); dfs(1, 0, 0); while (q--) { int x, y; scanf("%d%d", &x, &y); printf("%lld\n", lca(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 4e5; vector<tuple<long long, long long, long long> > edge; priority_queue<long long> q; long long d[N]; set<long long> se[N]; long long pa[N]; vector<long long> qr[N]; vector<pair<long long, long long> > ke[N]; long long Res[N]; long long anc(long long u) { if (pa[u] > 0) { pa[u] = anc(pa[u]); return pa[u]; } else return u; } void join(long long u, long long v, long long z) { u = anc(u); v = anc(v); if (u == v) { return; } if (pa[u] > pa[v]) swap(u, v); pa[u] += pa[v]; pa[v] = u; for (auto& vse : se[v]) { if (se[u].size()) if (se[u].find(vse) != se[u].end()) { Res[vse] = z; } } for (auto& vse : se[v]) se[u].insert(vse); } int main() { ios_base::sync_with_stdio(0); cin.tie(0); long long n, m, k, Q; cin >> n >> m >> k >> Q; for (long long i = 1; i <= m; i++) { long long first, second, z; cin >> first >> second >> z; ke[first].push_back(pair<long long, long long>(second, z)); ke[second].push_back(pair<long long, long long>(first, z)); edge.push_back(tuple<long long, long long, long long>(first, second, z)); } priority_queue<pair<long long, long long> > q; for (long long i = 1; i <= k; i++) { q.push(pair<long long, long long>(0, i)); d[i] = 0; } for (long long i = k + 1; i <= n; i++) d[i] = 1e18; while (q.size()) { long long u; u = q.top().second; q.pop(); for (auto& v : ke[u]) { long long first, second; tie(second, first) = v; if (d[second] > d[u] + first) { d[second] = d[u] + first; q.push(pair<long long, long long>(-d[second], second)); } } } for (auto& i : edge) { long long first, second, z; tie(first, second, z) = i; get<2>(i) = d[first] + d[second] + z; } sort(edge.begin(), edge.end(), [](const tuple<long long, long long, long long>& a, const tuple<long long, long long, long long>& b) -> bool { return get<2>(a) < get<2>(b); }); for (long long i = 1; i <= Q; i++) { long long first, second; cin >> first >> second; se[first].insert(i); se[second].insert(i); } for (long long i = 1; i <= n; i++) pa[i] = -1; for (auto& i : edge) { long long first, second, z; tie(first, second, z) = i; join(first, second, z); } for (long long i = 1; i <= Q; i++) { cout << Res[i] << "\n"; } }
#include <bits/stdc++.h> using namespace std; const long long N = 3e5 + 5; const long long M = 1; const long long K = 1; const long long mod = 1e9 + 7; const long long inf = 2e9; const long long Inf = 2e18; long long n, m, k, q; vector<pair<long long, long long> > adj[N]; vector<pair<long long, pair<long long, long long> > > ed; long long d[N]; void dick() { priority_queue<pair<long long, long long>, vector<pair<long long, long long> >, greater<pair<long long, long long> > > q; memset(d, 0x3f, sizeof d); for (long long i = 1; i <= k; ++i) { d[i] = 0; q.push({0, i}); } while (q.size()) { pair<long long, long long> top = q.top(); q.pop(); long long pd = top.first; long long p = top.second; if (pd != d[p]) continue; for (pair<long long, long long> u : adj[p]) if (pd + u.second < d[u.first]) { d[u.first] = pd + u.second; q.push({d[u.first], u.first}); } } } vector<pair<long long, long long> > re[N]; long long par[N], res[N]; vector<long long> con[N]; void init() { for (long long i = 1; i <= n; ++i) { par[i] = i; con[i].push_back(i); } } long long get(long long x) { if (x == par[x]) return x; return par[x] = get(par[x]); } void mix(long long x, long long y, long long w) { long long u = get(x); long long v = get(y); if (u == v) return; if (con[u].size() > con[v].size()) swap(u, v); for (long long x : con[u]) { for (pair<long long, long long> i : re[x]) { long long id = i.second; long long j = i.first; if (get(j) == v) res[id] = w; } con[v].push_back(x); } par[u] = v; } signed main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (long long i = 1; i <= m; ++i) { long long u, v, w; cin >> u >> v >> w; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } dick(); for (long long i = 1; i <= n; ++i) for (pair<long long, long long> x : adj[i]) { long long dis = x.second + d[i] + d[x.first]; ed.push_back({dis, {i, x.first}}); } for (long long i = 1; i <= q; ++i) { long long u, v; cin >> u >> v; re[u].push_back({v, i}); re[v].push_back({u, i}); } init(); sort(ed.begin(), ed.end()); for (auto x : ed) mix(x.second.first, x.second.second, x.first); for (long long i = 1; i <= q; ++i) cout << res[i] << '\n'; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1); const long long mod = 1e9 + 7; inline long long read() { long long x = 0, f = 1; char ch = getchar(); while (ch > '9' || ch < '0') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); } return x * f; } int n, m, k, q; int inde[100005], tot; long long dis[100005]; struct p { int u, v, w, nxt; } e[600005 * 4]; void add(int u, int v, int w) { e[++tot] = {u, v, w, inde[u]}, inde[u] = tot; } priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> Q; bool vis[100005]; void bfs() { int i, v, u; Q.push({0, 0}); while (!Q.empty()) { pair<long long, int> tp = Q.top(); Q.pop(); u = tp.second; if (dis[u] != tp.first) continue; for (i = inde[u]; i; i = e[i].nxt) { v = e[i].v; if (dis[v] > dis[u] + e[i].w) { dis[v] = dis[u] + e[i].w; Q.push({dis[v], v}); } } } } int f[100005]; struct q { int u, v; long long w; bool operator<(const q &a) const { return dis[u] + dis[v] + w < dis[a.u] + dis[a.v] + a.w; } } edge[600005]; int getf(int x) { return x == f[x] ? x : f[x] = getf(f[x]); } struct pp { int u, v, id; } qe[600005]; long long ans[600005]; vector<int> g[100005]; int main() { int i, j, u, v, w; n = read(), m = read(), k = read(), q = read(); for (i = 1; i <= m; i++) { u = read(), v = read(), w = read(); edge[i] = {u, v, w}; add(u, v, w); add(v, u, w); } for (i = 1; i <= n; i++) dis[i] = 0x3f3f3f3f3f3f3f3f; for (i = 1; i <= k; i++) add(0, i, 0); bfs(); tot = 0; for (i = 1; i <= n; i++) f[i] = i; for (i = 1; i <= q; i++) { u = read(), v = read(); qe[i] = pp{u, v, i}; g[u].push_back(i); g[v].push_back(i); } sort(edge + 1, edge + m + 1); for (i = 1; i <= m; i++) { u = edge[i].u, v = edge[i].v, w = edge[i].w; int f1 = getf(u), f2 = getf(v); if (f1 == f2) continue; if (g[f1].size() < g[f2].size()) swap(f1, f2); f[f2] = f1; for (j = 0; j < g[f2].size(); j++) { int x = qe[g[f2][j]].u, y = qe[g[f2][j]].v; if (getf(x) == getf(y)) { if (!ans[g[f2][j]]) ans[g[f2][j]] = edge[i].w + dis[u] + dis[v]; } else g[f1].push_back(g[f2][j]); } } for (i = 1; i <= q; i++) printf("%lld\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = (int)1e5 + 100; const int mod = (int)1e9 + 7; const long long INF = (long long)2e18; int n, m, k, q, fa[maxn]; long long dis[maxn], ans[maxn * 6]; vector<pair<int, long long> > g[maxn * 6]; vector<pair<int, int> > que[maxn]; vector<tuple<long long, int, int> > e; set<int> ele[maxn]; void dij() { priority_queue<pair<long long, int> > Q; for (int i = 1; i <= n; i++) if (i <= k) Q.push({0, i}); else dis[i] = INF; while (!Q.empty()) { int u = Q.top().second; Q.pop(); for (auto [v, w] : g[u]) if (dis[u] + w < dis[v]) { dis[v] = dis[u] + w; Q.push({-dis[v], v}); } } } int find(int x) { return x == fa[x] ? x : fa[x] = find(fa[x]); } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 1; i <= m; i++) { int u, v; long long w; scanf("%d%d%lld", &u, &v, &w); g[u].push_back({v, w}); g[v].push_back({u, w}); } dij(); for (int u = 1; u <= n; u++) for (auto [v, w] : g[u]) if (u < v) e.push_back({dis[u] + dis[v] + w, u, v}); sort(e.begin(), e.end()); for (int i = 1; i <= q; i++) { int u, v; scanf("%d%d", &u, &v); que[u].push_back({v, i}); que[v].push_back({u, i}); } for (int i = 1; i <= n; i++) { fa[i] = i; ele[i].insert(i); } for (auto [w, x, y] : e) { x = find(x); y = find(y); if (x == y) continue; if (ele[x].size() < ele[y].size()) swap(x, y); fa[y] = x; for (auto u : ele[y]) for (auto [v, id] : que[u]) if (ele[x].count(v)) ans[id] = w; for (auto u : ele[y]) ele[x].insert(u); } for (int i = 1; i <= q; i++) printf("%lld\n", ans[i]); }
#include <bits/stdc++.h> using namespace std; int n, m, k, q; vector<pair<int, int> > gr[100007]; int LCA[100007][19]; long long mx[100007][19]; int lvl[100007]; vector<pair<int, long long> > v[100007]; long long opt[100007]; int ori[100007]; struct tuhla { int vertex; long long dist; int origin; tuhla() { vertex = dist = origin = 0; } tuhla(int _vertex, long long _dist, int _origin) { vertex = _vertex; dist = _dist; origin = _origin; } bool operator<(tuhla other) const { return (dist > other.dist); } }; priority_queue<struct tuhla> pq; struct edge { int x, y; long long cost; edge() { x = y = cost = 0; } edge(int _x, int _y, long long _cost) { x = _x; y = _y; cost = _cost; } bool operator<(edge other) const { return (cost < other.cost); } }; vector<struct edge> srt; void dijkstra() { for (int i = 1; i <= k; ++i) { pq.push(tuhla(i, 0, i)); opt[i] = 0; ori[i] = i; } for (int i = k + 1; i <= n; ++i) { opt[i] = -1; } while (pq.empty() == false) { tuhla aux = pq.top(); pq.pop(); if (opt[aux.vertex] != aux.dist) { continue; } if (ori[aux.vertex] != aux.origin) { continue; } int sz = gr[aux.vertex].size(); for (int i = 0; i < sz; ++i) { int h = gr[aux.vertex][i].first; int c = gr[aux.vertex][i].second; if (opt[h] == -1 || opt[h] > aux.dist + c) { opt[h] = aux.dist + c; ori[h] = aux.origin; pq.push(tuhla(h, opt[h], ori[h])); } } } } int prv[100007]; int rnk[100007]; int find(int x) { if (prv[x] == -1) { return x; } int y = find(prv[x]); prv[x] = y; return y; } void unite(edge aux) { int k1 = find(aux.x); int k2 = find(aux.y); if (k1 != k2) { v[aux.x].push_back({aux.y, aux.cost}); v[aux.y].push_back({aux.x, aux.cost}); if (rnk[k1] >= rnk[k2]) { if (rnk[k1] == rnk[k2]) { ++rnk[k1]; } prv[k2] = k1; } else { prv[k1] = k2; } } } void dfs(int vertex, int lst) { for (int i = 1; i < 19; ++i) { LCA[vertex][i] = LCA[LCA[vertex][i - 1]][i - 1]; mx[vertex][i] = max(mx[vertex][i - 1], mx[LCA[vertex][i - 1]][i - 1]); } int sz = v[vertex].size(); for (int i = 0; i < sz; ++i) { if (v[vertex][i].first == lst) { continue; } LCA[v[vertex][i].first][0] = vertex; mx[v[vertex][i].first][0] = v[vertex][i].second; lvl[v[vertex][i].first] = lvl[vertex] + 1; dfs(v[vertex][i].first, vertex); } } long long f(int x, int y) { long long ret = 0; for (int i = 19 - 1; i >= 0; --i) { if (lvl[x] - (1 << i) >= lvl[y]) { ret = max(ret, mx[x][i]); x = LCA[x][i]; } if (lvl[y] - (1 << i) >= lvl[x]) { ret = max(ret, mx[y][i]); y = LCA[y][i]; } } for (int i = 19 - 1; i >= 0; --i) { if (LCA[x][i] != LCA[y][i]) { ret = max(ret, mx[x][i]); x = LCA[x][i]; ret = max(ret, mx[y][i]); y = LCA[y][i]; } } if (x != y) { ret = max(ret, mx[x][0]); ret = max(ret, mx[y][0]); } return ret; } void input() { cin >> n >> m >> k >> q; for (int i = 1; i <= m; ++i) { int x, y, z; cin >> x >> y >> z; gr[x].push_back({y, z}); gr[y].push_back({x, z}); } } void solve() { dijkstra(); for (int i = 1; i <= n; ++i) { int sz = gr[i].size(); for (int j = 0; j < sz; ++j) { int h = gr[i][j].first; int c = gr[i][j].second; if (ori[h] != ori[i] && ori[h] < ori[i]) { srt.push_back(edge(ori[h], ori[i], opt[i] + opt[h] + c)); } } } sort(srt.begin(), srt.end()); for (int i = 1; i <= n; ++i) { prv[i] = -1; } int sz = srt.size(); for (int i = 0; i < sz; ++i) { unite(srt[i]); } dfs(1, -1); while (q--) { int x, y; cin >> x >> y; cout << f(x, y) << "\n"; } } int main() { ios_base ::sync_with_stdio(false); cin.tie(NULL); input(); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; struct UnionFind { vector<int> nxt; void init(int x) { nxt.clear(); nxt.resize(x); for (int i = 0; i < x; i++) { nxt[i] = i; } } int find(int x) { if (nxt[x] == x) return x; return nxt[x] = find(nxt[x]); } inline void unite(int x, int y) { nxt[find(y)] = find(x); } }; long long N, M, K, Q; vector<pair<long long, long long>> uvt[101010], cnt[101010], subcnt[101010]; long long dps[101010]; pair<long long, long long> pc[101010][30]; long long i, j, k, ans; void crecntg() { priority_queue<pair<long long, pair<long long, long long>>> pq; vector<pair<long long, long long>> mk(N + 2, {0, 0}); long long ct = 0; for (i = 0; i < K; i++) { pq.push({0, {i + 1, i + 1}}); } while (pq.size()) { auto qa = pq.top(); pq.pop(); long long c = qa.first; long long a = qa.second.first; long long p = qa.second.second; if (mk[a].second != 0) { if (mk[a].second == p) continue; subcnt[p].push_back({mk[a].second, mk[a].first - c}); subcnt[mk[a].second].push_back({p, mk[a].first - c}); continue; } mk[a] = {-c, p}; for (i = 0; i < uvt[a].size(); i++) { auto b = uvt[a][i]; if (mk[b.first].second == p) continue; pq.push({c - b.second, {b.first, p}}); } } } void krus() { priority_queue<pair<long long, pair<long long, long long>>> pq; UnionFind uf; uf.init(K + 1); long long i, j; for (i = 0; i < K; i++) { for (j = 0; j < subcnt[i + 1].size(); j++) { pq.push({-subcnt[i + 1][j].second, {i + 1, subcnt[i + 1][j].first}}); } } while (pq.size()) { auto qa = pq.top(); pq.pop(); long long a = qa.second.first; long long b = qa.second.second; if (uf.find(a) == uf.find(b)) continue; cnt[a].push_back({b, -qa.first}); cnt[b].push_back({a, -qa.first}); uf.unite(a, b); } } void dfs(long long a, long long p, long long c, long long d) { long long i = 0; dps[a] = d; pc[a][0] = {p, c}; for (i = 0; i < cnt[a].size(); i++) { if (cnt[a][i].first != p) dfs(cnt[a][i].first, a, cnt[a][i].second, d + 1); } } void setpp() { long long i, j; for (i = 0; i < 20; i++) { for (j = 0; j < K; j++) { pair<long long, long long> b = pc[j + 1][i]; pair<long long, long long> c = pc[b.first][i]; pc[j + 1][i + 1] = {c.first, max(c.second, b.second)}; } } } void solve() { long long a, b; scanf("%lld%lld", &a, &b); if (dps[a] > dps[b]) { swap(a, b); } long long acp = 0, bcp = 0; long long i; for (i = 20; i >= 0; i--) { if (dps[b] - (1 << i) >= dps[a]) { bcp = max(pc[b][i].second, bcp); b = pc[b][i].first; } } if (a == b) { printf("%lld\n", bcp); return; } for (i = 20; i >= 0; i--) { if (pc[a][i].first != pc[b][i].first) { acp = max(pc[a][i].second, acp); bcp = max(pc[b][i].second, bcp); a = pc[a][i].first; b = pc[b][i].first; } } acp = max(pc[a][0].second, acp); bcp = max(pc[b][0].second, bcp); printf("%lld\n", max(acp, bcp)); } int main() { scanf("%lld%lld%lld%lld", &N, &M, &K, &Q); for (i = 0; i < M; i++) { long long u, v, w; scanf("%lld%lld%lld", &u, &v, &w); uvt[u].push_back({v, w}); uvt[v].push_back({u, w}); } crecntg(); krus(); dfs(1, 0, 0, 1); setpp(); while (Q--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MAXN = 3e5 + 5; long long k, n, m, q, ta, tb, tc; long long dis[MAXN]; long long dkt[MAXN]; long long dep[MAXN]; long long ma[22][MAXN]; long long p[22][MAXN]; vector<long long> v0[MAXN]; vector<long long> w0[MAXN]; vector<long long> v[MAXN]; vector<long long> w[MAXN]; vector<pair<long long, pair<long long, long long> > > isi; long long P[MAXN]; void djik() { priority_queue<pair<long long, pair<long long, long long> > > pq; for (long long i = 1; i <= n; i++) { dis[i] = 1e18; if (i <= k) { dis[i] = 0; dkt[i] = i; pq.push(make_pair(0, make_pair(i, i))); } } while (!pq.empty()) { long long jar = -pq.top().first; long long u = pq.top().second.first; long long dk = pq.top().second.second; pq.pop(); for (long long i = 0; i < v0[u].size(); i++) { long long nx = v0[u][i]; long long wx = jar + w0[u][i]; if (dis[nx] > wx) { dis[nx] = wx; dkt[nx] = dk; pq.push(make_pair(-wx, make_pair(nx, dk))); } else if (dkt[nx] != dk) { isi.push_back(make_pair(dis[nx] + wx, make_pair(dkt[nx], dk))); } } } } void dfs(long long pos, long long par, long long dlm) { dep[pos] = dlm; p[0][pos] = par; for (long long i = 1; i <= 20; i++) { p[i][pos] = p[i - 1][p[i - 1][pos]]; ma[i][pos] = max(ma[i - 1][pos], ma[i - 1][p[i - 1][pos]]); } for (long long i = 0; i < v[pos].size(); i++) { long long nx = v[pos][i]; if (nx == par) continue; ma[0][nx] = w[pos][i]; dfs(nx, pos, dlm + 1); } } long long LCA(long long A, long long B) { long long H = 0; if (dep[A] < dep[B]) swap(A, B); for (long long i = 20; i >= 0; i--) if (dep[A] - (1 << i) >= dep[B]) { H = max(H, ma[i][A]); A = p[i][A]; } if (A == B) return H; for (long long i = 20; i >= 0; i--) if (p[i][A] != p[i][B]) { H = max(H, ma[i][A]); H = max(H, ma[i][B]); A = p[i][A]; B = p[i][B]; } H = max(H, ma[0][A]); H = max(H, ma[0][B]); return H; } long long car(long long A) { if (P[A] == A) return A; else return P[A] = car(P[A]); } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (long long i = 1; i <= m; i++) { P[i] = i; cin >> ta >> tb >> tc; v0[ta].push_back(tb); w0[ta].push_back(tc); v0[tb].push_back(ta); w0[tb].push_back(tc); } djik(); sort(isi.begin(), isi.end()); for (long long i = 0; i < isi.size(); i++) { if (car(isi[i].second.first) != car(isi[i].second.second)) { v[isi[i].second.first].push_back(isi[i].second.second); w[isi[i].second.first].push_back(isi[i].first); v[isi[i].second.second].push_back(isi[i].second.first); w[isi[i].second.second].push_back(isi[i].first); P[car(isi[i].second.first)] = car(isi[i].second.second); } } dfs(1, 1, 0); while (q--) { cin >> ta >> tb; cout << LCA(ta, tb) << "\n"; } }
#include <bits/stdc++.h> #pragma GCC target("avx2") #pragma GCC optimization("O3") #pragma GCC optimization("unroll-loops") const long long INF = 0x3f3f3f3f3f3f3f3f; const long long llinf = (1LL << 62); const int inf = (1 << 30); const int nmax = 3e5 + 50; const long long mod = 1e9 + 7; using namespace std; int n, m, k, q, i, x, y, sz[nmax], p[nmax], ex[nmax], ey[nmax]; long long w, ew[nmax], d[nmax], rs[nmax]; vector<pair<int, int> > qr[nmax], tmp; vector<pair<int, long long> > a[nmax]; vector<pair<long long, pair<int, int> > > vc; set<pair<long long, int> > s; vector<int> v[nmax]; int fnd(int x) { if (p[x] == x) return x; return p[x] = fnd(p[x]); } void uni(int x, int y, long long w) { x = fnd(x), y = fnd(y); if (sz[x] < sz[y]) swap(x, y); int u; for (int i = 0; i < (int)v[y].size(); i++) { u = v[y][i]; tmp.clear(); for (int j = 0; j < (int)qr[u].size(); j++) { if (fnd(qr[u][j].first) == x) rs[qr[u][j].second] = w; else tmp.push_back(qr[u][j]); } qr[u] = tmp; v[x].push_back(u); } v[y].clear(); sz[x] += sz[y]; p[y] = x; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cerr.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (i = 1; i <= m; i++) { cin >> ex[i] >> ey[i] >> ew[i]; a[ex[i]].push_back(make_pair(ey[i], ew[i])); a[ey[i]].push_back(make_pair(ex[i], ew[i])); } for (i = k + 1; i <= n; i++) d[i] = llinf; for (i = 1; i <= k; i++) s.insert(make_pair(d[i], i)); while (!s.empty()) { x = s.begin()->second; s.erase(s.begin()); for (i = 0; i < (int)a[x].size(); i++) { y = a[x][i].first, w = a[x][i].second; if (d[y] > d[x] + w) { if (d[y] != llinf) s.erase(s.find(make_pair(d[y], y))); d[y] = d[x] + w; s.insert(make_pair(d[y], y)); } } } for (i = 1; i <= m; i++) { vc.push_back( make_pair(d[ex[i]] + d[ey[i]] + ew[i], make_pair(ex[i], ey[i]))); } sort(vc.begin(), vc.end()); for (i = 1; i <= q; i++) { cin >> x >> y; qr[x].push_back(make_pair(y, i)); qr[y].push_back(make_pair(x, i)); } for (i = 1; i <= n; i++) { sz[i] = 1; p[i] = i; v[i].push_back(i); } for (i = 0; i < m; i++) { x = vc[i].second.first, y = vc[i].second.second, w = vc[i].first; if (fnd(x) == fnd(y)) continue; uni(x, y, w); } for (i = 1; i <= q; i++) cout << rs[i] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; using P = pair<int, long long>; using LL = long long; const int Maxn = 1e5 + 20, Maxm = (3e5 + 20) * 3; const LL inf = 0x3f3f3f3f3f3f3f3f; struct edge { int next, from, to; LL cost; bool operator<(const edge& val) const { return cost < val.cost; } } es[Maxm]; int head[Maxn], cnt; void addedge(int u, int v, LL w) { es[cnt].next = head[u]; es[cnt].from = u; es[cnt].to = v; es[cnt].cost = w; head[u] = cnt++; } int n, m, k, q; vector<P> ee[Maxn]; LL dis[Maxn]; void dijkstra() { memset(dis, inf, sizeof(dis)); priority_queue<P, vector<P>, greater<P>> que; for (int i = 1; i <= k; ++i) { dis[i] = 0; que.push(P(0, i)); } while (!que.empty()) { P tmp = que.top(); que.pop(); int u = tmp.second; if (dis[u] < tmp.first) continue; for (auto xx : ee[u]) { int v = xx.first; LL w = xx.second; if (dis[v] > dis[u] + w) { dis[v] = dis[u] + w; que.push(P(dis[v], v)); } } } for (int u = 1; u <= n; ++u) { for (auto xx : ee[u]) { int v = xx.first; LL w = xx.second; addedge(u, v, w + dis[v] + dis[u]); } } } int Par[Maxn], Rank[Maxn]; int Find(int x) { if (Par[x] == -1) return x; return Par[x] = Find(Par[x]); } void Unite(int x, int y) { x = Find(x), y = Find(y); if (x == y) return; if (Rank[x] < Rank[y]) { Par[x] = y; } else { Par[y] = x; if (Rank[x] == Rank[y]) Rank[x]++; } } bool isSame(int x, int y) { if (Find(x) == Find(y)) return true; return false; } vector<P> vs[Maxn]; void Kruskal() { sort(es, es + cnt); int u, v; for (int i = 0; i < cnt; ++i) { int u = es[i].from, v = es[i].to; LL w = es[i].cost; if (!isSame(u, v)) { Unite(u, v); vs[u].push_back(P(v, w)); vs[v].push_back(P(u, w)); } } } int anc[Maxn][21], dep[Maxn]; LL cost[Maxn][21]; void preLCA(int u = 1, int fa = 0) { for (int i = 1; (1 << i) <= dep[u]; ++i) { anc[u][i] = anc[anc[u][i - 1]][i - 1]; cost[u][i] = max(cost[u][i - 1], cost[anc[u][i - 1]][i - 1]); } for (auto tmp : vs[u]) { int v = tmp.first; if (v == fa) continue; dep[v] = dep[u] + 1; anc[v][0] = u; cost[v][0] = tmp.second; preLCA(v, u); } } int LCA(int a, int b) { if (dep[a] > dep[b]) swap(a, b); for (int i = 20; i >= 0; --i) { if (dep[a] <= dep[b] - (1 << i)) b = anc[b][i]; } if (a == b) return a; for (int i = 20; i >= 0; --i) { if (anc[a][i] == anc[b][i]) continue; else a = anc[a][i], b = anc[b][i]; } return anc[b][0]; } LL getMax(int u, int sta) { LL res = 0; for (int i = 0; i <= 20; ++i) { if (sta & (1 << i)) res = max(res, cost[u][i]), u = anc[u][i]; } return res; } void init() { cnt = 0; memset(head, -1, sizeof(head)); memset(Par, -1, sizeof(Par)); memset(Rank, 0, sizeof(Rank)); memset(anc, 0, sizeof(anc)); } int main() { ios::sync_with_stdio(false); init(); cin >> n >> m >> k >> q; int u, v; LL w; for (int i = 0; i < m; ++i) { cin >> u >> v >> w; ee[u].push_back(P(v, w)); ee[v].push_back(P(u, w)); } dijkstra(); Kruskal(); preLCA(); int x, y; int lca; while (q--) { cin >> x >> y; lca = LCA(x, y); cout << max(getMax(x, dep[x] - dep[lca]), getMax(y, dep[y] - dep[lca])) << '\n'; } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize "03" using namespace std; const long long int N = 1e5 + 5; const long long int mod = 1e9 + 7; const long long int inf = 1e18 + 9; long long int dis[N], par[N], dep[N], p[N][18], dp[N][18]; vector<pair<long long int, long long int> > g[N], h[N]; vector<pair<pair<long long int, long long int>, long long int> > ed; vector<pair<long long int, pair<long long int, long long int> > > mst; long long int root(long long int x) { return (par[x] == x) ? x : par[x] = root(par[x]); } void merge(long long int x, long long int y) { x = root(x); y = root(y); par[x] = y; } void dfs(long long int u, long long int pp) { dep[u] = dep[pp] + 1; for (auto i : h[u]) { if (i.first == pp) continue; p[i.first][0] = u; dp[i.first][0] = i.second; dfs(i.first, u); } } long long int query(long long int a, long long int b) { if (dep[a] <= dep[b]) swap(a, b); long long int ans = 0; for (long long int i = 17; i >= 0; i--) { if (dep[p[a][i]] >= dep[b]) ans = max(ans, dp[a][i]), a = p[a][i]; } if (a == b) return ans; for (long long int i = 17; i >= 0; i--) { if (p[a][i] == p[b][i]) continue; ans = max(ans, dp[a][i]); ans = max(ans, dp[b][i]); a = p[a][i]; b = p[b][i]; } ans = max(ans, dp[a][0]); ans = max(ans, dp[b][0]); return ans; } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long int n, mm, k, q; cin >> n >> mm >> k >> q; for (long long int i = 1; i <= mm; i++) { long long int u, v, w; cin >> u >> v >> w; g[u].push_back({v, w}); g[v].push_back({u, w}); ed.push_back({{u, v}, w}); } multiset<pair<long long int, pair<long long int, long long int> > > m; for (long long int i = 1; i <= n; i++) { if (i <= k) m.insert({0, {i, i}}), dis[i] = 0; else dis[i] = inf; } while (!m.empty()) { auto x = *m.begin(); m.erase(m.begin()); if (dis[x.second.first] != x.first) continue; par[x.second.first] = x.second.second; for (auto i : g[x.second.first]) { if (dis[i.first] > dis[x.second.first] + i.second) { dis[i.first] = dis[x.second.first] + i.second; m.insert({dis[i.first], {i.first, x.second.second}}); } } } for (auto i : ed) { if (par[i.first.first] == par[i.first.second]) continue; mst.push_back({dis[i.first.first] + dis[i.first.second] + i.second, {par[i.first.first], par[i.first.second]}}); } for (long long int i = 1; i <= k; i++) par[i] = i; sort(mst.begin(), mst.end()); for (auto i : mst) { if (root(i.second.first) == root(i.second.second)) continue; merge(i.second.first, i.second.second); h[i.second.first].push_back({i.second.second, i.first}); h[i.second.second].push_back({i.second.first, i.first}); } dfs(1, 0); for (long long int j = 1; j < 18; j++) { for (long long int i = 1; i <= k; i++) { p[i][j] = p[p[i][j - 1]][j - 1]; dp[i][j] = max(dp[i][j - 1], dp[p[i][j - 1]][j - 1]); } } while (q--) { long long int a, b; cin >> a >> b; cout << query(a, b) << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long INF = 1e18 + 100; const int MAXP = 20; int n, m, k, q; vector<vector<pair<int, long long>>> g; vector<pair<pair<int, int>, long long>> sg; vector<pair<long long, pair<int, int>>> sg2; vector<int> pp; vector<vector<pair<int, long long>>> dp; vector<int> tin; vector<int> tout; vector<vector<pair<int, long long>>> g2; int ttm = 0; void dfs(int v, int p, long long x) { tin[v] = ttm++; dp[v].resize(MAXP); dp[v][0] = make_pair((p), (x)); for (int i = 1; i < MAXP; ++i) { dp[v][i].first = dp[dp[v][i - 1].first][i - 1].first; dp[v][i].second = max(dp[v][i - 1].second, dp[dp[v][i - 1].first][i - 1].second); } for (auto e : g2[v]) { if (e.first != p) { dfs(e.first, v, e.second); } } tout[v] = ttm++; } bool ok(int v, int u) { return ((tin[v] <= tin[u]) && (tout[u] <= tout[v])); } long long dp_g(int v, int u) { if (ok(v, u)) return 0; long long ans = 0; for (int i = MAXP - 1; i >= 0; --i) { if (!ok(dp[v][i].first, u)) { ans = max(ans, dp[v][i].second); v = dp[v][i].first; } } return max(ans, dp[v][0].second); } long long dp_get(int v, int u) { return max(dp_g(v, u), dp_g(u, v)); } void Init() { pp.resize(k); for (int i = 0; i < k; ++i) { pp[i] = i; } } int Get(int v) { if (pp[v] == v) { return v; } else { return (pp[v] = Get(pp[v])); } } void Union(int v, int u) { v = Get(v); u = Get(u); pp[u] = v; } int main() { ios::sync_with_stdio(false); cout.tie(0); cin.tie(0); cin >> n >> m >> k >> q; g.resize(n); for (int i = 0; i < m; ++i) { int v1, v2; long long x; cin >> v1 >> v2 >> x; v1--; v2--; g[v1].push_back(make_pair((v2), (x))); g[v2].push_back(make_pair((v1), (x))); sg.push_back(make_pair((make_pair((v1), (v2))), (x))); } set<pair<long long, int>> st; vector<long long> dist(n, INF); vector<int> p(n); for (int i = 0; i < k; ++i) { dist[i] = 0; p[i] = i; st.insert(make_pair((0), (i))); } while (!st.empty()) { int v = st.begin()->second; st.erase(st.begin()); for (auto e : g[v]) { int to = e.first; long long w = e.second; if (dist[to] > dist[v] + w) { p[to] = p[v]; st.erase(make_pair((dist[to]), (to))); dist[to] = dist[v] + w; st.insert(make_pair((dist[to]), (to))); } } } for (auto e : sg) { sg2.push_back( make_pair((dist[e.first.first] + dist[e.first.second] + e.second), (make_pair((p[e.first.first]), (p[e.first.second]))))); } sort(sg2.begin(), sg2.end()); g2.resize(k); Init(); for (auto e : sg2) { if (Get(e.second.first) != Get(e.second.second)) { g2[e.second.first].push_back(make_pair((e.second.second), (e.first))); g2[e.second.second].push_back(make_pair((e.second.first), (e.first))); Union(e.second.first, e.second.second); } } dp.resize(k); tin.resize(k); tout.resize(k); dfs(0, 0, 0); while (q--) { int a, b; cin >> a >> b; a--; b--; cout << dp_get(a, b) << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const int NR = 1e6 + 10; void Min(long long& x, long long y) { x = min(x, y); } void Max(long long& x, long long y) { x = max(x, y); } int read() { int x = 0, f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 3) + (x << 1) + (ch ^ 48); ch = getchar(); } return x * f; } int n, m, k, q, S; struct Edge { int u, v; long long w; bool operator<(const Edge& A) const { return w < A.w; } } e[NR]; int to[NR], nxt[NR], head[NR], tot = 1; long long val[NR]; void add(int x, int y, long long z) { to[tot] = y, val[tot] = z, nxt[tot] = head[x], head[x] = tot++; } struct Nd { int x; long long d; bool operator<(const Nd& A) const { return d > A.d; } }; Nd md(int x, long long d) { Nd tmp; tmp.x = x, tmp.d = d; return tmp; } bool vis[NR]; long long dis[NR]; void dijkstra() { memset(vis, 0, sizeof(vis)); memset(dis, 0x3f, sizeof(dis)); priority_queue<Nd> q; q.push(md(S, 0)); dis[S] = 0; while (!q.empty()) { int x = q.top().x; q.pop(); if (vis[x]) continue; vis[x] = 1; for (int i = head[x]; i; i = nxt[i]) { int y = to[i]; if (dis[y] > dis[x] + val[i]) dis[y] = dis[x] + val[i], q.push(md(y, dis[y])); } } } struct bcj { int fa[NR]; void init() { for (int i = 1; i <= n; i++) fa[i] = i; } int find(int x) { return (x == fa[x]) ? x : fa[x] = find(fa[x]); } bool merge(int x, int y) { int fx = find(x), fy = find(y); if (fx == fy) return 0; fa[fx] = fy; return 1; } } T; void rebuild() { memset(head, 0, sizeof(head)); tot = 1; sort(e + 1, e + m + 1); T.init(); int cnt = 0; for (int i = 1; i <= m; i++) { if (cnt >= n - 1) return; if (T.merge(e[i].u, e[i].v)) add(e[i].u, e[i].v, e[i].w), add(e[i].v, e[i].u, e[i].w), cnt++; } } int lg[NR], dep[NR], f[NR][20]; long long g[NR][20]; void dfs(int x, int fa_, long long v) { dep[x] = dep[fa_] + 1; f[x][0] = fa_; g[x][0] = v; for (int i = 1; i <= lg[dep[x]]; i++) f[x][i] = f[f[x][i - 1]][i - 1], g[x][i] = max(g[x][i - 1], g[f[x][i - 1]][i - 1]); for (int i = head[x]; i; i = nxt[i]) if (to[i] != fa_) dfs(to[i], x, val[i]); } long long getmx(int x, int y) { long long res = 0; if (dep[x] < dep[y]) swap(x, y); while (dep[x] > dep[y]) Max(res, g[x][lg[dep[x] - dep[y]] - 1]), x = f[x][lg[dep[x] - dep[y]] - 1]; if (x == y) return res; for (int i = lg[dep[x]]; i >= 0; i--) if (f[x][i] ^ f[y][i]) Max(res, g[x][i]), Max(res, g[y][i]), x = f[x][i], y = f[y][i]; return max(res, max(g[x][0], g[y][0])); } int main() { n = read(), m = read(), k = read(), q = read(); for (int i = 1; i <= m; i++) { e[i].u = read(), e[i].v = read(), e[i].w = read(); add(e[i].u, e[i].v, e[i].w), add(e[i].v, e[i].u, e[i].w); } for (int i = 1; i <= k; i++) add(S, i, 0); dijkstra(); for (int i = 1; i <= m; i++) e[i].w += dis[e[i].u] + dis[e[i].v]; for (int i = 1; i <= n; i++) lg[i] = (lg[i - 1] + ((1 << lg[i - 1]) == i)); rebuild(); dfs(1, 0, 0); for (int i = 1; i <= q; i++) { int x = read(), y = read(); printf("%lld\n", getmx(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = (int)1e5 + 100; const int mod = (int)1e9 + 7; const long long INF = (long long)2e18; int n, m, k, q, fa[maxn]; long long dis[maxn], ans[maxn * 6]; vector<pair<int, long long> > g[maxn * 6]; vector<pair<int, int> > que[maxn]; vector<tuple<long long, int, int> > e; set<int> ele[maxn]; void dij() { priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > Q; for (int i = (1); i <= (n); ++i) { if (i <= k) Q.push({0, i}); else dis[i] = INF; } while (!Q.empty()) { int u = Q.top().second, d = Q.top().first; Q.pop(); if (d > dis[u]) continue; for (auto [v, w] : g[u]) { if (dis[u] + w < dis[v]) { dis[v] = dis[u] + w; Q.push({dis[v], v}); } } } } void init() { for (int i = (1); i <= (n); ++i) fa[i] = i, ele[i].insert(i); } int find(int x) { return x == fa[x] ? x : fa[x] = find(fa[x]); } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = (1); i <= (m); ++i) { int u, v; long long w; scanf("%d%d%lld", &u, &v, &w); g[u].push_back({v, w}); g[v].push_back({u, w}); } dij(); for (int u = (1); u <= (n); ++u) for (auto [v, w] : g[u]) if (u < v) e.push_back({dis[u] + dis[v] + w, u, v}); sort(e.begin(), e.end()); for (int i = (1); i <= (q); ++i) { int u, v; scanf("%d%d", &u, &v); que[u].push_back({v, i}); que[v].push_back({u, i}); } init(); for (auto [w, x, y] : e) { x = find(x); y = find(y); if (x == y) continue; if (ele[x].size() < ele[y].size()) swap(x, y); fa[y] = x; for (auto u : ele[y]) for (auto [v, id] : que[u]) if (ele[x].count(v)) ans[id] = w; for (auto u : ele[y]) ele[x].insert(u); } for (int i = (1); i <= (q); ++i) printf("%lld\n", ans[i]); }
#include <bits/stdc++.h> using namespace std; const long long N = 1e5 + 100; const long long M = 21; const long long mod = 1e9 + 7; const long long MOD = 998244353; const long long P = 1336; const long double eps = 0.000000001; const long long inf = 1e16 + 7; mt19937 gen(chrono::high_resolution_clock::now().time_since_epoch().count()); vector<pair<long long, long long> > g[N], ng[N]; long long sz[N], pr[N], tin[N], tout[N]; long long tim = 0; pair<long long, long long> w[N][M]; long long r[N]; long long get(long long v) { if (pr[v] == v) return v; return pr[v] = get(pr[v]); } void unite(long long a, long long b) { a = get(a); b = get(b); if (a == b) return; if (sz[a] < sz[b]) swap(a, b); sz[a] += sz[b]; pr[b] = a; } void DFS(long long v, long long pr, long long zn) { w[v][0].first = pr; w[v][0].second = zn; for (long long i = 1; i < M; i++) { w[v][i].first = w[w[v][i - 1].first][i - 1].first; w[v][i].second = max(w[v][i - 1].second, w[w[v][i - 1].first][i - 1].second); } tim++; tin[v] = tim; for (auto to : ng[v]) { if (to.first == pr) continue; DFS(to.first, v, to.second); } tim++; tout[v] = tim; } bool upper(long long a, long long b) { return ((tin[a] <= tin[b]) && (tout[a] >= tout[b])); } long long LCA(long long a, long long b) { if (upper(b, a)) swap(a, b); long long mx = 0; for (long long i = M - 1; i >= 0; i--) { if (!upper(w[b][i].first, a)) { mx = max(mx, w[b][i].second); b = w[b][i].first; } } mx = max(mx, w[b][0].second); b = w[b][0].first; for (long long i = M - 1; i >= 0; i--) { if (!upper(w[a][i].first, b)) { mx = max(mx, w[a][i].second); a = w[a][i].first; } } if (a != b) mx = max(mx, w[a][0].second); return mx; } int32_t main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); srand(time(0)); long long n, m, k, T; cin >> n >> m >> k >> T; for (long long i = 0; i < m; i++) { long long x, y, z; cin >> x >> y >> z; x--; y--; g[x].push_back({y, z}); g[y].push_back({x, z}); } for (long long i = 0; i < n; i++) { r[i] = inf; } priority_queue<pair<long long, long long> > q; for (long long i = 0; i < k; i++) { q.push({0, i}); } while (!q.empty()) { long long v = q.top().second; long long ra = q.top().first; ra = -ra; q.pop(); if (ra > r[v]) continue; r[v] = ra; for (auto to : g[v]) { if (r[to.first] > r[v] + to.second) { r[to.first] = r[v] + to.second; q.push({-r[to.first], to.first}); } } } vector<pair<long long, pair<long long, long long> > > e; for (long long i = 0; i < n; i++) { for (auto to : g[i]) { e.push_back({r[i] + r[to.first] + to.second, {i, to.first}}); } } for (long long i = 0; i < n; i++) { pr[i] = i; sz[i] = 1; } sort(e.begin(), e.end()); for (auto to : e) { if (get(to.second.first) != get(to.second.second)) { unite(to.second.first, to.second.second); ng[to.second.first].push_back({to.second.second, to.first}); ng[to.second.second].push_back({to.second.first, to.first}); } } DFS(0, 0, 0); while (T--) { long long a, b; cin >> a >> b; a--; b--; cout << LCA(a, b) << '\n'; } }
#include <bits/stdc++.h> using namespace std; struct ed { long long u; long long v; long long cost; bool operator<(const ed &e) const { return cost < e.cost; } }; int n, m, k, q; long long dist[300004]; int tin[300004], tout[300004], cnt, f[300004], sz[300004]; vector<ed> edges; vector<pair<long long, long long> > graph[300004]; vector<pair<long long, long long> > mst[300004]; int par[300004][30]; long long wei[300004][30]; int fath(int x) { return (f[x] == x) ? x : fath(f[x]); } bool is_same_set(int x, int y) { int fx = fath(x); int fy = fath(y); return fx == fy; } void join(int x, int y) { int fx = fath(x); int fy = fath(y); if (sz[fy] < sz[fx]) swap(fx, fy); sz[fy] += sz[fx]; f[fx] = fy; return; } void dijkstra() { for (int i = k + 1; i < n + 1; i++) dist[i] = 1e18; priority_queue<pair<long long, long long> > pq; for (int i = 1; i < k + 1; i++) pq.push(make_pair(0, i)); while (!pq.empty()) { pair<long long, long long> cur = pq.top(); pq.pop(); cur.first *= -1; if (cur.first > dist[cur.second]) continue; for (int i = 0; i < graph[cur.second].size(); i++) { int v = graph[cur.second][i].first; long long c = graph[cur.second][i].second; if (dist[v] > cur.first + c) { dist[v] = cur.first + c; pq.push(make_pair(-dist[v], v)); } } } return; } void init(int cur, int p) { par[cur][0] = p; tin[cur] = cnt++; for (int i = 0; i < mst[cur].size(); i++) { int v = mst[cur][i].first; long long c = mst[cur][i].second; if (v == p) continue; wei[v][0] = c; init(v, cur); } tout[cur] = cnt; return; } bool is_ancestor(int x, int y) { return (tin[x] <= tin[y] && tout[x] >= tout[y]); } int get_par(int node, int p) { if (par[node][p] != -1) return par[node][p]; return par[node][p] = get_par(get_par(node, p - 1), p - 1); } long long get_wei(int node, int p) { if (wei[node][p] != -1) return wei[node][p]; return wei[node][p] = max(get_wei(get_par(node, p - 1), p - 1), get_wei(node, p - 1)); } int get_lca(int x, int y) { if (is_ancestor(x, y)) return x; if (is_ancestor(y, x)) return y; for (int i = 29; i >= 0; i--) { if (!is_ancestor(get_par(x, i), y)) x = get_par(x, i); } return get_par(x, 0); } long long solve(int x, int y) { int lca = get_lca(x, y); long long ans = 0; for (int i = 29; i >= 0; i--) { if (!is_ancestor(get_par(x, i), lca)) { ans = max(ans, get_wei(x, i)); x = get_par(x, i); } } if (!is_ancestor(x, lca)) ans = max(ans, get_wei(x, 0)); for (int i = 29; i >= 0; i--) { if (!is_ancestor(get_par(y, i), lca)) { ans = max(ans, get_wei(y, i)); y = get_par(y, i); } } if (!is_ancestor(y, lca)) ans = max(ans, get_wei(y, 0)); return ans; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cin >> n >> m >> k >> q; for (int i = 0; i < m; i++) { int a, b; long long c; cin >> a >> b >> c; graph[a].push_back(make_pair(b, c)); graph[b].push_back(make_pair(a, c)); } dijkstra(); for (int i = 1; i < n + 1; i++) { for (int j = 0; j < graph[i].size(); j++) { long long v = graph[i][j].first; if (v < i) continue; edges.push_back({i, v, dist[i] + dist[v] + graph[i][j].second}); } } sort(edges.begin(), edges.end()); for (int i = 1; i < n + 1; i++) { sz[i] = 1; f[i] = i; } for (int i = 0; i < edges.size(); i++) { int u = edges[i].u; int v = edges[i].v; long long cost = edges[i].cost; if (!is_same_set(u, v)) { join(u, v); mst[u].push_back(make_pair(v, cost)); mst[v].push_back(make_pair(u, cost)); } } memset(par, -1, sizeof par); memset(wei, -1, sizeof wei); wei[1][0] = 0; init(1, 1); for (int i = 0; i < q; i++) { long long a, b; cin >> a >> b; cout << solve(a, b) << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = 1e9 + 5; const int MOD = 1e9 + 7; const int MAXN = 300005; struct Edge { int u, v; long long w; bool operator<(const Edge &e) const { return w > e.w; } }; int N, M, K, Q, vis[MAXN]; long long ans[MAXN], dist[MAXN]; vector<Edge> es, G[MAXN]; int pa[MAXN], sz[MAXN], root1[MAXN], root2[MAXN]; vector<int> qid[MAXN]; void init() { for (int i = 1; i <= N; i++) { pa[i] = i; sz[i] = 1; } } int find_root(int x) { return x == pa[x] ? x : pa[x] = find_root(pa[x]); } void merge(Edge e) { int u = find_root(e.u), v = find_root(e.v); if (u == v) return; if (sz[u] < sz[v]) swap(u, v); pa[v] = u; sz[u] += sz[v]; for (int q : qid[v]) { if (root1[q] == u || root2[q] == u) { root1[q] = root2[q] = -1; ans[q] = e.w; } else if (root1[q] != -1) { if (root1[q] == v) root1[q] = u; if (root2[q] == v) root2[q] = u; qid[u].push_back(q); } } qid[v].clear(); } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> N >> M >> K >> Q; for (int i = 0; i < M; i++) { int u, v, w; cin >> u >> v >> w; es.push_back({u, v, w}); G[u].push_back({u, v, w}); G[v].push_back({v, u, w}); } priority_queue<Edge> pq; for (int i = 1; i <= K; i++) { pq.push({-1, i, 0}); } while (!pq.empty()) { Edge e = pq.top(); pq.pop(); if (vis[e.v]) continue; vis[e.v] = 1; dist[e.v] = e.w; for (Edge e2 : G[e.v]) { if (!vis[e2.v]) { pq.push({-1, e2.v, e.w + e2.w}); } } } for (int i = 0; i < Q; i++) { int u, v; cin >> u >> v; qid[u].push_back(i); qid[v].push_back(i); root1[i] = u; root2[i] = v; } for (Edge &e : es) { e.w += dist[e.u] + dist[e.v]; } sort(es.begin(), es.end()); init(); for (int i = (int)es.size() - 1; i >= 0; i--) { merge(es[i]); } for (int i = 0; i < Q; i++) { cout << ans[i] << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { for (auto i = begin(v); i != end(v); i++) os << *i << (i == end(v) - 1 ? "" : " "); return os; } template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto i = begin(v); i != end(v); i++) is >> *i; return is; } int n, m, k, q; vector<pair<int, int>> edg[101000]; vector<long long> best_dists(101000, 10000000000000000LL); set<int> markers[101000]; int dsu[101000]; int drank[101000]; vector<long long> ans(301000, 10000000000000000LL); struct Edg { int u, v; long long w; }; int dsu_find(int a) { if (dsu[a] == a) return a; return dsu[a] = dsu_find(dsu[a]); } void dsu_union(int a, int b, long long curr_ans) { a = dsu_find(a); b = dsu_find(b); if (a == b) return; if (drank[a] >= drank[b]) { dsu[b] = a; drank[a] += drank[b]; } else { dsu[a] = b; swap(a, b); drank[a] += drank[b]; } if (markers[a].size() < markers[b].size()) swap(markers[a], markers[b]); for (int x : markers[b]) { if (markers[a].find(x) != markers[a].end()) { ans[x] = curr_ans; markers[a].erase(x); } else { markers[a].insert(x); } } } int main() { cin.tie(NULL); ios_base::sync_with_stdio(false); cout.tie(NULL); cin >> n >> m >> k >> q; vector<Edg> edges; for (int i = 0; i < m; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; edg[u].push_back({v, w}); edg[v].push_back({u, w}); edges.push_back(Edg{u, v, w}); } set<pair<long long, int>> ss; for (int i = 0; i < k; i++) { ss.insert({0, i}); best_dists[i] = 0; } while (ss.size() > 0) { auto curr = *ss.begin(); ss.erase(curr); for (auto x : edg[curr.second]) { long long new_dist = curr.first + x.second; if (new_dist < best_dists[x.first]) { ss.erase({best_dists[x.first], x.first}); best_dists[x.first] = new_dist; ss.insert({best_dists[x.first], x.first}); } } } for (int i = 0; i < m; i++) { edges[i].w += best_dists[edges[i].u] + best_dists[edges[i].v]; } sort(edges.begin(), edges.end(), [&](Edg& x, Edg& y) { return x.w < y.w; }); vector<pair<int, int>> qs(q); for (int i = 0; i < q; i++) { int a, b; cin >> a >> b; a--, b--; qs[i] = {a, b}; markers[a].insert(i); markers[b].insert(i); } for (int i = 0; i < n; i++) { dsu[i] = i; drank[i] = 1; } for (int i = 0; i < m; i++) { dsu_union(edges[i].u, edges[i].v, edges[i].w); } for (int i = 0; i < q; i++) cout << ans[i] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; vector<pair<int, unsigned long long> > g[300001]; pair<int, unsigned long long> dist[300001]; pair<int, int> queries[300001]; int done[300001]; set<int> mp[300001]; unsigned long long result[300001]; void merge(int xs, int ys, unsigned long long w) { for (set<int>::iterator it = mp[xs].begin(); it != mp[xs].end(); it++) { unsigned long long x = *it; if (mp[ys].find(x) == mp[ys].end()) { mp[ys].insert(x); } else { result[x] = w; } } } struct find_union { vector<int> S; find_union(int n) : S(n) { for (int i = 0; i < n; ++i) S[i] = i; } unsigned long long find(int a) { return S[a] == a ? a : (S[a] = find(S[a])); } bool unite(int a, int b) { a = find(a); b = find(b); if (a == b) return false; S[a] = b; return true; } }; int main() { int n, m, k, q; cin >> n >> m >> k >> q; unsigned long long inf = ULLONG_MAX; for (int i = 0; i < m; ++i) { int u, v, w; scanf("%d %d %d", &u, &v, &w); g[u].push_back(make_pair(v, w)); g[v].push_back(make_pair(u, w)); } for (int i = 0; i < q; ++i) { int a, b; scanf("%d %d", &a, &b); queries[i] = make_pair(a, b); } priority_queue<pair<unsigned long long, unsigned long long>, vector<pair<unsigned long long, unsigned long long> >, greater<pair<unsigned long long, unsigned long long> > > qu; for (int i = 1; i <= n; ++i) { dist[i].first = i; if (i <= k) dist[i].second = 0; else dist[i].second = inf; } for (int i = 1; i <= k; ++i) { qu.push(make_pair(0, i)); } while (!qu.empty()) { unsigned long long u = qu.top().second; qu.pop(); if (done[u] == 0) { done[u] = 1; for (int i = 0; i < g[u].size(); ++i) { unsigned long long v = g[u][i].first; if (done[v] == 0) { unsigned long long w = g[u][i].second; if (dist[v].second > dist[u].second + w) { dist[v].first = dist[u].first; dist[v].second = dist[u].second + w; qu.push(make_pair(dist[v].second, v)); } } } } } map<pair<unsigned long long, unsigned long long>, unsigned long long> e; for (unsigned long long v = 1; v <= n; ++v) { for (unsigned long long j = 0; j < g[v].size(); ++j) { unsigned long long u = g[v][j].first; if (dist[v].first != dist[u].first) { unsigned long long x = dist[v].first; unsigned long long y = dist[u].first; pair<unsigned long long, unsigned long long> p = make_pair(min(x, y), max(x, y)); unsigned long long cost = dist[v].second + dist[u].second + g[v][j].second; if (e.find(p) == e.end()) { e[p] = cost; } else if (e[p] > cost) { e[p] = cost; } } } } vector< pair<unsigned long long, pair<unsigned long long, unsigned long long> > > edges; for (map<pair<unsigned long long, unsigned long long>, unsigned long long>::iterator it = e.begin(); it != e.end(); ++it) { edges.push_back(make_pair(it->second, it->first)); } sort(edges.begin(), edges.end()); vector<pair<unsigned long long, pair<int, int> > > tree; find_union dsu(k + 1); for (int i = 0; i < edges.size(); ++i) { pair<int, int> ed = edges[i].second; if (dsu.find(ed.first) != dsu.find(ed.second)) { dsu.unite(ed.first, ed.second); tree.push_back(edges[i]); } } sort(tree.begin(), tree.end()); for (int i = 0; i < q; ++i) { int a = queries[i].first; int b = queries[i].second; mp[a].insert(i); mp[b].insert(i); } set<int> xs, ys; find_union un(k + 1); for (int i = 0; i < tree.size(); ++i) { int a = tree[i].second.first; int b = tree[i].second.second; unsigned long long w = tree[i].first; int x = un.find(a); int y = un.find(b); if (mp[x].size() < mp[y].size()) { merge(x, y, w); un.unite(x, y); } else { merge(y, x, w); un.unite(y, x); } } for (int i = 0; i < q; ++i) printf("%I64d\n", result[i]); }
#include <bits/stdc++.h> using namespace std; struct tree_edge { int u, v; long long w; bool friend operator<(tree_edge i, tree_edge j) { return i.w < j.w; } } edg[100039 * 3]; struct point { int u, v; long long w; bool friend operator<(point i, point j) { return i.w > j.w; } } stp; struct edge { int to, next; long long w; } grap[100039 << 3], tree[100039 << 1]; int n, m, k, q, tot[2], head[2][100039], fro[100039], fa[100039], dep[100039], gra[100039][17]; long long dis[100039], mx[100039][17]; priority_queue<point> que; void add(edge net[], int s, int u, int v, long long w) { net[++tot[s]] = (edge){v, head[s][u], w}, head[s][u] = tot[s]; net[++tot[s]] = (edge){u, head[s][v], w}, head[s][v] = tot[s]; } void dijkstra() { que.push((point){0, 0, 0}); while (!que.empty()) { stp = que.top(), que.pop(); if (dis[stp.v] == dis[n + 1]) { dis[stp.v] = stp.w; fro[stp.v] = (stp.v <= k ? stp.v : fro[stp.u]); for (int a = head[0][stp.v]; a; a = grap[a].next) { if (dis[grap[a].to] == dis[n + 1]) { que.push((point){stp.v, grap[a].to, stp.w + grap[a].w}); } } } } } int find(int k) { return fa[k] == k ? k : fa[k] = find(fa[k]); } void dfs(int pos) { dep[pos] = dep[gra[pos][0]] + 1; for (int a = 1, b = 2; b <= dep[pos]; a++, b <<= 1) { gra[pos][a] = gra[gra[pos][a - 1]][a - 1]; mx[pos][a] = max(mx[pos][a - 1], mx[gra[pos][a - 1]][a - 1]); } for (int a = head[1][pos]; a; a = tree[a].next) { if (tree[a].to != gra[pos][0]) { gra[tree[a].to][0] = pos; mx[tree[a].to][0] = tree[a].w; dfs(tree[a].to); } } } long long get_ans(int u, int v) { long long res = 0; if (dep[u] < dep[v]) swap(u, v); for (int a = 16; ~a; a--) { if (dep[gra[u][a]] >= dep[v]) { res = max(res, mx[u][a]); u = gra[u][a]; } } if (u == v) return res; for (int a = 16; ~a; a--) { if (gra[u][a] != gra[v][a]) { res = max(res, mx[u][a]), u = gra[u][a]; res = max(res, mx[v][a]), v = gra[v][a]; } } res = max(res, mx[u][0]); res = max(res, mx[v][0]); return res; } int main() { memset(dis, 63, sizeof(dis)); scanf("%d%d%d%d", &n, &m, &k, &q); for (int a = 1, b, c, d; a <= m; a++) { scanf("%d%d%d", &b, &c, &d); add(grap, 0, b, c, d); } for (int a = 1; a <= k; a++) { add(grap, 0, 0, a, 0); } dijkstra(); for (int a = 1; a <= n; a++) { for (int b = head[0][a]; b; b = grap[b].next) { if (grap[b].to && b % 2) { edg[b / 2 + 1].u = fro[a], edg[b / 2 + 1].v = fro[grap[b].to]; edg[b / 2 + 1].w = dis[a] + grap[b].w + dis[grap[b].to]; } } fa[a] = a; } sort(edg + 1, edg + m + 1); for (int a = 1, b, c; a <= m; a++) { b = find(edg[a].u), c = find(edg[a].v); if (b != c) { add(tree, 1, edg[a].u, edg[a].v, edg[a].w); fa[c] = b; } } dep[0] = -1, dfs(1); for (int a = 1, b, c; a <= q; a++) { scanf("%d%d", &b, &c); printf("%I64d\n", get_ans(b, c)); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class S, class T> ostream& operator<<(ostream& os, const pair<S, T>& p) { return os << "(" << p.first << ", " << p.second << ")"; } template <class T> ostream& operator<<(ostream& os, const vector<T>& p) { os << "[ "; for (auto& it : p) os << it << " "; return os << "]"; } template <class T> ostream& operator<<(ostream& os, const unordered_set<T>& p) { os << "[ "; for (auto& it : p) os << it << " "; return os << "]"; } template <class S, class T> ostream& operator<<(ostream& os, const unordered_map<S, T>& p) { os << "[ "; for (auto& it : p) os << it << " "; return os << "]"; } template <class T> ostream& operator<<(ostream& os, const set<T>& p) { os << "[ "; for (auto& it : p) os << it << " "; return os << "]"; } template <class T> ostream& operator<<(ostream& os, const multiset<T>& p) { os << "[ "; for (auto& it : p) os << it << " "; return os << "]"; } template <class S, class T> ostream& operator<<(ostream& os, const map<S, T>& p) { os << "[ "; for (auto& it : p) os << it << " "; return os << "]"; } template <class T> void dbs(string str, T t) { cerr << str << " : " << t << "\n"; } template <class T, class... S> void dbs(string str, T t, S... s) { long long idx = str.find(','); cerr << str.substr(0, idx) << " : " << t << ","; dbs(str.substr(idx + 1), s...); } template <class T> void prc(T a, T b) { cerr << "["; for (T i = a; i != b; ++i) { if (i != a) cerr << ", "; cerr << *i; } cerr << "]\n"; } long long power(long long x, long long y) { long long res = 1; while (y) { if (y & 1) res = (res * x) % 1000000007; y = y / 2, x = (x * x) % 1000000007; } return res % 1000000007; } struct UnionFind { long long n, set_size, *parent, *rank; UnionFind() {} UnionFind(long long a) { n = set_size = a; parent = new long long[n + 1]; rank = new long long[n + 1]; for (long long i = 1; i <= n; ++i) parent[i] = i, rank[i] = 1; } long long find(long long x) { if (x != parent[x]) return parent[x] = find(parent[x]); return x; } void merge(long long x, long long y) { long long xroot = find(x), yroot = find(y); if (xroot != yroot) { if (rank[xroot] >= rank[yroot]) { parent[yroot] = xroot; rank[xroot] += rank[yroot]; } else { parent[xroot] = yroot; rank[yroot] += rank[xroot]; } set_size -= 1; } } void reset() { set_size = n; for (long long i = 1; i <= n; i++) parent[i] = i, rank[i] = 1; } long long size() { return set_size; } void prll() { for (long long i = 1; i <= n; ++i) cout << i << " -> " << parent[i] << "\n"; } }; vector<vector<pair<long long, long long>>> g; bool vis[100001]; long long dis[100001]; long long col[100001]; class prioritize { public: bool operator()(pair<long long, long long>& p1, pair<long long, long long>& p2) { return p1.second > p2.second; } }; vector<vector<pair<long long, long long>>> kconnect; long long par[100100][19]; long long depth[100100]; long long dp[100100][19]; void dfs(long long nn, long long pp, long long dd, long long mm) { par[nn][0] = pp; dp[nn][0] = mm; depth[nn] = dd; for (long long i = 1; i <= 18; i++) { par[nn][i] = par[par[nn][i - 1]][i - 1]; dp[nn][i] = max(dp[nn][i - 1], dp[par[nn][i - 1]][i - 1]); } for (auto v : kconnect[nn]) { if (v.first == pp) continue; dfs(v.first, nn, dd + 1, v.second); } } long long lcalol(long long u, long long v) { if (depth[u] < depth[v]) swap(u, v); long long ans = 0; for (long long i = 18; i >= 0; i--) { if (depth[u] - depth[v] >= (1LL << i)) ans = max(ans, dp[u][i]), u = par[u][i]; } if (u == v) return ans; for (long long i = 18; i >= 0; i--) { if (par[u][i] != par[v][i]) { ans = max(ans, max(dp[u][i], dp[v][i])); u = par[u][i]; v = par[v][i]; } } ans = max(ans, max(dp[u][0], dp[v][0])); return ans; } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long n, m, k, q, i; cin >> n >> m >> k >> q; g.resize(n + 1); set<pair<long long, pair<long long, long long>>> edges; for (long long i = 0; i < m; i++) { long long a, b, c; cin >> a >> b >> c; g[a].emplace_back(b, c); g[b].emplace_back(a, c); } for (long long i = 1; i <= n; i++) { vis[i] = 0; dis[i] = 1e18; } priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, prioritize> pq; for (i = 1; i <= k; i++) { pq.push(make_pair(i, 0)); dis[i] = 0; col[i] = i; } while (!pq.empty()) { pair<long long, long long> top = pq.top(); pq.pop(); long long uu = top.first; long long vv = top.second; if (vis[uu]) continue; vis[uu] = 1; for (auto v : g[uu]) { if (vis[v.first]) { if (col[v.first] != col[uu]) { edges.insert(make_pair(dis[v.first] + dis[uu] + v.second, make_pair(min(col[uu], col[v.first]), max(col[uu], col[v.first])))); } } else { if (vv + v.second < dis[v.first]) { dis[v.first] = vv + v.second; col[v.first] = col[uu]; pq.push(make_pair(v.first, dis[v.first])); } } } } kconnect.resize(k + 1); UnionFind uf(k); long long sz = k; for (auto v : edges) { if (uf.find(v.second.first) != uf.find(v.second.second)) { kconnect[v.second.first].emplace_back(v.second.second, v.first); kconnect[v.second.second].emplace_back(v.second.first, v.first); uf.merge(v.second.first, v.second.second); sz--; } if (sz == 1) break; } dfs(1, 0, 0, 0); for (long long i = 0; i < q; i++) { long long a, b; cin >> a >> b; cout << lcalol(a, b) << "\n"; } }
#include <bits/stdc++.h> #pragma GCC target("avx2") #pragma GCC optimization("O3") #pragma GCC optimization("unroll-loops") const long long INF = 0x3f3f3f3f3f3f3f3f; const long long llinf = (1LL << 62); const int inf = (1 << 30); const int nmax = 3e5 + 50; const long long mod = 1e9 + 7; using namespace std; int n, m, k, q, i, x, y, sz[nmax], p[nmax], ex[nmax], ey[nmax]; long long w, ew[nmax], d[nmax], rs[nmax]; vector<pair<int, int> > qr[nmax], tmp; vector<pair<int, long long> > a[nmax]; vector<pair<long long, pair<int, int> > > vc; set<pair<long long, int> > s; vector<int> v[nmax]; int fnd(int x) { if (p[x] == x) return x; return p[x] = fnd(p[x]); } void uni(int x, int y, long long w) { x = fnd(x), y = fnd(y); if (sz[x] < sz[y]) swap(x, y); int u; for (int i = 0; i < (int)v[y].size(); i++) { u = v[y][i]; tmp.clear(); for (int j = 0; j < (int)qr[u].size(); j++) { if (fnd(qr[u][j].first) == x) rs[qr[u][j].second] = w; else tmp.push_back(qr[u][j]); } qr[u] = tmp; v[x].push_back(u); } for (int i = 0; i < (int)v[y].size(); i++) { u = v[y][i]; p[u] = x; } v[y].clear(); sz[x] += sz[y]; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cerr.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (i = 1; i <= m; i++) { cin >> ex[i] >> ey[i] >> ew[i]; a[ex[i]].push_back(make_pair(ey[i], ew[i])); a[ey[i]].push_back(make_pair(ex[i], ew[i])); } for (i = k + 1; i <= n; i++) d[i] = llinf; for (i = 1; i <= k; i++) s.insert(make_pair(d[i], i)); while (!s.empty()) { x = s.begin()->second; s.erase(s.begin()); for (i = 0; i < (int)a[x].size(); i++) { y = a[x][i].first, w = a[x][i].second; if (d[y] > d[x] + w) { if (d[y] != llinf) s.erase(s.find(make_pair(d[y], y))); d[y] = d[x] + w; s.insert(make_pair(d[y], y)); } } } for (i = 1; i <= m; i++) { vc.push_back( make_pair(d[ex[i]] + d[ey[i]] + ew[i], make_pair(ex[i], ey[i]))); } sort(vc.begin(), vc.end()); for (i = 1; i <= q; i++) { cin >> x >> y; qr[x].push_back(make_pair(y, i)); qr[y].push_back(make_pair(x, i)); } for (i = 1; i <= n; i++) { sz[i] = 1; p[i] = i; v[i].push_back(i); } for (i = 0; i < m; i++) { x = vc[i].second.first, y = vc[i].second.second, w = vc[i].first; if (fnd(x) == fnd(y)) continue; uni(x, y, w); } for (i = 1; i <= q; i++) cout << rs[i] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; using LL = long long; using PLI = pair<LL, int>; const LL INF = 1e18; class DSU { vector<int> par; int find(int u) { if (u == par[u]) return u; return par[u] = find(par[u]); } public: DSU(int n) : par(n) { iota(par.begin(), par.end(), 0); } bool merge(int u, int v) { u = find(u), v = find(v); if (u == v) return false; par[v] = u; return true; } }; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n, m, k, q; cin >> n >> m >> k >> q; vector<vector<PLI>> adj(n); vector<tuple<LL, int, int>> edges; for (int i = 0; i < m; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; edges.emplace_back(w, u, v); adj[u].emplace_back(w, v); adj[v].emplace_back(w, u); } vector<LL> dis(n, INF); vector<bool> done(n, false); vector<int> par(n, -1); priority_queue<PLI> heap; for (int u = 0; u < k; u++) { dis[u] = 0; par[u] = u; heap.emplace(0, u); } while (!heap.empty()) { int u = heap.top().second; heap.pop(); if (done[u]) continue; done[u] = true; for (auto [w, v] : adj[u]) { if (dis[v] > dis[u] + w) { dis[v] = dis[u] + w; par[v] = par[u]; heap.emplace(-dis[v], v); } } } vector<tuple<LL, int, int>> sub_edges; for (auto [w, u, v] : edges) { if (par[u] != par[v]) { sub_edges.emplace_back(dis[u] + dis[v] + w, par[u], par[v]); } } sort(sub_edges.begin(), sub_edges.end()); vector<vector<PLI>> tree(k); DSU dsu(k); for (auto [w, u, v] : sub_edges) { if (dsu.merge(u, v)) { tree[u].emplace_back(w, v); tree[v].emplace_back(w, u); } } const int LOG = 20; vector<vector<int>> anc(k, vector<int>(20, -1)); vector<vector<LL>> best(k, vector<LL>(20, 0)); vector<int> dep(k, 0); function<void(int, int, LL)> dfs = [&](int u, int p, LL pw) { dep[u] = dep[p] + 1; anc[u][0] = p; best[u][0] = pw; for (int i = 1; i < LOG; i++) { int v = anc[u][i - 1]; anc[u][i] = anc[v][i - 1]; best[u][i] = max(best[u][i - 1], best[v][i - 1]); } for (auto [w, v] : tree[u]) { if (v != p) { dfs(v, u, w); } } }; dfs(0, 0, 0); auto LCA = [&](int u, int v) { if (dep[u] > dep[v]) swap(u, v); int diff = dep[v] - dep[u]; for (int i = 0; i < LOG; i++) { if (diff & (1 << i)) { v = anc[v][i]; } } if (u == v) return u; for (int i = LOG - 1; i >= 0; i--) { int pu = anc[u][i], pv = anc[v][i]; if (pu != pv) { u = pu, v = pv; } } return anc[u][0]; }; auto get_path = [&](int u, int l) { int diff = dep[u] - dep[l]; LL res = 0; for (int i = 0; i < LOG; i++) { if (diff & (1 << i)) { res = max(res, best[u][i]); u = anc[u][i]; } } return res; }; while (q--) { int a, b; cin >> a >> b; a--, b--; int l = LCA(a, b); LL ans = max(get_path(a, l), get_path(b, l)); cout << ans << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = (int)1e5 + 100; const int mod = (int)1e9 + 7; const long long INF = (long long)1ll << 61; int n, m, k, q, fa[maxn]; long long dis[maxn], ans[maxn * 6]; vector<pair<int, long long> > g[maxn * 6]; vector<pair<int, int> > que[maxn]; vector<tuple<long long, int, int> > e; set<int> ele[maxn]; void dij() { priority_queue<pair<long long, int> > Q; for (int i = (1); i <= (n); ++i) { if (i <= k) Q.push({0, i}); else dis[i] = INF; } while (!Q.empty()) { int u = Q.top().second; Q.pop(); for (auto [v, w] : g[u]) { if (dis[u] + w < dis[v]) { dis[v] = dis[u] + w; Q.push({-dis[v], v}); } } } } void init() { for (int i = (1); i <= (n); ++i) fa[i] = i, ele[i].insert(i); } int find(int x) { return x == fa[x] ? x : fa[x] = find(fa[x]); } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = (1); i <= (m); ++i) { int u, v; long long w; scanf("%d%d%lld", &u, &v, &w); g[u].push_back({v, w}); g[v].push_back({u, w}); } dij(); for (int u = (1); u <= (n); ++u) for (auto [v, w] : g[u]) if (u < v) e.push_back({dis[u] + dis[v] + w, u, v}); sort(e.begin(), e.end()); for (int i = (1); i <= (q); ++i) { int u, v; scanf("%d%d", &u, &v); que[u].push_back({v, i}); que[v].push_back({u, i}); } init(); for (auto [w, x, y] : e) { x = find(x); y = find(y); if (x == y) continue; if (ele[x].size() < ele[y].size()) swap(x, y); fa[y] = x; for (auto u : ele[y]) for (auto [v, id] : que[u]) if (ele[x].count(v)) ans[id] = w; for (auto u : ele[y]) ele[x].insert(u); } for (int i = (1); i <= (q); ++i) printf("%lld\n", ans[i]); }
#include <bits/stdc++.h> using namespace std; struct data { int y, z, nxt; } e[600010]; struct edge { int x, y; long long z; } a[300010]; struct qwq { long long dis; int x; }; struct que { int x, y, id; } b[300010]; vector<que> v[200010]; bool operator<(const qwq &u, const qwq &v) { return u.dis > v.dis; } long long ans[300010]; long long dis[200010]; int siz[200010]; int head[200010]; bool vis[200010]; int f[200010]; priority_queue<qwq> q; int n, m, k, Q, cnt; void add(int x, int y, long long z) { cnt++; e[cnt].y = y; e[cnt].z = z; e[cnt].nxt = head[x]; head[x] = cnt; } bool cmp(edge x, edge y) { return x.z < y.z; } int find(int x) { return x != f[x] ? f[x] = find(f[x]) : x; } void dijkstra() { for (int i = 1; i <= k; i++) { q.push((qwq){0, i}); dis[i] = 0; } while (!q.empty()) { qwq x = q.top(); q.pop(), vis[x.x] = 0; for (int i = head[x.x]; i; i = e[i].nxt) { int y = e[i].y, z = e[i].z; if (dis[y] > dis[x.x] + z) { dis[y] = dis[x.x] + z; if (!vis[y]) { q.push((qwq){dis[y], y}); vis[y] = true; } } } } } int main() { int x, y, z; scanf("%d%d%d%d", &n, &m, &k, &Q); for (int i = 1; i <= n; i++) { dis[i] = 1e17; f[i] = i, siz[i] = 1; } for (int i = 1; i <= m; i++) { scanf("%d%d%lld", &a[i].x, &a[i].y, &a[i].z); add(a[i].x, a[i].y, a[i].z); add(a[i].y, a[i].x, a[i].z); } dijkstra(); for (int i = 1; i <= m; i++) a[i].z += dis[a[i].x] + dis[a[i].y]; sort(a + 1, a + m + 1, cmp); for (int i = 1; i <= Q; i++) { b[i].id = i; scanf("%d%d", &b[i].x, &b[i].y); v[b[i].x].push_back(b[i]); v[b[i].y].push_back(b[i]); } for (int i = 1; i <= m; i++) { int x = a[i].x, y = a[i].y; long long z = a[i].z; int fx = find(x), fy = find(y); if (fx == fy) continue; if (siz[fx] < siz[fy]) swap(fx, fy); f[fy] = fx, siz[fx] += siz[fy]; for (int j = 0; j < v[fy].size(); j++) { if (find(v[fy][j].x) == find(v[fy][j].y) && !ans[v[fy][j].id]) ans[v[fy][j].id] = z; else v[fx].push_back(v[fy][j]); } } for (int i = 1; i <= Q; i++) printf("%lld\n", ans[i]); }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 500; const int LOG = 20; int n, m, q, k; int v1[N], v2[N], w[N]; vector<pair<long long, int> > v[N], T[N]; long long dis[N]; int tko[N], par[N]; int lca[N][LOG], dep[N]; long long dp_lca[N][LOG]; int pr(int x) { if (par[x] == x) return x; return par[x] = pr(par[x]); } void mrg(int x, int y) { par[pr(x)] = pr(y); } void dfs(int x, int lst) { lca[x][0] = lst; dep[x] = dep[lst] + 1; for (pair<long long, int> nxt : T[x]) { if (nxt.second == lst) continue; dp_lca[nxt.second][0] = nxt.first; dfs(nxt.second, x); } } void precompute() { for (int j = 1; j < LOG; j++) { for (int i = 1; i <= n; i++) { lca[i][j] = lca[lca[i][j - 1]][j - 1]; dp_lca[i][j] = max(dp_lca[i][j - 1], dp_lca[lca[i][j - 1]][j - 1]); } } } long long get_lca(int x, int y) { long long ans = 0; if (dep[x] < dep[y]) swap(x, y); for (int i = LOG - 1; i >= 0; i--) if (dep[x] - (1 << i) >= dep[y]) { ans = max(ans, dp_lca[x][i]); x = lca[x][i]; } if (x == y) return ans; for (int i = LOG - 1; i >= 0; i--) if (lca[x][i] != lca[y][i]) { ans = max(ans, max(dp_lca[x][i], dp_lca[y][i])); x = lca[x][i], y = lca[y][i]; } return max(ans, max(dp_lca[x][0], dp_lca[y][0])); } void dijkstra() { memset(dis, -1, sizeof(dis)); set<pair<long long, int> > S; for (int i = 1; i <= k; i++) S.insert({0LL, i}), dis[i] = 0, tko[i] = i, par[i] = i; for (; !S.empty();) { pair<long long, int> cur = *S.begin(); S.erase(S.begin()); for (pair<long long, int> nxt : v[cur.second]) { if (dis[nxt.second] == -1 || dis[cur.second] + nxt.first < dis[nxt.second]) { if (dis[nxt.second] != -1) S.erase({dis[nxt.second], nxt.second}); dis[nxt.second] = dis[cur.second] + nxt.first; tko[nxt.second] = tko[cur.second]; S.insert({dis[nxt.second], nxt.second}); } } } } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 0; i < m; i++) { scanf("%d%d%d", v1 + i, v2 + i, w + i); v[v1[i]].push_back({w[i], v2[i]}); v[v2[i]].push_back({w[i], v1[i]}); } dijkstra(); vector<pair<long long, pair<int, int> > > edg; for (int i = 0; i < m; i++) { if (tko[v1[i]] != tko[v2[i]]) { edg.push_back({dis[v1[i]] + dis[v2[i]] + w[i], {tko[v1[i]], tko[v2[i]]}}); } } sort(edg.begin(), edg.end()); for (pair<long long, pair<int, int> > E : edg) { if (pr(E.second.first) == pr(E.second.second)) continue; mrg(E.second.first, E.second.second); T[E.second.first].push_back({E.first, E.second.second}); T[E.second.second].push_back({E.first, E.second.first}); } dfs(1, 1); precompute(); for (int i = 0; i < q; i++) { int x, y; scanf("%d%d", &x, &y); printf("%lld\n", get_lca(x, y)); } }
#include <bits/stdc++.h> using namespace std; const int N = 100005; const long long inf = (long long)1e15; int n, m, k, q, cnt, last[N], fro[N], f[N], sz[N]; long long dis[N], val[N]; struct edge { int to, next; long long w; } e[N * 6]; struct data { int x, y; long long w; } a[N * 3]; std::priority_queue<std::pair<long long, int> > que; bool vis[N]; void addedge(int u, int v, long long w) { e[++cnt].to = v; e[cnt].w = w; e[cnt].next = last[u]; last[u] = cnt; e[++cnt].to = u; e[cnt].w = w; e[cnt].next = last[v]; last[v] = cnt; } void dij() { for (int i = 1; i <= k; i++) dis[i] = 0, fro[i] = i, que.push(std::make_pair(0, i)); for (int i = k + 1; i <= n; i++) dis[i] = inf; while (!que.empty()) { int u = que.top().second; que.pop(); if (vis[u]) continue; vis[u] = 1; for (int i = last[u]; i; i = e[i].next) if (dis[u] + e[i].w < dis[e[i].to]) { dis[e[i].to] = dis[u] + e[i].w; fro[e[i].to] = fro[u]; que.push(std::make_pair(-dis[e[i].to], e[i].to)); } } } bool cmp(data a, data b) { return a.w < b.w; } int find(int x) { return f[x] == x ? x : find(f[x]); } long long query(int x, int y) { long long ans = 0; while (x != y) { if (sz[x] > sz[y]) std::swap(x, y); ans = std::max(ans, val[x]); x = f[x]; } return ans; } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 1; i <= m; i++) { int x, y; long long w; scanf("%d%d%lld", &x, &y, &w); addedge(x, y, w); } dij(); for (int i = 1; i <= cnt; i += 2) { int x = e[i].to, y = e[i + 1].to; long long w = dis[x] + dis[y] + e[i].w; a[i / 2 + 1] = (data){fro[x], fro[y], w}; } std::sort(a + 1, a + m + 1, cmp); for (int i = 1; i <= k; i++) f[i] = i, sz[i] = 1; for (int i = 1; i <= m; i++) { int x = find(a[i].x), y = find(a[i].y); if (x == y) continue; if (sz[x] > sz[y]) std::swap(x, y); f[x] = y; sz[y] += sz[x]; val[x] = a[i].w; } while (q--) { int x, y; scanf("%d%d", &x, &y); printf("%lld\n", query(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; template <class T> using V = vector<T>; template <int NV> class Dsu { vector<int> ancestor; public: Dsu() { ancestor.resize(NV); init(); } inline void init(int n = NV) { iota(ancestor.begin(), next(ancestor.begin(), n), 0); } inline int find(int x) { if (x == ancestor[x]) return x; return ancestor[x] = find(ancestor[x]); } inline bool unite(int u, int v) { int a = find(u), b = find(v); if (a == b) return false; return (ancestor[b] = a), true; } }; struct edge { int v; ll w; }; Dsu<202020> D; int n, m, k, q; bool vis[202020]; V<edge> G[202020]; V<tuple<ll, int, int>> E; int anc[202020][20], dep[202020]; ll dis[202020], weight[202020][20]; void dfs(int u, int f) { anc[u][0] = f; for (int i = 1; i < 20; i++) { anc[u][i] = anc[anc[u][i - 1]][i - 1]; weight[u][i] = max(weight[u][i - 1], weight[anc[u][i - 1]][i - 1]); } for (auto& e : G[u]) { if (e.v != f) { dep[e.v] = dep[u] + 1; weight[e.v][0] = e.w; dfs(e.v, u); } } } ll getans(int x, int y) { ll ret = 0; if (dep[x] < dep[y]) swap(x, y); for (int i = 19; i >= 0; i--) { if (dep[anc[x][i]] >= dep[y]) { ret = max(ret, weight[x][i]); x = anc[x][i]; } } if (x == y) return ret; for (int i = 19; i >= 0; i--) { if (anc[x][i] != anc[y][i]) { ret = max({ret, weight[x][i], weight[y][i]}); x = anc[x][i], y = anc[y][i]; } } return max({ret, weight[x][0], weight[y][0]}); } int main() { ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cin >> n >> m >> k >> q; for (int i = 1; i <= m; i++) { int x, y, z; cin >> x >> y >> z; G[x].push_back({y, z}), G[y].push_back({x, z}); } priority_queue<pair<ll, int>> Q; for (int i = 1; i <= n; i++) { if (i <= k) { dis[i] = 0, Q.push({0, i}); } else { dis[i] = 1ll << 60; } } while (!Q.empty()) { int u = Q.top().second; Q.pop(); if (vis[u]) { continue; } vis[u] = 1; for (auto& e : G[u]) { if (!vis[e.v] && dis[e.v] > dis[u] + e.w) { dis[e.v] = dis[u] + e.w; Q.push({-dis[e.v], e.v}); } } } for (int u = 1; u <= n; u++) { for (auto& e : G[u]) { if (u < e.v) { E.push_back({dis[u] + dis[e.v] + e.w, u, e.v}); } } G[u].clear(); } sort(E.begin(), E.end()); for (int i = 0; i < ((int)E.size()); i++) { ll z; int x, y; tie(z, x, y) = E[i]; if (D.unite(x, y)) { G[x].push_back({y, z}), G[y].push_back({x, z}); } } dfs(1, 0); while (q--) { int x, y; cin >> x >> y; cout << getans(x, y) << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int maxn = (int)1e5 + 100; const int mod = (int)1e9 + 7; const long long INF = (long long)2e18; int n, m, k, q, fa[maxn]; long long dis[maxn], ans[maxn * 6]; vector<pair<int, long long> > g[maxn * 6]; vector<pair<int, int> > que[maxn]; vector<tuple<long long, int, int> > e; set<int> ele[maxn]; void dij() { priority_queue<pair<long long, int> > Q; for (int i = (1); i <= (n); ++i) { if (i <= k) Q.push({0, i}); else dis[i] = INF; } while (!Q.empty()) { int u = Q.top().second; Q.pop(); for (auto [v, w] : g[u]) { if (dis[u] + w < dis[v]) { dis[v] = dis[u] + w; Q.push({-dis[v], v}); } } } } void init() { for (int i = (1); i <= (n); ++i) fa[i] = i, ele[i].insert(i); } int find(int x) { return x == fa[x] ? x : fa[x] = find(fa[x]); } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = (1); i <= (m); ++i) { int u, v; long long w; scanf("%d%d%lld", &u, &v, &w); g[u].push_back({v, w}); g[v].push_back({u, w}); } dij(); for (int u = (1); u <= (n); ++u) for (auto [v, w] : g[u]) if (u < v) e.push_back({dis[u] + dis[v] + w, u, v}); sort(e.begin(), e.end()); for (int i = (1); i <= (q); ++i) { int u, v; scanf("%d%d", &u, &v); que[u].push_back({v, i}); que[v].push_back({u, i}); } init(); for (auto [w, x, y] : e) { x = find(x); y = find(y); if (x == y) continue; if (ele[x].size() < ele[y].size()) swap(x, y); fa[y] = x; for (auto u : ele[y]) for (auto [v, id] : que[u]) if (ele[x].count(v)) ans[id] = w; for (auto u : ele[y]) ele[x].insert(u); } for (int i = (1); i <= (q); ++i) printf("%lld\n", ans[i]); }
#include <bits/stdc++.h> using namespace std; const int N = 100000; const long long oo = 1e18; int n, e, k, Q; vector<vector<pair<int, long long> > > g; int p[N]; int find(int u) { if (p[u] == u) return u; return p[u] = find(p[u]); } pair<int, long long> dp[17][N]; long long mx[N]; int d[N]; void DFS(int u, int p) { for (auto e : g[u]) { if (e.first == p) continue; dp[0][e.first] = {u, e.second}; d[e.first] = d[u] + 1; DFS(e.first, u); } } long long calc(int u, int v) { if (d[u] < d[v]) swap(u, v); int l = 0; while ((1 << l) <= d[u]) ++l; --l; long long res = 0; for (int i = l; i >= 0; --i) if (d[u] - (1 << i) >= d[v]) { res = max(res, dp[i][u].second); u = dp[i][u].first; } if (u == v) return res; for (int i = l; i >= 0; --i) if (dp[i][u].first != dp[i][v].first) { res = max(res, dp[i][u].second); res = max(res, dp[i][v].second); u = dp[i][u].first; v = dp[i][v].first; } res = max(res, dp[0][u].second); res = max(res, dp[0][v].second); return res; } int main() { scanf("%d%d%d%d", &n, &e, &k, &Q); g.resize(n); for (int a, b, c, i = 0; i < e; ++i) { scanf("%d%d%d", &a, &b, &c); --a; --b; g[a].push_back({b, c}); swap(a, b); g[a].push_back({b, c}); } vector<long long> cost(k); cost.resize(n, oo); vector<bool> vis(n); priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > q; for (int i = 0; i < k; ++i) q.push({0, i}); while (!q.empty()) { int u = q.top().second; q.pop(); if (vis[u]) continue; vis[u] = true; for (auto e : g[u]) if (cost[e.first] > cost[u] + e.second) { cost[e.first] = cost[u] + e.second; q.push({cost[e.first], e.first}); } } vector<pair<long long, pair<int, int> > > edges; for (int u = 0; u < n; ++u) for (auto e : g[u]) { int v = e.first; edges.push_back({cost[u] + cost[v] + e.second, {u, v}}); } sort(edges.begin(), edges.end()); g.clear(); g.resize(n); for (int i = 0; i < n; ++i) p[i] = i; for (auto e : edges) { int u = e.second.first; int v = e.second.second; if (find(u) != find(v)) { g[u].push_back({v, e.first}); g[v].push_back({u, e.first}); p[find(u)] = find(v); } } memset(dp, -1, sizeof(dp)); DFS(0, -1); for (int k = 1; k < 17; ++k) for (int i = 0; i < n; ++i) if (dp[k - 1][i].first != -1) { dp[k][i].first = dp[k - 1][dp[k - 1][i].first].first; dp[k][i].second = max(dp[k - 1][i].second, dp[k - 1][dp[k - 1][i].first].second); } while (Q--) { int u, v; scanf("%d%d", &u, &v); --u; --v; printf("%lld\n", calc(u, v)); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> using p_que = priority_queue<T, vector<T>, greater<T>>; constexpr int N = 112345, M = 18; vector<pair<int, long long>> g[N]; p_que<pair<long long, pair<int, int>>> que; int u[N]; long long d[N]; class UF { public: int p[N], d[N] = {}; UF() { iota(p, p + N, 0); } int grp(int a) { auto &ret = p[a]; if (ret != a) ret = grp(ret); return ret; } bool mrg(int a, int b) { a = grp(a), b = grp(b); if (a == b) return false; if (d[a] > d[b]) swap(a, b); p[a] = b; ((d[b]) = max((d[b]), (d[a] + 1))); return true; } } uf; class { public: vector<pair<int, long long>> g[N]; void edge(int a, int b, long long p) { g[a].emplace_back(b, p); g[b].emplace_back(a, p); } int p[N][M] = {}; int d[N]; long long c[N][M]; void build() { d[0] = 0; fill(c[0], c[0] + M, 0); dfs(0); } void dfs(int a) { for (auto &e : g[a]) { int b = e.first; if (b == p[a][0]) continue; p[b][0] = a; for (int i = (1); i < (M); i++) p[b][i] = p[p[b][i - 1]][i - 1]; d[b] = d[a] + 1; c[b][0] = e.second; for (int i = (1); i < (M); i++) c[b][i] = max(c[b][i - 1], c[p[b][i - 1]][i - 1]); dfs(b); } } long long ans(int a, int b) { if (d[a] > d[b]) swap(a, b); ; long long ret = 0; ; for (int i = M - 1; i >= 0; i--) { if (d[a] <= (d[b] - (1 << i))) { ; ((ret) = max((ret), (c[b][i]))); b = p[b][i]; } }; for (int i = M - 1; i >= 0; i--) { if (p[a][i] != p[b][i]) { ; ((ret) = max((ret), (c[a][i]))); ((ret) = max((ret), (c[b][i]))); a = p[a][i]; b = p[b][i]; } } if (a != b) { ; ((ret) = max((ret), (c[a][0]))); ((ret) = max((ret), (c[b][0]))); } return ret; } } t; int main() { int n, m, k, q; scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = (0); i < ((m)); i++) { int u, v; long long w; scanf("%d%d%lld", &u, &v, &w); u--; v--; g[u].emplace_back(v, w); g[v].emplace_back(u, w); }; fill(u, u + N, -1); for (int i = (0); i < ((k)); i++) que.emplace(0, make_pair(i, i)); while (que.size()) { auto tp = que.top(); que.pop(); int i = tp.second.first; if (~u[i]) continue; u[i] = tp.second.second; d[i] = tp.first; ; for (auto &e : g[i]) { int j = e.first; que.emplace(d[i] + e.second, make_pair(j, u[i])); } }; while (que.size()) que.pop(); for (int i = (0); i < ((n)); i++) for (auto &e : g[i]) { int j = e.first; if (u[i] >= u[j]) continue; ; que.emplace(d[i] + d[j] + e.second, make_pair(u[i], u[j])); }; while (que.size()) { auto tp = que.top(); que.pop(); int i = tp.second.first, j = tp.second.second; if (!uf.mrg(i, j)) continue; ; t.edge(i, j, tp.first); } t.build(); for (int iq = (0); iq < ((q)); iq++) { int a, b; scanf("%d%d", &a, &b); a--; b--; printf("%lld\n", t.ans(a, b)); } }
#include <bits/stdc++.h> using namespace std; template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { for (auto i = begin(v); i != end(v); i++) os << *i << (i == end(v) - 1 ? "" : " "); return os; } template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto i = begin(v); i != end(v); i++) is >> *i; return is; } int n, m, k, q; vector<pair<int, int>> edg[101000]; vector<long long> best_dists(101000, 10000000000000000LL); set<int> markers[101000]; int dsu[101000]; int drank[101000]; vector<long long> ans(301000, 10000000000000000LL); struct Edg { int u, v; long long w; }; int dsu_find(int a) { if (dsu[a] == a) return a; return dsu_find(dsu[a]); } void dsu_union(int a, int b, long long curr_ans) { a = dsu_find(a); b = dsu_find(b); if (a == b) return; if (drank[a] >= drank[b]) { dsu[b] = a; drank[a] = max(drank[a], drank[b] + 1); } else { dsu[a] = b; swap(a, b); drank[a] = max(drank[a], drank[b] + 1); } if (markers[a].size() < markers[b].size()) swap(markers[a], markers[b]); for (int x : markers[b]) { if (markers[a].find(x) != markers[a].end()) { ans[x] = curr_ans; } else { markers[a].insert(x); } } } int main() { cin.tie(NULL); ios_base::sync_with_stdio(false); cout.tie(NULL); cin >> n >> m >> k >> q; vector<Edg> edges; for (int i = 0; i < m; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; edg[u].push_back({v, w}); edg[v].push_back({u, w}); edges.push_back(Edg{u, v, w}); } set<pair<long long, int>> ss; for (int i = 0; i < k; i++) { ss.insert({0, i}); best_dists[i] = 0; } while (ss.size() > 0) { auto curr = *ss.begin(); ss.erase(curr); for (auto x : edg[curr.second]) { long long new_dist = curr.first + x.second; if (new_dist < best_dists[x.first]) { ss.erase({best_dists[x.first], x.first}); best_dists[x.first] = new_dist; ss.insert({best_dists[x.first], x.first}); } } } for (int i = 0; i < m; i++) { edges[i].w += best_dists[edges[i].u] + best_dists[edges[i].v]; } sort(edges.begin(), edges.end(), [&](Edg& x, Edg& y) { return x.w < y.w; }); vector<pair<int, int>> qs(q); for (int i = 0; i < q; i++) { int a, b; cin >> a >> b; a--, b--; qs[i] = {a, b}; markers[a].insert(i); markers[b].insert(i); } for (int i = 0; i < n; i++) { dsu[i] = i; } for (int i = 0; i < m; i++) { dsu_union(edges[i].u, edges[i].v, edges[i].w); } for (int i = 0; i < q; i++) cout << ans[i] << "\n"; return 0; }
#include <bits/stdc++.h> const int INF = (int)1e9 + 7; const int N = (int)3e5 + 7; const int MAXN = (int)5e5 + 228; using namespace std; int n, m, k, q; int came[N]; long long d[N]; vector<pair<int, int> > g[N]; vector<pair<long long, pair<int, int> > > edges; void shortest_paths() { set<pair<long long, int> > S; for (int i = 1; i <= k; ++i) { d[i] = 0; came[i] = i; S.insert(make_pair(d[i], i)); } for (int i = k + 1; i <= n; ++i) d[i] = (long long)1e18; while (!S.empty()) { int v = S.begin()->second; S.erase(S.begin()); for (auto &it : g[v]) { int to = it.first, w = it.second; if (d[to] > d[v] + w) { S.erase(make_pair(d[to], to)); d[to] = d[v] + w; came[to] = came[v]; S.insert(make_pair(d[to], to)); } } } } void construct() { for (int i = 1; i <= n; ++i) { for (auto &it : g[i]) { int to = it.first; if (came[to] != came[i]) { edges.push_back( make_pair(it.second + d[to] + d[i], make_pair(came[to], came[i]))); } } } sort(edges.begin(), edges.end()); } int p[N]; set<int> queries[N]; void init() { for (int i = 1; i <= n; ++i) p[i] = i; } int get(int v) { if (v == p[v]) return v; return p[v] = get(p[v]); } long long ans[N]; void unite(int v, int u, long long w) { v = get(v); u = get(u); if (u == v) return; if (queries[v].size() < queries[u].size()) swap(v, u); for (auto &to : queries[u]) { if (queries[v].count(to)) { queries[v].erase(to); ans[to] = w; } else { queries[v].insert(to); } } queries[u].clear(); p[u] = v; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> n >> m >> k >> q; for (int i = 1; i <= m; ++i) { int x, y, z; cin >> x >> y >> z; g[x].push_back(make_pair(y, z)); g[y].push_back(make_pair(x, z)); } init(); for (int i = 1; i <= q; ++i) { int x, y; cin >> x >> y; queries[x].insert(i); queries[y].insert(i); } shortest_paths(); construct(); for (auto &to : edges) { int x = to.second.first, y = to.second.second; long long w = to.first; unite(x, y, w); } for (int i = 1; i <= q; ++i) cout << ans[i] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = (int)1e9 + 7; const int FFTMOD = 119 << 23 | 1; const int INF = (int)1e9 + 23111992; const long long LINF = (long long)1e18 + 23111992; const long double PI = acos((long double)-1); const long double EPS = 1e-9; inline long long gcd(long long a, long long b) { long long r; while (b) { r = a % b; a = b; b = r; } return a; } inline long long lcm(long long a, long long b) { return a / gcd(a, b) * b; } inline long long fpow(long long n, long long k, int p = MOD) { long long r = 1; for (; k; k >>= 1) { if (k & 1) r = r * n % p; n = n * n % p; } return r; } template <class T> inline int chkmin(T& a, const T& val) { return val < a ? a = val, 1 : 0; } template <class T> inline int chkmax(T& a, const T& val) { return a < val ? a = val, 1 : 0; } inline unsigned long long isqrt(unsigned long long k) { unsigned long long r = sqrt(k) + 1; while (r * r > k) r--; return r; } inline long long icbrt(long long k) { long long r = cbrt(k) + 1; while (r * r * r > k) r--; return r; } inline void addmod(int& a, int val, int p = MOD) { if ((a = (a + val)) >= p) a -= p; } inline void submod(int& a, int val, int p = MOD) { if ((a = (a - val)) < 0) a += p; } inline int mult(int a, int b, int p = MOD) { return (long long)a * b % p; } inline int inv(int a, int p = MOD) { return fpow(a, p - 2, p); } inline int sign(long double x) { return x < -EPS ? -1 : x > +EPS; } inline int sign(long double x, long double y) { return sign(x - y); } mt19937 mt(chrono::high_resolution_clock::now().time_since_epoch().count()); inline int mrand() { return abs((int)mt()); } void solve() { int n, m, k, q; cin >> n >> m >> k >> q; vector<vector<pair<int, int>>> adj(n); for (int i = (0); i < (m); ++i) { int u, v, w; cin >> u >> v >> w; u--, v--; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } vector<tuple<long long, int, int>> edges; map<pair<int, int>, long long> d; vector<int> ids(n, -1); priority_queue<tuple<long long, int, int>> heap; for (int u = (0); u < (k); ++u) { d[make_pair(u, u)] = 0, ids[u] = u, heap.push({-d[make_pair(u, u)], u, u}); } while (int((heap).size())) { long long t; int u, v; tie(t, u, v) = heap.top(); t = -t; heap.pop(); if (d[make_pair(u, v)] ^ t) continue; if (ids[u] != -1 && ids[u] != v) { edges.push_back({d[make_pair(u, ids[u])] + t, ids[u], v}); } else { ids[u] = v; for (auto e : adj[u]) { int nu = e.first; int w = e.second; if (!d.count(make_pair(nu, v))) d[make_pair(nu, v)] = LINF; if (chkmin(d[make_pair(nu, v)], d[make_pair(u, v)] + w)) { heap.push({-d[make_pair(nu, v)], nu, v}); } } } } sort((edges).begin(), (edges).end()); vector<int> dj(n); function<int(int)> find = [&](int u) { return dj[u] == u ? dj[u] : dj[u] = find(dj[u]); }; auto join = [&](int u, int v) { u = find(u); v = find(v); if (u ^ v) { dj[u] = v; return 1; } return 0; }; for (int u = (0); u < (n); ++u) dj[u] = u; vector<vector<pair<int, long long>>> adj2(k); for (auto e : edges) { int u, v; long long w; tie(w, u, v) = e; if (join(u, v)) { adj2[u].push_back({v, w}); adj2[v].push_back({u, w}); } } int logn = 20; vector<int> lev(n); vector<vector<int>> par(logn, vector<int>(n)); vector<vector<long long>> val(logn, vector<long long>(n)); function<void(int, int)> dfs = [&](int u, int p) { for (int i = (1); i < (logn); ++i) { par[i][u] = par[i - 1][par[i - 1][u]]; val[i][u] = max(val[i - 1][u], val[i - 1][par[i - 1][u]]); } for (auto e : adj2[u]) { int v = e.first; long long w = e.second; if (v ^ p) { lev[v] = lev[u] + 1; par[0][v] = u; val[0][v] = w; dfs(v, u); } } }; auto query = [&](int u, int v) { if (lev[u] < lev[v]) swap(u, v); long long res = 0; for (int i = (logn)-1; i >= (0); --i) { if (lev[v] <= lev[par[i][u]]) { chkmax(res, val[i][u]); u = par[i][u]; } } if (u == v) return res; for (int i = (logn)-1; i >= (0); --i) { if (par[i][u] ^ par[i][v]) { chkmax(res, val[i][u]); chkmax(res, val[i][v]); u = par[i][u]; v = par[i][v]; } } chkmax(res, val[0][u]); chkmax(res, val[0][v]); return res; }; dfs(0, -1); while (q--) { int u, v; cin >> u >> v; u--, v--; cout << query(u, v) << "\n"; } } int main(int argc, char* argv[]) { ios_base::sync_with_stdio(0), cin.tie(0); if (argc > 1) { assert(freopen(argv[1], "r", stdin)); } if (argc > 2) { assert(freopen(argv[2], "wb", stdout)); } solve(); cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n"; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; constexpr int kMaxN = 1e5 + 3; constexpr ll inf = 1e18 + 7; vector<pair<int, int>> edges[kMaxN]; int parent[kMaxN]; int r[kMaxN]; unordered_set<int> tokens[kMaxN]; int find_parent(int u) { if (u == parent[u]) { return u; } return parent[u] = find_parent(parent[u]); } vector<int> unite(int u, int v) { u = find_parent(u), v = find_parent(v); if (u == v) { return {}; } if (r[u] < r[v]) { swap(u, v); } if (r[u] == r[v]) { ++r[u]; } parent[v] = u; vector<int> connected; for (int token : tokens[v]) { if (tokens[u].count(token)) { connected.emplace_back(token); } else { tokens[u].emplace(token); } } return connected; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int n, m, k, q; cin >> n >> m >> k >> q; for (int i = 0; i < m; ++i) { int u, v, w; cin >> u >> v >> w; --u, --v; edges[u].emplace_back(v, w); edges[v].emplace_back(u, w); } vector<ll> d(n, inf); priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq; for (int i = 0; i < k; ++i) { d[i] = 0; pq.emplace(0, i); } while (!pq.empty()) { auto [du, u] = pq.top(); pq.pop(); if (du != d[u]) { continue; } for (auto [v, w] : edges[u]) { if (du + w < d[v]) { d[v] = du + w; pq.emplace(d[v], v); } } } vector<tuple<ll, int, int>> all_edges; all_edges.reserve(m); for (int u = 0; u < n; ++u) { for (auto& [v, w] : edges[u]) { if (u < v) { all_edges.emplace_back(w + d[u] + d[v], u, v); } } parent[u] = u; } sort(all_edges.begin(), all_edges.end()); for (int i = 0; i < q; ++i) { int u, v; cin >> u >> v; --u, --v; tokens[u].emplace(i); tokens[v].emplace(i); } vector<ll> queries(q); for (auto [w, u, v] : all_edges) { for (int query : unite(u, v)) { queries[query] = w; } } for (ll query : queries) { cout << query << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { for (auto i = begin(v); i != end(v); i++) os << *i << (i == end(v) - 1 ? "" : " "); return os; } template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto i = begin(v); i != end(v); i++) is >> *i; return is; } int n, m, k, q; vector<pair<int, int>> edg[101000]; vector<long long> best_dists(101000, 10000000000000000LL); set<int> markers[101000]; int dsu[101000]; int drank[101000]; vector<long long> ans(301000, 10000000000000000LL); struct Edg { int u, v; long long w; }; int dsu_find(int a) { if (dsu[a] == a) return a; return dsu[a] = dsu_find(dsu[a]); } void dsu_union(int a, int b, long long curr_ans) { a = dsu_find(a); b = dsu_find(b); if (a == b) return; if (drank[a] >= drank[b]) { dsu[b] = a; drank[a] = max(drank[a], drank[b] + 1); } else { dsu[a] = b; swap(a, b); drank[a] = max(drank[a], drank[b] + 1); } if (markers[a].size() < markers[b].size()) swap(markers[a], markers[b]); for (int x : markers[b]) { if (markers[a].find(x) != markers[a].end()) { ans[x] = curr_ans; markers[a].erase(x); } else { markers[a].insert(x); } } } int main() { cin.tie(NULL); ios_base::sync_with_stdio(false); cout.tie(NULL); cin >> n >> m >> k >> q; vector<Edg> edges; for (int i = 0; i < m; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; edg[u].push_back({v, w}); edg[v].push_back({u, w}); edges.push_back(Edg{u, v, w}); } set<pair<long long, int>> ss; for (int i = 0; i < k; i++) { ss.insert({0, i}); best_dists[i] = 0; } while (ss.size() > 0) { auto curr = *ss.begin(); ss.erase(curr); for (auto x : edg[curr.second]) { long long new_dist = curr.first + x.second; if (new_dist < best_dists[x.first]) { ss.erase({best_dists[x.first], x.first}); best_dists[x.first] = new_dist; ss.insert({best_dists[x.first], x.first}); } } } for (int i = 0; i < m; i++) { edges[i].w += best_dists[edges[i].u] + best_dists[edges[i].v]; } sort(edges.begin(), edges.end(), [&](Edg& x, Edg& y) { return x.w < y.w; }); vector<pair<int, int>> qs(q); for (int i = 0; i < q; i++) { int a, b; cin >> a >> b; a--, b--; qs[i] = {a, b}; markers[a].insert(i); markers[b].insert(i); } for (int i = 0; i < n; i++) { dsu[i] = i; drank[i] = 1; } for (int i = 0; i < m; i++) { dsu_union(edges[i].u, edges[i].v, edges[i].w); } for (int i = 0; i < q; i++) cout << ans[i] << "\n"; return 0; }
#include <bits/stdc++.h> const int N = 3e5 + 5; struct Edge { int u; int v; long long w; int next; bool operator<(const Edge& other) const { return w < other.w; } }; int head[N]; Edge e[2 * N]; struct Node { int u; long long w; Node(int u, long long w) : u(u), w(w) {} bool operator<(const Node& other) const { return w > other.w; } }; long long dis[N]; int fix[N]; int p[N]; int Head[N]; Edge E[2 * N]; long long f[N][19 + 5]; long long w[N][19 + 5]; int Q[N]; void addEdge(int u, int v, long long w, int& size) { size++; e[size].u = u; e[size].v = v; e[size].w = w; e[size].next = head[u]; head[u] = size; } void dijkstra(int n, int k) { std::priority_queue<Node> Q; for (int i = 1; i <= n; i++) { if (i > k) dis[i] = 1e18 + 7; else { dis[i] = 0; Q.push(Node(i, 0)); } } while (Q.size()) { while (Q.size() && fix[Q.top().u]) Q.pop(); if (!Q.size()) break; int u = Q.top().u; dis[u] = Q.top().w; fix[u] = 1; Q.pop(); for (int i = head[u]; i; i = e[i].next) { int v = e[i].v; if (!fix[v] && dis[u] + e[i].w < dis[v]) { dis[v] = dis[u] + e[i].w; Q.push(Node(v, dis[v])); } } } } int find(int u) { if (p[u] == u) return u; else return p[u] = find(p[u]); } void buildTree(int u, int v, long long w, int& size) { size++; E[size].u = u, E[size].v = v; E[size].w = w; E[size].next = Head[u]; Head[u] = size; } long long max(long long a, long long b) { return a > b ? a : b; } long long lca(int x, int y) { if (fix[x] < fix[y]) { int t = x; x = y; y = t; } long long res = 0; for (int i = 17; i >= 0; i--) { if (f[x][i] && fix[f[x][i]] >= fix[y]) { res = max(res, w[x][i]); x = f[x][i]; } } if (x == y) return res; for (int i = 17; i >= 0; i--) { if (f[x][i] != f[y][i]) { res = max(res, w[x][i]); res = max(res, w[y][i]); x = f[x][i], y = f[y][i]; } } res = max(res, w[x][0]); res = max(res, w[y][0]); return res; } void initTree(int n, int s) { for (int i = 1; i <= n; i++) fix[i] = 0; int h = 0, t = -1; Q[++t] = s; fix[s] = 1; while (h <= t) { int u = Q[h++]; for (int i = Head[u]; i; i = E[i].next) { int v = E[i].v; long long W = E[i].w; if (fix[v]) continue; fix[v] = fix[u] + 1; f[v][0] = u; w[v][0] = W; Q[++t] = v; } } for (int j = 1; j <= 17; j++) { for (int i = 1; i <= n; i++) { int middle = f[i][j - 1]; if (!middle || !f[middle][j - 1]) continue; w[i][j] = max(w[i][j - 1], w[middle][j - 1]); f[i][j] = f[middle][j - 1]; } } } int main() { int n, m, k, q; scanf("%d%d%d%d", &n, &m, &k, &q); int size = 0; for (int i = 0; i < m; i++) { int u, v; long long w; scanf("%d%d%lld", &u, &v, &w); addEdge(u, v, w, size); addEdge(v, u, w, size); } dijkstra(n, k); for (int i = 1; i <= size; i++) { int u = e[i].u, v = e[i].v; long long w = e[i].w; e[i].w = dis[u] + dis[v] + w; } std::sort(e + 1, e + size + 1); for (int i = 1; i <= n; i++) p[i] = i; int Size = 0; for (int i = 1; i <= size; i++) { if (Size == (2 * n - 2)) break; int x = find(e[i].u), y = find(e[i].v); if (x != y) { p[x] = y; buildTree(e[i].u, e[i].v, e[i].w, Size); buildTree(e[i].v, e[i].u, e[i].w, Size); } } initTree(n, 1); while (q--) { int u, v; scanf("%d%d", &u, &v); printf("%lld\n", lca(u, v)); } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using pii = pair<int, int>; using pll = pair<ll, ll>; ll n, m, k, q, a, b, c; ll p[300100], res[300100], d[300100]; vector<pll> E[300100]; map<int, bool> token[300100]; bool compare(const pll a, const pll b) { return a > b; } int _find(int x) { return p[x] ? p[x] = _find(p[x]) : x; } void dijkstra() { vector<pll> que; memset(d, 0x3f, sizeof(d)); for (int i = 1; i <= k; i++) { d[i] = 0; for (auto it : E[i]) que.push_back({it.second, it.first}); } make_heap(que.begin(), que.end(), compare); while (que.size()) { pll qw = que.front(); pop_heap(que.begin(), que.end(), compare); que.pop_back(); if (d[qw.second] <= qw.first) continue; d[qw.second] = qw.first; for (auto it : E[qw.second]) que.push_back({qw.first + it.second, it.first}), push_heap(que.begin(), que.end(), compare); } } int main() { cin >> n >> m >> k >> q; for (int i = 1; i <= m; i++) cin >> a >> b >> c, E[a].push_back({b, c}), E[b].push_back({a, c}); dijkstra(); vector<pair<ll, pair<int, int> > > e; for (int i = 1; i <= n; i++) for (auto it : E[i]) if (i < it.first) e.push_back({d[i] + d[it.first] + it.second, {i, it.first}}); for (int i = 1; i <= q; i++) cin >> a >> b, token[a][i] = true, token[b][i] = true; sort(e.begin(), e.end()); for (auto x : e) { if (_find(x.second.first) == _find(x.second.second)) continue; int pA = _find(x.second.first); int pB = _find(x.second.second); if (token[pA].size() > token[pB].size()) swap(pA, pB); p[pA] = pB; for (auto y : token[pA]) { if (token[pB][y.first]) { res[y.first] = x.first; token[pB].erase(y.first); } else token[pB][y.first] = true; } } for (int i = 1; i <= q; i++) cout << res[i] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, k, q; int x[300100], y[300100], w[300100]; set<int> mp[300100]; int dsu[300100], sz[300100]; bool ch[300100]; long long d[300100], ans[300100]; vector<pair<int, long long>> v[300100]; vector<pair<long long, pair<int, int>>> p; void multisource_dijkstra() { priority_queue<pair<long long, int>> q; for (int i = 1; i <= k; i++) { q.push({0, i}); } while (!q.empty()) { long long a = q.top().first; int b = q.top().second; q.pop(); if (ch[b]) continue; ch[b] = true; a = -a; d[b] = a; for (auto i : v[b]) { if (ch[i.first]) continue; q.push({-(a + i.second), i.first}); } } } int root(int s) { while (s != dsu[s]) { dsu[s] = dsu[dsu[s]]; s = dsu[s]; } return s; } void spoj(int a, int b, long long wgh) { if (sz[a] > sz[b]) swap(a, b); dsu[a] = b; sz[b] += sz[a]; for (auto i : mp[a]) { auto it = mp[b].find(i); if (it != mp[b].end()) { ans[i] = min(ans[i], wgh); } mp[b].insert(i); } } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); ; for (int i = 0; i <= 3e5; i++) { dsu[i] = i; sz[i] = 1; ans[i] = 2e18; } memset((d), 0, sizeof((d))); cin >> n >> m >> k >> q; for (int i = 1; i <= m; i++) { cin >> x[i] >> y[i] >> w[i]; v[x[i]].push_back({y[i], w[i]}); v[y[i]].push_back({x[i], w[i]}); } for (int i = 1; i <= q; i++) { int a, b; cin >> a >> b; mp[a].insert(i); mp[b].insert(i); } multisource_dijkstra(); for (int i = 1; i <= m; i++) { long long u = w[i] + d[x[i]] + d[y[i]]; p.push_back({u, {x[i], y[i]}}); } sort((p).begin(), (p).end()); for (auto i : p) { int a = root(i.second.first); int b = root(i.second.second); if (a == b) continue; spoj(a, b, i.first); } for (int i = 1; i <= q; i++) { cout << ans[i] << " "; } return 0; }
#include <bits/stdc++.h> using namespace std; using llg = long long; const int maxNod = (int)(1e5) + 5; const int maxEdges = 3 * (int)(1e5) + 5; const int maxQueries = 3 * (int)(1e5) + 5; const int maxTokens = 2 * maxQueries; const llg BIG = (llg)(1e9) * (llg)(1e9); int nbNod, nbEdges, nbCentrals, nbQueries; llg rep[maxQueries]; int dsuRepr[maxNod]; int dsuSize[maxNod]; vector<int> tokenIn[maxNod]; int baseTok[maxTokens]; void dsuInit() { for (int nod = 0; nod < maxNod; ++nod) { dsuRepr[nod] = nod; dsuSize[nod] = 1; } } int dsuFind(int x) { if (x != dsuRepr[x]) { dsuRepr[x] = dsuFind(dsuRepr[x]); } return dsuRepr[x]; } void dsuMerge(int small, int big, llg curCap) { small = dsuFind(small); big = dsuFind(big); if (small == big) return; if (dsuSize[small] > dsuSize[big]) swap(small, big); for (int token : tokenIn[small]) { int oth = token ^ 1; int query = token / 2; if (dsuFind(baseTok[oth]) == big) { rep[query] = curCap; } tokenIn[big].push_back(token); } tokenIn[small].clear(); tokenIn[small].shrink_to_fit(); dsuSize[big] += dsuSize[small]; dsuRepr[small] = big; } vector<pair<int, llg>> adj[maxNod]; llg mdis[maxNod]; void dijkstra() { priority_queue<pair<llg, int>> pq; for (int nod = 0; nod < nbNod; ++nod) { if (nod < nbCentrals) { pq.push({0, nod}); } else { mdis[nod] = BIG; } } while (!pq.empty()) { llg dist = -pq.top().first; int nod = pq.top().second; pq.pop(); if (dist != mdis[nod]) continue; for (auto rawNeigh : adj[nod]) { int neighbor = rawNeigh.first; llg newDis = dist + rawNeigh.second; if (newDis < mdis[neighbor]) { mdis[neighbor] = newDis; pq.push({-newDis, neighbor}); } } } } struct Edge { llg weight, n1, n2; }; bool operator<(Edge a, Edge b) { return a.weight < b.weight; } vector<Edge> tabEdges; int main() { ios::sync_with_stdio(false); cin.tie(0); dsuInit(); cin >> nbNod >> nbEdges >> nbCentrals >> nbQueries; for (int iEdge = 0; iEdge < nbEdges; ++iEdge) { int n1, n2; llg weight; cin >> n1 >> n2 >> weight; --n1; --n2; adj[n1].emplace_back(n2, weight); adj[n2].emplace_back(n1, weight); tabEdges.push_back({weight, n1, n2}); } for (int query = 0; query < nbQueries; ++query) { int n1, n2; cin >> n1 >> n2; --n1; --n2; int tk1 = 2 * query, tk2 = 2 * query + 1; baseTok[tk1] = n1; baseTok[tk2] = n2; tokenIn[n1].push_back(tk1); tokenIn[n2].push_back(tk2); } dijkstra(); for (auto &edge : tabEdges) { edge.weight += mdis[edge.n1] + mdis[edge.n2]; } sort(tabEdges.begin(), tabEdges.end()); for (auto edge : tabEdges) { dsuMerge(edge.n1, edge.n2, edge.weight); } for (int query = 0; query < nbQueries; ++query) { cout << rep[query] << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int maxn = 3e5 + 10; pair<pair<int, int>, long long> edges[maxn]; pair<int, int> queries[maxn]; long long ans[maxn]; vector<int> Q[maxn]; vector<int> G[maxn]; vector<int> H[maxn]; long long dist[maxn]; int realm[maxn]; vector<int> comp[maxn]; int par[maxn]; int n, m, k, q; vector<pair<long long, pair<int, int>>> C; set<pair<long long, int>> prq; inline int get_other(int i, int v) { if (edges[i].first.first == v) return edges[i].first.second; return edges[i].first.first; } inline int get_other_Q(int i, int x) { if (queries[i].first == x) return queries[i].second; return queries[i].first; } inline void mark(int v, long long d, int r) { prq.insert({d, v}); dist[v] = d; realm[v] = r; } inline void connect(int v, int u, long long w) { int x = realm[v]; int y = realm[u]; long long d = dist[v] + dist[u] + w; if (x != y) C.push_back({d, {x, y}}); } inline void dijkstra() { for (int i = 0; i < k; i++) { mark(i, 0ll, i); } while (!prq.empty()) { int v = prq.begin()->second; prq.erase({dist[v], v}); for (int i : G[v]) { int u = get_other(i, v); long long w = edges[i].second; if (dist[v] + w < dist[u]) { prq.erase({dist[u], u}); mark(u, dist[v] + w, realm[v]); } } } } inline void init() { memset(dist, 63, sizeof dist); for (int i = 0; i < n; i++) { comp[i].push_back(i); par[i] = i; } } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); init(); for (int i = 0; i < m; i++) { int x, y; long long w; scanf("%d%d%lld", &x, &y, &w); x--; y--; edges[i] = {{x, y}, w}; G[x].push_back(i); G[y].push_back(i); } dijkstra(); for (int i = 0; i < m; i++) { connect(edges[i].first.first, edges[i].first.second, edges[i].second); } for (int i = 0; i < q; i++) { int x, y; scanf("%d%d", &x, &y); x--; y--; queries[i] = {x, y}; Q[x].push_back(i); Q[y].push_back(i); } sort(C.begin(), C.end()); for (auto ed : C) { long long d = ed.first; int v = par[ed.second.first]; int u = par[ed.second.second]; if (u == v) continue; if (comp[v].size() < comp[u].size()) { swap(v, u); } for (int a : comp[u]) { for (int idx : Q[a]) { int b = get_other_Q(idx, a); if (par[b] == v) { ans[idx] = d; } } } for (int a : comp[u]) { comp[v].push_back(a); par[a] = v; } comp[u].clear(); } for (int i = 0; i < q; i++) { printf("%lld\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long inf = 1e18 + 7; const int maxN = 1e5 + 5; int n, m, k, q, a, b, w; set<pair<long long, long long> > s; vector<pair<long long, long long> > graph[maxN], newGraph[maxN]; long long cost[maxN]; int parent[maxN], ranga[maxN]; vector<pair<long long, pair<long long, long long> > > edges; int pre[maxN], treeSize[maxN]; bool vis[maxN]; int counter = 0; pair<long long, long long> P[18][maxN]; void dijkstra() { for (int i = (k + 1); i <= (n); ++i) { cost[i] = inf; s.insert(pair<long long, long long>(cost[i], i)); } for (int i = (1); i <= ((k)); ++i) { cost[i] = 0; s.insert(pair<long long, long long>(cost[i], i)); } while (!s.empty()) { pair<long long, long long> p = *s.begin(); s.erase(s.begin()); for (auto x : graph[p.second]) { if (cost[x.first] > cost[p.second] + x.second) { s.erase(s.find(pair<long long, long long>(cost[x.first], x.first))); cost[x.first] = cost[p.second] + x.second; s.insert(pair<long long, long long>(cost[x.first], x.first)); } } } } int find(int x) { if (parent[x] != x) { parent[x] = find(parent[x]); } return parent[x]; } void Union(int x, int y) { int fx = find(x); int fy = find(y); if (fy == fx) return; if (ranga[fx] < ranga[fy]) { swap(fx, fy); } parent[fy] = fx; if (ranga[fy] == ranga[fx]) ranga[fx]++; } bool children(int u, int v) { return (pre[u] >= pre[v] && pre[u] < pre[v] + treeSize[v]); } int lca(int u, int v) { if (children(u, v)) return v; if (children(v, u)) return u; int i = u, j = 18 - 1; while (j >= 0) { if (children(v, P[j][i].first)) j--; else i = P[j][i].first; } return P[0][i].first; } void dfs(int v) { counter++; pre[v] = counter; for (auto i : newGraph[v]) { int to = i.first; long long cost = i.second; if (!vis[to]) { P[0][to] = pair<long long, long long>(v, cost); vis[to] = true; dfs(to); } } treeSize[v] = counter + 1 - pre[v]; } long long getMax(int a, int x) { int cnt = 0; long long maxim = 0; while (a != x) { while (children(P[cnt][a].first, x) && P[cnt][a].first != x) { cnt++; } if (children(x, P[cnt][a].first) && x != P[cnt][a].first) cnt--; maxim = max(maxim, P[cnt][a].second); a = P[cnt][a].first; cnt = 0; } return maxim; } int main() { ios_base::sync_with_stdio(0); cin >> n >> m >> k >> q; for (int i = (0); i <= ((m)-1); ++i) { cin >> a >> b >> w; graph[a].push_back(pair<long long, long long>(b, w)); graph[b].push_back(pair<long long, long long>(a, w)); } dijkstra(); for (int i = (1); i <= ((n)); ++i) { parent[i] = i; ranga[i] = 0; for (auto x : graph[i]) { if (i < x.first) { edges.push_back(pair<long long, pair<long long, long long> >( cost[i] + cost[x.first] + x.second, pair<long long, long long>(i, x.first))); } } } sort(edges.begin(), edges.end()); for (auto p : edges) { long long cost = p.first; int x = p.second.first; int y = p.second.second; if (find(x) != find(y)) { Union(x, y); newGraph[x].push_back(pair<long long, long long>(y, cost)); newGraph[y].push_back(pair<long long, long long>(x, cost)); } } for (int i = 0; i < 18; i++) for (int j = 0; j <= n; j++) P[i][j] = pair<long long, long long>(0, 0); vis[1] = true; dfs(1); P[0][1] = pair<long long, long long>(1, 0); for (int i = 1; i < 18; i++) { for (int j = 1; j <= n; j++) { pair<long long, long long> half = P[i - 1][j]; P[i][j].first = P[i - 1][half.first].first; P[i][j].second = max(half.second, P[i - 1][half.first].second); } } for (int i = (0); i <= ((q)-1); ++i) { cin >> a >> b; int x = lca(a, b); cout << max(getMax(a, x), getMax(b, x)) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 3e6 + 10; const int mod = 998244353; void read(int &a) { a = 0; int d = 1; char ch; while (ch = getchar(), ch > '9' || ch < '0') if (ch == '-') d = -1; a = ch ^ 48; while (ch = getchar(), ch >= '0' && ch <= '9') a = (a << 3) + (a << 1) + (ch ^ 48); a *= d; } int f[N], head[N], cnt; long long ans[N], dis[N]; bool vis[N]; vector<pair<int, int> > tmp[N]; struct note { int u, v, next; long long w; } edge[N]; void add(int u, int v, long long w) { edge[++cnt].next = head[u]; edge[cnt].v = v; edge[cnt].w = w; head[u] = cnt; } struct node { int u, v; long long w; bool operator<(const node &x) const { return w < x.w; } } e[N]; priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > q; void distra(int k, int n) { fill(dis, dis + n + 1, 1e18); for (register int i = 1; i <= k; i++) dis[i] = 0, q.push({0, i}); while (!q.empty()) { int t = q.top().second; q.pop(); if (vis[t]) continue; vis[t] = 1; for (register int i = head[t]; i; i = edge[i].next) { int v = edge[i].v; if (!vis[v] && dis[v] > dis[t] + edge[i].w) q.push({dis[v] = dis[t] + edge[i].w, v}); } } } int getv(int v) { return f[v] = v == f[v] ? v : getv(f[v]); } int main() { int n, m, k, q; read(n), read(m), read(k), read(q); for (register int i = 1; i <= m; i++) { int u, v, w; read(u), read(v), read(w); add(u, v, w), add(v, u, w); e[i] = node{u, v, w}; } distra(k, n); for (register int i = 1; i <= m; i++) e[i].w += dis[e[i].u] + dis[e[i].v]; sort(e + 1, e + 1 + m); for (register int i = 1; i <= n; i++) f[i] = i; for (register int i = 1; i <= q; i++) { int u, v; read(u), read(v); tmp[u].push_back({v, i}); tmp[v].push_back({u, i}); } for (register int i = 1; i <= m; i++) { int t1 = getv(e[i].u), t2 = getv(e[i].v); if (t1 == t2) continue; if (tmp[t1].size() > tmp[t2].size()) swap(t1, t2); for (auto it : tmp[t1]) { if (getv(it.first) == t2) ans[it.second] = e[i].w; else tmp[t2].push_back(it); } f[t1] = t2; } for (register int i = 1; i <= q; i++) printf("%I64d\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; using llg = long long; const int maxNod = (int)(1e5) + 5; const int maxEdges = 3 * (int)(1e5) + 5; const int maxQueries = 3 * (int)(1e5) + 5; const int maxTokens = 2 * maxQueries; const llg BIG = (llg)(1e9) * (llg)(1e9); int nbNod, nbEdges, nbCentrals, nbQueries; llg rep[maxQueries]; int dsuRepr[maxNod]; int dsuSize[maxNod]; vector<int> tokenIn[maxNod]; int baseTok[maxTokens]; void dsuInit() { for (int nod = 0; nod < maxNod; ++nod) { dsuRepr[nod] = nod; dsuSize[nod] = 1; } } int dsuFind(int x) { if (x != dsuRepr[x]) { dsuRepr[x] = dsuFind(dsuRepr[x]); } return dsuRepr[x]; } void dsuMerge(int small, int big, llg curCap) { small = dsuFind(small); big = dsuFind(big); if (small == big) return; if (dsuSize[small] > dsuSize[big]) swap(small, big); for (int token : tokenIn[small]) { int oth = token ^ 1; int query = token / 2; if (dsuFind(baseTok[oth]) == big) { rep[query] = curCap; } tokenIn[big].push_back(token); } tokenIn[small].clear(); tokenIn[small].shrink_to_fit(); dsuSize[big] += dsuSize[small]; dsuRepr[small] = big; } vector<pair<int, llg>> adj[maxNod]; llg mdis[maxNod]; void dijkstra() { priority_queue<pair<llg, int>> pq; for (int nod = 0; nod < nbNod; ++nod) { if (nod < nbCentrals) { pq.push({0, nod}); } else { mdis[nod] = BIG; } } while (!pq.empty()) { llg dist = -pq.top().first; int nod = pq.top().second; pq.pop(); if (dist != mdis[nod]) continue; for (auto rawNeigh : adj[nod]) { int neighbor = rawNeigh.first; llg newDis = dist + rawNeigh.second; if (newDis < mdis[neighbor]) { mdis[neighbor] = newDis; pq.push({-newDis, neighbor}); } } } } struct Edge { llg weight, n1, n2; }; bool operator<(Edge a, Edge b) { return a.weight < b.weight; } vector<Edge> tabEdges; int t; int main() { ios::sync_with_stdio(false); cin.tie(0); dsuInit(); cin >> nbNod >> nbEdges >> nbCentrals >> nbQueries; for (int iEdge = 0; iEdge < nbEdges; ++iEdge) { int n1, n2; llg weight; cin >> n1 >> n2 >> weight; --n1; --n2; adj[n1].emplace_back(n2, weight); adj[n2].emplace_back(n1, weight); tabEdges.push_back({weight, n1, n2}); } for (int query = 0; query < nbQueries; ++query) { int n1, n2; cin >> n1 >> n2; --n1; --n2; int tk1 = 2 * query, tk2 = 2 * query + 1; baseTok[tk1] = n1; baseTok[tk2] = n2; tokenIn[n1].push_back(tk1); tokenIn[n2].push_back(tk2); } dijkstra(); for (auto &edge : tabEdges) { edge.weight += mdis[edge.n1] + mdis[edge.n2]; } sort(tabEdges.begin(), tabEdges.end()); for (auto edge : tabEdges) { dsuMerge(edge.n1, edge.n2, edge.weight); } for (int query = 0; query < nbQueries; ++query) { cout << rep[query] << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 500; const int LOG = 20; int n, m, q, k; int v1[N], v2[N], w[N]; vector<pair<long long, int> > v[N], T[N]; long long dis[N]; int tko[N], par[N]; int lca[N][LOG], dep[N]; long long dp_lca[N][LOG]; int pr(int x) { if (par[x] == x) return x; return par[x] = pr(par[x]); } void mrg(int x, int y) { par[pr(x)] = pr(y); } void dfs(int x, int lst) { lca[x][0] = lst; dep[x] = dep[lst] + 1; for (pair<long long, int> nxt : T[x]) { if (nxt.second == lst) continue; dp_lca[nxt.second][0] = nxt.first; dfs(nxt.second, x); } } void precompute() { for (int j = 1; j < LOG; j++) { for (int i = 1; i <= n; i++) { lca[i][j] = lca[lca[i][j - 1]][j - 1]; dp_lca[i][j] = max(dp_lca[i][j - 1], dp_lca[lca[i][j - 1]][j - 1]); } } } long long get_lca(int x, int y) { long long ans = 0; if (dep[x] < dep[y]) swap(x, y); for (int i = LOG - 1; i >= 0; i--) if (dep[x] - (1 << i) >= dep[y]) { ans = max(ans, dp_lca[x][i]); x = lca[x][i]; } if (x == y) return ans; for (int i = LOG - 1; i >= 0; i--) if (lca[x][i] != lca[y][i]) { ans = max(ans, max(dp_lca[x][i], dp_lca[y][i])); x = lca[x][i], y = lca[y][i]; } return max(ans, max(dp_lca[x][0], dp_lca[y][0])); } void dijkstra() { memset(dis, -1, sizeof(dis)); priority_queue<pair<long long, int> > S; for (int i = 1; i <= k; i++) S.push({0LL, i}), dis[i] = 0, tko[i] = i, par[i] = i; for (; !S.empty();) { pair<long long, int> cur = S.top(); S.pop(); for (pair<long long, int> nxt : v[cur.second]) { if (dis[nxt.second] == -1 || dis[cur.second] + nxt.first < dis[nxt.second]) { dis[nxt.second] = dis[cur.second] + nxt.first; tko[nxt.second] = tko[cur.second]; S.push({-dis[nxt.second], nxt.second}); } } } } int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 0; i < m; i++) { scanf("%d%d%d", v1 + i, v2 + i, w + i); v[v1[i]].push_back({w[i], v2[i]}); v[v2[i]].push_back({w[i], v1[i]}); } dijkstra(); vector<pair<long long, pair<int, int> > > edg; for (int i = 0; i < m; i++) { if (tko[v1[i]] != tko[v2[i]]) { edg.push_back({dis[v1[i]] + dis[v2[i]] + w[i], {tko[v1[i]], tko[v2[i]]}}); } } sort(edg.begin(), edg.end()); for (pair<long long, pair<int, int> > E : edg) { if (pr(E.second.first) == pr(E.second.second)) continue; mrg(E.second.first, E.second.second); T[E.second.first].push_back({E.first, E.second.second}); T[E.second.second].push_back({E.first, E.second.first}); } dfs(1, 1); precompute(); for (int i = 0; i < q; i++) { int x, y; scanf("%d%d", &x, &y); printf("%lld\n", get_lca(x, y)); } }
#include <bits/stdc++.h> using namespace std; struct edge { long long u, v, w; }; bool cmp(const edge &x, const edge &y) { return x.w < y.w; } const long long N = 1e5 + 5; long long start[N]; vector<pair<long long, long long>> adj[N]; long long length[N]; long long res[3 * N]; vector<pair<long long, long long>> query[N]; vector<long long> p(N, -1); set<long long> nodes[N]; long long globalWeight; long long find(long long x) { return p[x] < 0 ? x : p[x] = find(p[x]); } void merge(long long x, long long y) { if ((x = find(x)) == (y = find(y))) return; if (p[y] < p[x]) swap(x, y); p[x] += p[y]; p[y] = x; for (long long node : nodes[y]) { for (auto &qu : query[node]) { const long long otherNode = qu.first; const long long index = qu.second; if (nodes[x].count(otherNode)) { if (res[index] == -1) { res[index] = globalWeight; } } } } for (long long node : nodes[y]) { nodes[x].insert(node); } } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long n, m, k, Q; cin >> n >> m >> k >> Q; for (long long i = 0; i < m; ++i) { long long u, v, w; cin >> u >> v >> w; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } for (long long i = 1; i <= n; ++i) { nodes[i].insert(i); length[i] = 1e18; } set<pair<long long, long long>> q; for (long long i = 1; i <= k; ++i) { length[i] = 0; q.insert({0, i}); start[i] = i; } vector<edge> arr; while (!q.empty()) { auto it = q.begin(); long long node = it->second; q.erase(it); for (auto &p : adj[node]) { long long to = p.first; long long weight = p.second; if (length[to] > weight + length[node]) { q.erase({length[to], to}); start[to] = start[node]; length[to] = weight + length[node]; q.insert({length[to], to}); } else if (start[to] != start[node]) { arr.push_back( {start[to], start[node], weight + length[to] + length[node]}); } } } sort(arr.begin(), arr.end(), cmp); for (long long i = 0; i < Q; ++i) { res[i] = -1; long long u, v; cin >> u >> v; query[u].push_back({v, i}); query[v].push_back({u, i}); } for (auto &e : arr) { globalWeight = e.w; merge(e.u, e.v); } for (long long i = 0; i < Q; ++i) { cout << res[i] << '\n'; } }
#include <bits/stdc++.h> using namespace std; const long long INF = 1e18; long long dist[300005], ans[300005]; vector<pair<int, long long>> vec[300005]; vector<pair<int, int>> qrs[300005]; int par[300005]; set<int> se[300005]; struct edge { int u, v; long long c; edge(int u, int v, long long c) : u(u), v(v), c(c) {} bool operator<(const edge& rhs) const { return c < rhs.c; } }; int main() { int n, m, k, q; scanf("%d %d %d %d", &n, &m, &k, &q); for (int i = 1; i <= m; i++) { int u, v; long long w; scanf("%d %d %lld", &u, &v, &w); vec[u].push_back({v, w}); vec[v].push_back({u, w}); } for (int i = 1; i <= q; i++) { int a, b; scanf("%d %d", &a, &b); qrs[a].push_back({b, i}); qrs[b].push_back({a, i}); } for (int i = 1; i <= n; i++) dist[i] = INF; priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq; for (int i = 1; i <= k; i++) { dist[i] = 0; pq.push({dist[i], i}); } while (!pq.empty()) { pair<long long, int> cur = pq.top(); pq.pop(); int u = cur.second; if (cur.first > dist[u]) continue; for (pair<int, long long> nxt : vec[u]) { int v = nxt.first; long long c = nxt.second; if (dist[v] > dist[u] + c) { dist[v] = dist[u] + c; pq.push({dist[v], v}); } } } vector<edge> edges; for (int i = 1; i <= n; i++) { for (pair<int, long long> p : vec[i]) { int v = p.first; long long w = p.second; edges.push_back(edge(i, v, dist[i] + dist[v] + w)); } } sort(edges.begin(), edges.end()); for (int i = 1; i <= n; i++) { par[i] = i; se[i].insert(i); } for (edge e : edges) { int u = e.u, v = e.v; long long c = e.c; if (par[u] == par[v]) continue; if (se[par[u]].size() > se[par[v]].size()) swap(u, v); int pp = par[u]; for (int x : se[pp]) { for (pair<int, int> p : qrs[x]) { int nv = p.first, idx = p.second; if (par[nv] == par[v]) ans[idx] = c; } } for (int x : se[pp]) { par[x] = par[v]; se[par[v]].insert(x); } se[pp].clear(); } for (int i = 1; i <= q; i++) printf("%lld\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, head[100000 + 5], cnt = 0, fa[100000 + 5], ans, dep[100000 + 5], f[20][100000 + 5]; long long g[20][100000 + 5], d[100000 + 5]; struct node { int uu, vv; long long w; } a[300000 + 5]; struct edge { int end, next; long long val; } e[700000 + 5]; struct node1 { int id; long long dis; bool operator<(const node1& x) const { return x.dis < dis; } }; bool vis[100000 + 5]; bool cmp(node A, node B) { return A.w < B.w; } void add_edge(int u, int v, long long c) { e[++cnt].end = v; e[cnt].val = c; e[cnt].next = head[u]; head[u] = cnt; } priority_queue<node1> Q; void dijkstra() { while (!Q.empty()) { node1 now = Q.top(); Q.pop(); int u = now.id; if (vis[u]) continue; vis[u] = true; for (int i = head[u]; i > 0; i = e[i].next) if (d[e[i].end] > d[u] + e[i].val) { int v = e[i].end; d[v] = d[u] + e[i].val; node1 b; b.id = v; b.dis = d[v]; Q.push(b); } } } int get(int x) { if (fa[x] == x) return x; return fa[x] = get(fa[x]); } void merge(int u, int v) { fa[get(v)] = get(u); } void kruskal() { int t = 0; for (int i = 1; i <= m; i++) if (get(a[i].uu) != get(a[i].vv)) { t++; ans += a[i].w; add_edge(a[i].uu, a[i].vv, a[i].w); add_edge(a[i].vv, a[i].uu, a[i].w); merge(a[i].uu, a[i].vv); if (t == n - 1) return; } } void dfs(int u) { int i, v; for (i = head[u]; i > 0; i = e[i].next) { v = e[i].end; if (v == f[0][u]) continue; f[0][v] = u; g[0][v] = e[i].val; dep[v] = dep[u] + 1; dfs(v); } } long long lca(int u, int v) { int i; long long ans = 0; if (dep[u] > dep[v]) swap(u, v); for (i = 18; i >= 0; i--) if (dep[u] <= dep[f[i][v]]) { ans = max(ans, g[i][v]); v = f[i][v]; } if (u == v) return ans; for (i = 18; i >= 0; i--) if (f[i][u] != f[i][v]) { ans = max(ans, max(g[i][u], g[i][v])); u = f[i][u]; v = f[i][v]; } ans = max(ans, max(g[0][u], g[0][v])); return ans; } int main() { int k, q, i, j, u, v; scanf("%d%d%d%d", &n, &m, &k, &q); for (i = 1; i <= m; i++) { scanf("%d%d%lld", &a[i].uu, &a[i].vv, &a[i].w); add_edge(a[i].uu, a[i].vv, a[i].w); add_edge(a[i].vv, a[i].uu, a[i].w); } for (i = 1; i <= k; i++) add_edge(0, i, 0); for (i = 1; i <= n; i++) d[i] = 1e16; node1 now; now.dis = 0; now.id = 0; d[0] = 0; Q.push(now); dijkstra(); for (i = 1; i <= m; i++) { a[i].w = a[i].w + d[a[i].uu] + d[a[i].vv]; } sort(a + 1, a + m + 1, cmp); memset(e, 0, sizeof(e)); memset(head, 0, sizeof(head)); cnt = 0; for (i = 1; i <= n; i++) fa[i] = i; kruskal(); f[0][1] = 1; dep[1] = 1; dfs(1); for (i = 1; i <= 18; i++) for (j = 1; j <= n; j++) { f[i][j] = f[i - 1][f[i - 1][j]]; g[i][j] = max(g[i - 1][j], g[i - 1][f[i - 1][j]]); } for (i = 1; i <= q; i++) { scanf("%d%d", &u, &v); printf("%lld\n", lca(u, v)); } }
#include <bits/stdc++.h> using namespace std; #pragma GCC optimize("unroll-loops") #pragma GCC optimize("Ofast") #pragma GCC optimize("O0") #pragma GCC optimize("O1") long long pw(int a, int b) { long long ret = 1; long long mul = a; while (b > 0) { if (b & 1) ret *= mul; mul *= mul; b /= 2; } return ret; } long long to_int(string s) { long long ret = 0; for (int(i) = (0); (i) < (s.size()); (i)++) { ret += pw(10, s.size() - i - 1) * (long long)(s[i] - '0'); } return ret; } const int MAXN = 1e5 + 15; int n, m, k, q, par[MAXN], rnk[MAXN], tin[MAXN], tout[MAXN], tme; long long up[MAXN][20][2]; long long dis[MAXN]; vector<pair<int, int> > adj[MAXN]; vector<pair<long long, long long> > adj2[MAXN]; pair<pair<long long, long long>, long long> ed[3 * MAXN]; int get(int v) { return par[v] = (par[v] == v ? v : get(par[v])); } void uni(int a, int b) { a = get(a), b = get(b); if (rnk[a] < rnk[b]) swap(a, b); par[b] = a; rnk[a] += (rnk[a] == rnk[b]); } void dij() { priority_queue<pair<long long, long long>, vector<pair<long long, long long> >, greater<pair<long long, long long> > > pq; for (int(i) = (0); (i) < (k); (i)++) dis[i] = 0, pq.push({0, i}); for (int(i) = (k); (i) < (n); (i)++) dis[i] = 2e15; while (pq.size()) { int v = pq.top().second; long long dv = pq.top().first; pq.pop(); if (dv != dis[v]) continue; for (int(i) = (0); (i) < (adj[v].size()); (i)++) { int u = adj[v][i].first, c = adj[v][i].second; if (dis[u] > dis[v] + c) dis[u] = dis[v] + c, pq.push({dis[u], u}); } } } void dfs(int v, int p, long long w) { tin[v] = tme++; up[v][0][0] = p, up[v][0][1] = w; for (int(i) = (1); (i) < (20); (i)++) up[v][i][0] = up[up[v][i - 1][0]][i - 1][0], up[v][i][1] = max(up[v][i - 1][1], up[up[v][i - 1][0]][i - 1][1]); for (int(i) = (0); (i) < (adj2[v].size()); (i)++) { int u = adj2[v][i].first; long long ww = adj2[v][i].second; if (u != p) dfs(u, v, ww); } tout[v] = tme; } bool isAnc(int u, int v) { return (tin[u] <= tin[v] and tout[u] >= tout[v]); } long long mx(int u, int v) { long long ret = 0; int lca = v; for (int(i) = (19); (i) >= (0); (i)--) { if (!isAnc(up[lca][i][0], u)) ret = max(ret, up[lca][i][1]), lca = up[lca][i][0]; } if (!isAnc(lca, u)) ret = max(ret, up[lca][0][1]); lca = u; for (int(i) = (19); (i) >= (0); (i)--) { if (!isAnc(up[lca][i][0], v)) ret = max(ret, up[lca][i][1]), lca = up[lca][i][0]; } if (!isAnc(lca, v)) ret = max(ret, up[lca][0][1]); return ret; } bool cmp(pair<pair<long long, long long>, long long> a, pair<pair<long long, long long>, long long> b) { return dis[a.first.first] + dis[a.first.second] + a.second < dis[b.first.first] + dis[b.first.second] + b.second; } int main() { ios::sync_with_stdio(false); cin.tie(0); ; cin >> n >> m >> k >> q; for (int(i) = (0); (i) < (n); (i)++) par[i] = i; for (int(i) = (0); (i) < (m); (i)++) { int s, e, w; cin >> s >> e >> w; s--, e--; adj[s].push_back({e, w}); adj[e].push_back({s, w}); ed[i] = {{s, e}, w}; } dij(); sort(ed, ed + m, cmp); for (int(i) = (0); (i) < (m); (i)++) { int a = ed[i].first.first, b = ed[i].first.second; long long w = ed[i].second + dis[ed[i].first.first] + dis[ed[i].first.second]; if (get(a) != get(b)) { uni(a, b); adj2[a].push_back({b, w}); adj2[b].push_back({a, w}); } } dfs(0, 0, 0); while (q--) { int a, b; cin >> a >> b; a--, b--; cout << mx(a, b) << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 5, LG = 20; const long long infll = 1e16; vector<pair<int, int>> g[N]; long long dist[N]; int from[N]; int p[N]; int find(int x) { return p[x] < 0 ? x : p[x] = find(p[x]); } vector<pair<int, long long>> tree[N]; int lv[N], par[LG][N]; long long val[LG][N]; bool merge(int u, int v) { if ((u = find(u)) == (v = find(v))) return false; if (-p[u] > -p[v]) swap(u, v); p[v] += p[u]; p[u] = v; return true; } void dfs(int v) { for (int i = 0; i + 1 < LG; ++i) { par[i + 1][v] = par[i][par[i][v]]; val[i + 1][v] = max(val[i][v], val[i][par[i][v]]); } for (auto e : tree[v]) { if (e.first == par[0][v]) continue; par[0][e.first] = v; val[0][e.first] = e.second; lv[e.first] = lv[v] + 1; dfs(e.first); } } long long solve(int u, int v) { if (lv[v] < lv[u]) swap(u, v); int diff = lv[v] - lv[u]; long long ret = 0; for (int i = 0; i < LG; ++i) { if (diff & (1 << i)) { ret = max(ret, val[i][v]); v = par[i][v]; } } if (u == v) return ret; for (int i = LG - 1; i >= 0; --i) { if (par[i][v] != par[i][u]) { ret = max(ret, max(val[i][u], val[i][v])); v = par[i][v]; u = par[i][u]; } } ret = max(ret, max(val[0][u], val[0][v])); return ret; } int main() { int n, m, k, q; scanf("%d %d %d %d", &n, &m, &k, &q); for (int i = 0; i < m; ++i) { int u, v, w; scanf("%d %d %d", &u, &v, &w); --u, --v; g[u].emplace_back(v, w); g[v].emplace_back(u, w); } fill(dist, dist + n, infll); priority_queue<pair<long long, int>> pq; for (int i = 0; i < k; ++i) { from[i] = i; dist[i] = 0; pq.emplace(0, i); } while (!pq.empty()) { int v = pq.top().second; long long w = -pq.top().first; pq.pop(); if (dist[v] != w) continue; for (auto e : g[v]) { long long cur = w + e.second; if (dist[e.first] > cur) { from[e.first] = from[v]; dist[e.first] = cur; pq.emplace(-cur, e.first); } } } vector<tuple<long long, int, int>> edges; for (int v = 0; v < n; ++v) { for (auto e : g[v]) { if (from[v] == from[e.first]) continue; edges.emplace_back(dist[v] + e.second + dist[e.first], from[v], from[e.first]); } } fill(p, p + n, -1); sort(edges.begin(), edges.end()); for (auto e : edges) { int u, v; long long w; tie(w, u, v) = e; if (merge(u, v)) { tree[u].emplace_back(v, w); tree[v].emplace_back(u, w); } } par[0][0] = 0; val[0][0] = 0; lv[0] = 0; dfs(0); for (int i = 0; i < q; ++i) { int a, b; scanf("%d %d", &a, &b); --a, --b; printf("%lld\n", solve(a, b)); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MAXN = 2e5 + 5; const long long MAXM = 3e5 + 5; const long long INF = 1e9 + 7; const long long mod = 1e9 + 7; struct edge { long long from, to, w, nxt; } e[MAXM << 2], E[MAXM], E2[MAXM << 1]; long long head[MAXN], num_edge = 0; long long Head[MAXN], Num_edge = 0; struct node { long long bh, val; bool operator<(const node &b) const { return val > b.val; } }; long long n, m, k, Q, cnt; long long dis[MAXN], fa[MAXN], f[MAXN][21], dep[MAXN], maxm[MAXN][21]; bool vis[MAXN]; priority_queue<node> q; long long read() { long long s = 0, f = 0; char ch = getchar(); while (!isdigit(ch)) f |= (ch == '-'), ch = getchar(); while (isdigit(ch)) s = (s << 1) + (s << 3) + ch - '0', ch = getchar(); return f ? -s : s; } bool cmp(edge x, edge y) { return x.w < y.w; } void add_edge(long long from, long long to, long long w) { e[++num_edge] = (edge){from, to, w, head[from]}, head[from] = num_edge; } void Add_edge(long long from, long long to, long long w) { E2[++Num_edge] = (edge){from, to, w, Head[from]}, Head[from] = Num_edge; } long long find(long long x) { return fa[x] == x ? x : fa[x] = find(fa[x]); } void dij() { memset(dis, 0x3f, sizeof dis); dis[0] = 0; q.push((node){0, 0}); while (!q.empty()) { node u = q.top(); q.pop(); if (vis[u.bh]) continue; vis[u.bh] = true; for (long long i = head[u.bh]; i; i = e[i].nxt) { long long v = e[i].to; if (dis[v] > dis[u.bh] + e[i].w) { dis[v] = dis[u.bh] + e[i].w; if (!vis[v]) q.push((node){v, dis[v]}); } } } } void kruskal() { for (long long i = 1; i <= n; ++i) fa[i] = i; for (long long i = 1; i <= m; ++i) { long long uf = find(E[i].from), vf = find(E[i].to); if (uf != vf) { fa[vf] = uf; Add_edge(E[i].from, E[i].to, E[i].w), Add_edge(E[i].to, E[i].from, E[i].w); cnt++; if (cnt == n - 1) return; } } } void dfs(long long u, long long fa) { f[u][0] = fa; for (long long i = Head[u]; i; i = E2[i].nxt) { long long v = E2[i].to; if (v == fa) continue; dep[v] = dep[u] + 1; maxm[v][0] = E2[i].w; dfs(v, u); } } void init() { for (long long i = 1; i <= 20; ++i) { for (long long j = 1; j <= n; ++j) { f[j][i] = f[f[j][i - 1]][i - 1]; maxm[j][i] = max(maxm[j][i - 1], maxm[f[j][i - 1]][i - 1]); } } } long long get_max(long long x, long long y) { long long ans = 0; if (dep[x] < dep[y]) swap(x, y); for (long long i = 20; i >= 0; --i) { if (dep[f[x][i]] < dep[y]) continue; ans = max(ans, maxm[x][i]); x = f[x][i]; } if (x == y) return ans; for (long long i = 20; i >= 0; --i) { if (f[x][i] == f[y][i]) continue; ans = max(ans, max(maxm[x][i], maxm[y][i])); x = f[x][i]; y = f[y][i]; } ans = max(ans, max(maxm[x][0], maxm[y][0])); return ans; } signed main() { n = read(), m = read(), k = read(), Q = read(); for (long long i = 1, u, v, w; i <= m; ++i) { u = read(), v = read(), w = read(); add_edge(u, v, w), add_edge(v, u, w); E[i].from = u, E[i].to = v, E[i].w = w; } for (long long i = 1; i <= k; ++i) { add_edge(0, i, 0), add_edge(i, 0, 0); } dij(); for (long long i = 1; i <= m; ++i) { E[i].w += dis[E[i].from] + dis[E[i].to]; } sort(E + 1, E + m + 1, cmp); kruskal(); dep[1] = 1; dfs(1, -1); init(); for (long long i = 1, u, v; i <= Q; ++i) { u = read(), v = read(); cout << get_max(u, v) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MOD = (long long)1e9 + 7; const long double PI = 3.141592653589793238462643383279502884197; long long fac[1] = {1}, inv[1] = {1}; long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } long long mp(long long a, long long b) { long long ret = 1; while (b) { if (b & 1) ret = ret * a % MOD; a = a * a % MOD; b >>= 1; } return ret; } long long cmb(long long r, long long c) { return fac[r] * inv[c] % MOD * inv[r - c] % MOD; } vector<pair<int, int>> ov[100000]; int p[100000]; int find(int a) { if (p[a] == -1) return a; return p[a] = find(p[a]); } void merge(int a, int b) { a = find(a); b = find(b); if (a == b) return; p[b] = a; } long long tdist[100000]; pair<int, int> lr[300000]; pair<int, int> qu[300000]; int wif[100000]; priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq; struct edg { int u, v; long long co; bool operator<(const edg v2) const { return co < v2.co; }; }; int main() { memset(tdist, 0x3f, sizeof(tdist)); int n, m, k, q; scanf("%d %d %d %d", &n, &m, &k, &q); int a, b, c; while (m--) { scanf("%d %d %d", &a, &b, &c); a--; b--; ov[a].push_back({c, b}); ov[b].push_back({c, a}); } for (int i = 0; i < k; i++) { pq.push({0, i}); wif[i] = i; tdist[i] = 0; } pair<long long, int> tv; vector<edg> se; while (!pq.empty()) { tv = pq.top(); pq.pop(); if (tv.first != tdist[tv.second]) continue; for (pair<int, int> i : ov[tv.second]) { if (tdist[i.second] > tv.first + i.first) { tdist[i.second] = tv.first + i.first; pq.push({tv.first + i.first, i.second}); wif[i.second] = wif[tv.second]; } if (wif[i.second] != wif[tv.second]) { a = wif[i.second], b = wif[tv.second]; if (a > b) swap(a, b); se.push_back({a, b, i.first + tv.first + tdist[i.second]}); } } } sort((se).begin(), (se).end()); memset(p, -1, sizeof(p)); for (int i = 0; i < q; i++) { scanf("%d %d", &a, &b); lr[i] = {0, (int)(se).size() - 1}; qu[i] = {a - 1, b - 1}; } vector<pair<int, int>> v; for (int cnt = 0; cnt < 25; cnt++) { memset(p, -1, sizeof(p)); v.clear(); for (int i = 0; i < q; i++) if (lr[i].first <= lr[i].second) v.push_back({(lr[i].first + lr[i].second) >> 1, i}); if (v.empty()) break; sort((v).begin(), (v).end()); int l = 0; for (pair<int, int> i : v) { while (l < (int)(se).size() && se[i.first].co >= se[l].co) { merge(se[l].u, se[l].v); l++; } if (find(qu[i.second].first) == find(qu[i.second].second)) lr[i.second].second = i.first - 1; else lr[i.second].first = i.first + 1; } } for (int i = 0; i < q; i++) printf("%lld\n", se[lr[i].first].co); }
#include <bits/stdc++.h> using namespace std; int n, m, k, q; struct Edge { int v; long long d; Edge() { v = 0; d = 0; } Edge(int rv, int rd) { v = rv; d = rd; } }; struct SortEdge { int u; int v; long long d; }; bool operator<(const SortEdge& a, const SortEdge& b) { if (a.d != b.d) return a.d < b.d; if (a.u != b.u) return a.u < b.u; return a.v < b.v; } vector<Edge> e[100005]; long long du[100005]; int pre[100005]; int fa[100005 * 4][21]; long long ans[100005 * 4]; int dsuFa[100005 * 4]; int topK; int level[100005 * 4]; int tl[100005 * 4]; int tr[100005 * 4]; vector<SortEdge> se; void dijstra() { priority_queue<pair<long long, int>> pq; int i; for (i = 1; i <= n; i++) { if (i <= k) { du[i] = 0; pq.push({0, i}); } else { du[i] = -1; } pre[i] = i; } while (!pq.empty()) { auto cur = pq.top(); pq.pop(); int u = cur.second; long long cd = -cur.first; for (auto& it : e[u]) { long long nd = cd + it.d; if (du[it.v] == -1 || du[it.v] > nd) { du[it.v] = nd; pq.push({-nd, it.v}); pre[it.v] = pre[u]; } } } } int dsuFind(int x) { if (dsuFa[x] != x) { dsuFa[x] = dsuFind(dsuFa[x]); } return dsuFa[x]; } void dsuUnion(int x, int y, long long val) { int xx = dsuFind(x); int yy = dsuFind(y); topK++; fa[xx][0] = topK; fa[yy][0] = topK; dsuFa[xx] = topK; dsuFa[yy] = topK; dsuFa[topK] = topK; ans[topK] = val; tl[topK] = xx; tr[topK] = yy; } void dfs(int u) { for (int j = 1; j < 21; j++) { fa[u][j] = fa[fa[u][j - 1]][j - 1]; } if (tl[u]) { level[tl[u]] = level[u] + 1; dfs(tl[u]); } if (tr[u]) { level[tr[u]] = level[u] + 1; dfs(tr[u]); } } int lca(int a, int b) { if (level[a] < level[b]) { int c = a; a = b; b = c; } int ha = level[a]; int hb = level[b]; int begina = a; int beginb = b; int beginlevela = level[a]; int beginlevelb = level[b]; int deltaH = ha - hb; for (int i = 0; i < 21; i++) { if (deltaH & (1 << i)) { a = fa[a][i]; } } for (int i = 20; i >= 0; i--) { if (fa[a][i] != fa[b][i]) { a = fa[a][i]; b = fa[b][i]; } } return fa[a][0]; } int main() { std::ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cin >> n >> m >> k >> q; int i; for (i = 0; i < m; i++) { int a, b, c; cin >> a >> b >> c; e[a].push_back({b, c}); e[b].push_back({a, c}); } dijstra(); for (i = 1; i <= n; i++) { for (int j = 0; j < e[i].size(); j++) { if (i > e[i][j].v) { if (pre[i] != pre[e[i][j].v]) { if (pre[i] <= k && pre[e[i][j].v] <= k) { se.push_back( {pre[i], pre[e[i][j].v], du[i] + du[e[i][j].v] + e[i][j].d}); } } } } } sort(se.begin(), se.end()); topK = k; for (i = 1; i <= k; i++) { dsuFa[i] = i; tl[i] = 0; tr[i] = 0; level[i] = 0; } for (i = 0; i < se.size(); i++) { if (dsuFind(se[i].u) != dsuFind(se[i].v)) { dsuUnion(se[i].u, se[i].v, se[i].d); } } level[topK] = 1; dfs(topK); while (q--) { int a, b; cin >> a >> b; int c = lca(a, b); if (c > 0) { cout << ans[c] << endl; } else { cout << a << " " << b << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 5; struct edge { int to; long long cost; }; struct path { int node; long long cost; bool operator<(const path &other) const { return cost > other.cost; } }; bool known[N]; long long dist[N]; int par[N], p[N], we[N]; vector<edge> adj[N]; set<int> queries[N]; long long ans[N]; int n, m, k, q; void Dijkstra() { priority_queue<path> pq; memset(known, 0, sizeof known); memset(dist, 63, sizeof dist); for (int i = 0; i < int(k); i++) { pq.push({i, 0}); dist[i] = 0; par[i] = i; } while (pq.size()) { int node = pq.top().node; long long cost = pq.top().cost; pq.pop(); if (known[node]) continue; known[node] = 1; for (auto &c : adj[node]) { if (dist[c.to] > dist[node] + c.cost) { dist[c.to] = dist[node] + c.cost; par[c.to] = par[node]; pq.push({c.to, dist[c.to]}); } } } } int f(int u) { if (u == p[u]) return u; return p[u] = f(p[u]); } bool is_connected(int a, int b) { return f(a) == f(b); } void connect(int a, int b, long long w) { a = f(a); b = f(b); if (a == b) return; if (we[a] < we[b]) swap(a, b); we[a] += we[b]; p[b] = a; if (int(queries[a].size()) < int(queries[b].size())) queries[a].swap(queries[b]); for (auto idx : queries[b]) { if (queries[a].count(idx)) { queries[a].erase(idx); ans[idx] = w; } else { queries[a].insert(idx); } } } void init() { for (int i = 0; i < N; i++) p[i] = i, we[i] = 1; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int a, b, w; cin >> n >> m >> k >> q; for (int i = 0; i < int(m); i++) { cin >> a >> b >> w; a--, b--; adj[a].push_back({b, w}); adj[b].push_back({a, w}); } Dijkstra(); vector<pair<long long, pair<int, int> > > edges; for (int i = 0; i < int(n); i++) { for (auto e : adj[i]) { if (par[e.to] != par[i]) { edges.push_back({dist[e.to] + dist[i] + e.cost, {par[e.to], par[i]}}); } } } sort(edges.begin(), edges.end()); init(); for (int i = 0; i < int(q); i++) { cin >> a >> b; --a, --b; queries[a].insert(i); queries[b].insert(i); } for (auto e : edges) { int u = e.second.first, v = e.second.second; long long W = e.first; if (is_connected(u, v)) continue; connect(u, v, W); } for (int i = 0; i < int(q); i++) cout << ans[i] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { for (auto i = begin(v); i != end(v); i++) os << *i << (i == end(v) - 1 ? "" : " "); return os; } template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto i = begin(v); i != end(v); i++) is >> *i; return is; } int n, m, k, q; vector<pair<int, int>> edg[101000]; vector<long long> best_dists(101000, 10000000000000000LL); set<int> markers[101000]; int dsu[101000]; int drank[101000]; vector<long long> ans(301000, 10000000000000000LL); struct Edg { int u, v; long long w; }; int dsu_find(int a) { if (dsu[a] == a) return a; return dsu[a] = dsu_find(dsu[a]); } void dsu_union(int a, int b, long long curr_ans) { a = dsu_find(a); b = dsu_find(b); if (a == b) return; if (markers[a].size() < markers[b].size()) swap(a, b); dsu[b] = a; for (int x : markers[b]) { if (markers[a].find(x) != markers[a].end()) { ans[x] = curr_ans; markers[a].erase(x); } else { markers[a].insert(x); } } } int main() { cin.tie(NULL); ios_base::sync_with_stdio(false); cout.tie(NULL); cin >> n >> m >> k >> q; vector<Edg> edges; for (int i = 0; i < m; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; edg[u].push_back({v, w}); edg[v].push_back({u, w}); edges.push_back(Edg{u, v, w}); } priority_queue<pair<long long, int>, vector<pair<long long, int>>, std::greater<pair<long long, int>>> ss; for (int i = 0; i < k; i++) { ss.push({0, i}); best_dists[i] = 0; } while (ss.size() > 0) { auto curr = ss.top(); ss.pop(); if (curr.first != best_dists[curr.second]) continue; for (auto x : edg[curr.second]) { long long new_dist = curr.first + x.second; if (new_dist < best_dists[x.first]) { best_dists[x.first] = new_dist; ss.push({best_dists[x.first], x.first}); } } } for (int i = 0; i < m; i++) { edges[i].w += best_dists[edges[i].u] + best_dists[edges[i].v]; } sort(edges.begin(), edges.end(), [&](Edg& x, Edg& y) { return x.w < y.w; }); vector<pair<int, int>> qs(q); for (int i = 0; i < q; i++) { int a, b; cin >> a >> b; a--, b--; qs[i] = {a, b}; markers[a].insert(i); markers[b].insert(i); } for (int i = 0; i < n; i++) { dsu[i] = i; drank[i] = 1; } for (int i = 0; i < m; i++) { dsu_union(edges[i].u, edges[i].v, edges[i].w); } for (int i = 0; i < q; i++) cout << ans[i] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; const long long INF = 8e18 + 5; const int maxn = 1e5 + 5; const int maxm = 3e5 + 5; struct edge { int v, nex, w; } e[maxm << 1]; int n, m, k, Q, tot; int head[maxn], par[maxn], deep[maxn], fa[maxn][21]; long long dis[maxn], va[maxn][21]; ; vector<pair<long long, int> > E[maxn]; bool vis[maxn]; int find(int x) { return par[x] == x ? x : par[x] = find(par[x]); } void add(int u, int v, int w) { e[++tot] = {v, head[u], w}, head[u] = tot; e[++tot] = {u, head[v], w}, head[v] = tot; } void dfs(int u, int gg, long long d) { par[u] = gg; for (int i = head[u]; i; i = e[i].nex) { int v = e[i].v, w = e[i].w; long long now = d + w; if (now == dis[v]) dfs(v, gg, now); } } void getdeep(int u, int pre, int d) { deep[u] = d; for (auto &v : E[u]) if (v.second != pre) { fa[v.second][0] = u, va[v.second][0] = v.first; getdeep(v.second, u, d + 1); } } void LCAinit() { getdeep(1, 0, 0); for (int i = 1; i <= 20; ++i) { for (int j = 1; j <= k; ++j) { if (deep[j] - (1 << i) < 0) continue; fa[j][i] = fa[fa[j][i - 1]][i - 1]; va[j][i] = max(va[j][i - 1], va[fa[j][i - 1]][i - 1]); } } } long long query(int x, int y) { long long res = 0; if (deep[x] < deep[y]) swap(x, y); for (int k = 0; k < 21; ++k) { if (deep[x] - deep[y] >> k & 1) res = max(res, va[x][k]), x = fa[x][k]; } if (x == y) return res; for (int k = 20; k >= 0; --k) { if (fa[x][k] != fa[y][k]) { res = max({res, va[x][k], va[y][k]}); x = fa[x][k], y = fa[y][k]; } } res = max({res, va[x][0], va[y][0]}); return res; } int main() { ios::sync_with_stdio(false); cin.tie(0); cin >> n >> m >> k >> Q; for (int i = 1; i <= n; ++i) dis[i] = INF; for (int i = 0; i < m; ++i) { int u, v, w; cin >> u >> v >> w; add(u, v, w); } for (int i = 1; i <= n; ++i) par[i] = i; priority_queue<pair<long long, int> > q; for (int i = 1; i <= k; ++i) q.push({0, i}), dis[i] = 0; while (!q.empty()) { auto now = q.top(); q.pop(); int u = now.second; if (vis[u]) continue; vis[u] = 1; for (int i = head[u]; i; i = e[i].nex) { int v = e[i].v, w = e[i].w; if (!vis[v] && dis[v] > w - now.first) { dis[v] = w - now.first; q.push({-w + now.first, v}); } } } for (int i = 1; i <= k; ++i) dfs(i, i, 0); vector<pair<long long, pair<int, int> > > a; for (int u = 1; u <= n; ++u) { for (int i = head[u]; i; i = e[i].nex) { int v = e[i].v; if (par[v] != par[u]) { a.push_back({dis[u] + dis[v] + e[i].w, {par[u], par[v]}}); } } } sort(a.begin(), a.end()); for (auto &x : a) { int u = x.second.first, v = x.second.second; u = find(u), v = find(v); if (u == v) continue; par[u] = par[v]; E[u].push_back({x.first, v}); E[v].push_back({x.first, u}); } LCAinit(); while (Q--) { int x, y; cin >> x >> y; cout << query(x, y) << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); const long long INF = (long long)1e15; const int N = 300300; int n, m, k, q; long long ANS[N]; vector<int> g[N]; vector<pair<int, int> > Q[N]; int par[N]; vector<int> a[N]; long long ed[N][3]; pair<long long, int> ord[N]; set<pair<long long, int> > setik; long long dist[N][2]; int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 0; i < m; i++) { scanf("%lld%lld%lld", &ed[i][0], &ed[i][1], &ed[i][2]); ed[i][0]--; ed[i][1]--; g[ed[i][0]].push_back(i); g[ed[i][1]].push_back(i); } for (int i = 0; i < n; i++) { if (i < k) { dist[i][0] = 0; dist[i][1] = i; } else dist[i][0] = INF; setik.insert(make_pair(dist[i][0], i)); } while (!setik.empty()) { int v = setik.begin()->second; 42; setik.erase(setik.begin()); for (int id : g[v]) { int u = ed[id][0] ^ ed[id][1] ^ v; long long w = dist[v][0] + ed[id][2]; if (w >= dist[u][0]) continue; setik.erase(make_pair(dist[u][0], u)); dist[u][0] = w; dist[u][1] = dist[v][1]; setik.insert(make_pair(dist[u][0], u)); } } for (int i = 0; i < m; i++) { ed[i][2] += dist[ed[i][0]][0] + dist[ed[i][1]][0]; ed[i][0] = dist[ed[i][0]][1]; ed[i][1] = dist[ed[i][1]][1]; ord[i] = make_pair(ed[i][2], i); } sort(ord, ord + m); for (int i = 0; i < k; i++) { par[i] = i; a[i].push_back(i); } for (int i = 0; i < q; i++) { int v, u; scanf("%d%d", &v, &u); v--; u--; Q[v].push_back(make_pair(u, i)); Q[u].push_back(make_pair(v, i)); } for (int i = 0; i < m; i++) { 42; int id = ord[i].second; int v = ed[id][0], u = ed[id][1]; v = par[v]; u = par[u]; if (v == u) continue; if ((int)a[v].size() > (int)a[u].size()) swap(v, u); for (int w : a[v]) { for (pair<int, int> QQ : Q[w]) { int z = QQ.first; if (par[z] == u) ANS[QQ.second] = ed[id][2]; } } for (int w : a[v]) { par[w] = u; a[u].push_back(w); } } for (int i = 0; i < q; i++) printf("%lld\n", ANS[i]); return 0; }
#include <bits/stdc++.h> using namespace std; const long long M = 6e5 + 10; const long long N = 4e5 + 10; long long read() { long long x = 0, f = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); } return f * x; } long long n, m, k, t; struct edge { long long u, v, w, nxt; } e[M << 1], E[M << 1], E2[M << 1]; long long head[M], cnt1; long long Head[M], cnt2; struct node { long long num, val; bool operator<(const node &b) const { return val > b.val; } }; long long fa[N], dis[N], vis[N]; bool cmp(edge x, edge y) { return x.w < y.w; } void add_edge(long long u, long long v, long long w) { e[++cnt1] = (edge){u, v, w, head[u]}, head[u] = cnt1; } void Add_edge(long long u, long long v, long long w) { E2[++cnt2] = (edge){u, v, w, Head[u]}, Head[u] = cnt2; } long long find(long long x) { return fa[x] == x ? x : fa[x] = find(fa[x]); } priority_queue<node> q; void dij() { memset(dis, 0x3f, sizeof dis); dis[0] = 0; q.push((node){0, 0}); while (!q.empty()) { node u = q.top(); q.pop(); if (vis[u.num]) continue; vis[u.num] = true; for (long long i = head[u.num]; i; i = e[i].nxt) { long long v = e[i].v; if (dis[v] > dis[u.num] + e[i].w) { dis[v] = dis[u.num] + e[i].w; if (!vis[v]) q.push((node){v, dis[v]}); } } } } long long cnt; void kruskal() { for (long long i = 1; i <= n; ++i) fa[i] = i; for (long long i = 1; i <= m; ++i) { long long uf = find(E[i].u), vf = find(E[i].v); if (uf != vf) { fa[vf] = uf; Add_edge(E[i].u, E[i].v, E[i].w), Add_edge(E[i].v, E[i].u, E[i].w); cnt++; if (cnt == n - 1) return; } } } long long f[N][22], dep[N], maxm[N][22]; void dfs(long long u, long long fa) { f[u][0] = fa; for (long long i = Head[u]; i; i = E2[i].nxt) { long long v = E2[i].v; if (v == fa) continue; dep[v] = dep[u] + 1; maxm[v][0] = E2[i].w; dfs(v, u); } } void init() { for (long long i = 1; i <= 20; ++i) { for (long long j = 1; j <= n; ++j) { f[j][i] = f[f[j][i - 1]][i - 1]; maxm[j][i] = max(maxm[j][i - 1], maxm[f[j][i - 1]][i - 1]); } } } long long get_max(long long x, long long y) { long long ans = 0; if (dep[x] < dep[y]) swap(x, y); for (long long i = 20; i >= 0; --i) { if (dep[f[x][i]] < dep[y]) continue; ans = max(ans, maxm[x][i]); x = f[x][i]; } if (x == y) return ans; for (long long i = 20; i >= 0; --i) { if (f[x][i] == f[y][i]) continue; ans = max(ans, max(maxm[x][i], maxm[y][i])); x = f[x][i]; y = f[y][i]; } ans = max(ans, max(maxm[x][0], maxm[y][0])); return ans; } signed main() { n = read(), m = read(), k = read(), t = read(); for (long long i = 1, u, v, w; i <= m; ++i) { u = read(), v = read(), w = read(); add_edge(u, v, w), add_edge(v, u, w); E[i].u = u, E[i].v = v, E[i].w = w; } for (long long i = 1; i <= k; ++i) add_edge(0, i, 0), add_edge(i, 0, 0); dij(); for (long long i = 1; i <= m; ++i) E[i].w += dis[E[i].u] + dis[E[i].v]; sort(E + 1, E + m + 1, cmp); kruskal(); dep[1] = 1; dfs(1, -1); init(); for (long long i = 1, u, v; i <= t; ++i) { u = read(), v = read(); cout << get_max(u, v) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 7; const int Q = 3e5 + 7; int d[N], ra[N]; vector<pair<int, int>> g[N]; unordered_set<int> tokens[N]; long long dist[N]; long long ans[Q]; vector<int> to_ans; int find(int idx) { if (d[idx] == 0) return idx; return d[idx] = find(d[idx]); } bool join(int x, int y) { x = find(x); y = find(y); if (x == y) return false; if (ra[x] > ra[y]) swap(x, y); d[x] = y; for (auto &v : tokens[x]) { if (tokens[y].count(v)) { to_ans.push_back(v); tokens[y].erase(v); } else tokens[y].insert(v); } if (ra[x] == ra[y]) ++ra[y]; return true; } struct Edge { int a, b; long long w; Edge() : a(0), b(0), w(0) {} Edge(int _a, int _b, long long _w) : a(_a), b(_b), w(_w) {} }; Edge el[Q], nel[Q]; int main() { ios::sync_with_stdio(false); cin.tie(0); clock_t ttt = clock(); int n, m, k, q; cin >> n >> m >> k >> q; for (int i = 1; i <= m; ++i) { cin >> el[i].a >> el[i].b >> el[i].w; nel[i].a = el[i].a; nel[i].b = el[i].b; g[el[i].a].emplace_back(el[i].b, el[i].w); g[el[i].b].emplace_back(el[i].a, el[i].w); } for (int i = 1; i <= q; ++i) { int a, b; cin >> a >> b; tokens[a].insert(i); tokens[b].insert(i); } for (int i = k + 1; i <= n; ++i) dist[i] = 1LL << 60; priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> dji; for (int i = 1; i <= k; ++i) dji.emplace(0LL, i); while (!dji.empty()) { auto v = dji.top(); dji.pop(); if (v.first > dist[v.second]) continue; for (auto &cc : g[v.second]) { if (dist[cc.first] > dist[v.second] + cc.second) { dist[cc.first] = dist[v.second] + cc.second; dji.emplace(dist[cc.first], (int)cc.first); } } } for (int i = 1; i <= m; ++i) { nel[i].w = dist[el[i].a] + dist[el[i].b] + el[i].w; } sort(nel + 1, nel + 1 + m, [](const Edge &lhs, const Edge &rhs) { return lhs.w < rhs.w; }); for (int i = 1; i <= m; ++i) { auto &v = nel[i]; if (!join(v.a, v.b)) continue; for (auto &letans : to_ans) { ans[letans] = v.w; } to_ans.clear(); } for (int i = 1; i <= q; ++i) { cout << ans[i] << '\n'; } cerr << "Time taken " << (double)(clock() - ttt) / CLOCKS_PER_SEC << " seconds\n"; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; const int N = 6e5 + 10, LG = 21; int n, m, k, t; int p[N], in[N], out[N], L[N][LG]; vector<vector<int>> tree(N, vector<int>()); int find_set(int x) { return x == p[x] ? x : p[x] = find_set(p[x]); } void add_edge(int u, int v) { tree[u].push_back(v); tree[v].push_back(u); } void dfs(int x, int p) { static int timer = 0; in[x] = ++timer; if (~p) L[x][0] = p; for (int i = 1; i < LG; ++i) { L[x][i] = L[L[x][i - 1]][i - 1]; } for (int to : tree[x]) { if (to != p) { dfs(to, x); } } out[x] = ++timer; } bool isAnc(int x, int y) { return !x || (in[x] <= in[y] && out[x] >= out[y]); } int LCA(int x, int y) { if (isAnc(x, y)) return x; if (isAnc(y, x)) return y; for (int i = LG - 1; i >= 0; --i) { if (!isAnc(L[x][i], y)) { x = L[x][i]; } } return L[x][0]; } int main() { ios::sync_with_stdio(0); cin.tie(0); cin >> n >> m >> k >> t; vector<vector<pair<int, int>>> edges(n + 1, vector<pair<int, int>>()); for (int i = 1; i <= m; ++i) { int u, v, w; cin >> u >> v >> w; edges[u].push_back({v, w}); edges[v].push_back({u, w}); } priority_queue<vector<ll>> q; for (int i = 1; i <= k; ++i) { q.push(vector<ll>{0, i, i}); } vector<bool> vis(n + 1); vector<ll> dist(n + 1), cent(n + 1); while (!q.empty()) { vector<ll> p = q.top(); q.pop(); ll distance = -p[0]; ll cur_vertex = p[1]; ll central = p[2]; if (vis[cur_vertex]) continue; vis[cur_vertex] = 1; dist[cur_vertex] = distance; cent[cur_vertex] = central; for (pair<int, int> p : edges[cur_vertex]) { vector<ll> next = {-distance - p.second, p.first, p.first <= k ? p.first : central}; q.push(next); } } vector<vector<ll>> v; for (int i = 1; i <= n; ++i) { for (pair<int, int> p : edges[i]) { int to = p.first; if (cent[i] != cent[to]) { v.push_back( vector<ll>{dist[i] + dist[to] + p.second, cent[i], cent[to]}); } } } sort(v.begin(), v.end()); for (int i = 0; i < N; ++i) p[i] = i; int fake = n + 1; vector<ll> weight; for (vector<ll> edge : v) { int u = edge[1]; int v = edge[2]; ll cost = edge[0]; u = find_set(u); v = find_set(v); if (u == v) continue; weight.push_back(cost); add_edge(u, fake); add_edge(v, fake); p[u] = p[v] = fake; ++fake; } dfs(fake - 1, -1); for (int i = 0; i < t; ++i) { int a, b; cin >> a >> b; int th = LCA(a, b) - n - 1; cout << weight[th] << '\n'; } }
#include <bits/stdc++.h> namespace input { const int size = 1 << 24; char buf[size], *p1, *p2; template <class type> void inline read(type &a) { int c = (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, size, stdin), p1 == p2) ? EOF : *p1++); for (; !(c >= '0' && c <= '9'); c = (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, size, stdin), p1 == p2) ? EOF : *p1++)) ; for (a = 0; (c >= '0' && c <= '9'); a *= 10, a += c ^ 48, c = (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, size, stdin), p1 == p2) ? EOF : *p1++)) ; } }; // namespace input namespace output { const int size = 1 << 24; char d[20], puf[size], *p = puf; template <class type> void inline write(type a, char c = '\n') { int s = 0; d[0] = 0; for (; a; d[s++] = a % 10, a /= 10) ; for (s = s ? s : 1; s; (*p++ = d[--s] + 48, p - puf == size ? (fwrite(puf, 1, p - puf, stdout), p = puf) : 0)) ; (*p++ = c, p - puf == size ? (fwrite(puf, 1, p - puf, stdout), p = puf) : 0); } }; // namespace output using namespace std; using namespace input; using namespace output; const int nsz = 1e5, msz = 3e5, lgsz = 17; const long long inf = 0x3f3f3f3f3f3f3f3f; bool vis[nsz + 5]; int n, m, k, q, rt = 1, fm[nsz + 5]; int t, pr[nsz + 5], dep[nsz + 5], siz[nsz + 5], hs[nsz + 5], top[nsz + 5], id[nsz + 5]; long long dis[nsz + 5], w[nsz + 5]; struct edge { int nxt, fm, to; long long w; edge(int nxt = 0, int fm = 0, int to = 0, long long w = 0) { this->nxt = nxt, this->fm = fm, this->to = to, this->w = w; } bool inline operator<(const edge oth) const { return this->w < oth.w; } }; struct graph { int sz, hd[nsz + 5]; edge e[2 * msz + 5]; void inline connect(int u, int v, long long w) { e[++sz] = edge(hd[u], u, v, w), hd[u] = sz; e[++sz] = edge(hd[v], v, u, w), hd[v] = sz; } }; graph g, tr; bool inline cmp(pair<long long, int> a, pair<long long, int> b) { return a.first > b.first; } struct heap { int sz; pair<long long, int> h[msz + 5]; heap() { sz = 0; } void inline push(pair<long long, int> e) { h[sz++] = e; push_heap(h, h + sz, cmp); } pair<long long, int> inline get() { pop_heap(h, h + sz, cmp); return h[--sz]; } }; heap h; struct union_find { int pr[nsz + 5]; void inline init() { for (int u = 1; u <= k; ++u) { pr[u] = u; } } int qry(int u) { return pr[u] == u ? u : pr[u] = qry(pr[u]); } bool inline unite(int u, int v) { int pu = qry(u), pv = qry(v); if (pu == pv) return 0; pr[pv] = pu; return 1; } }; union_find uf; struct sparse_table { int lg[nsz + 5]; long long st[nsz + 5][lgsz + 5]; void inline init() { for (int i = 1; i <= n; ++i) { lg[i] = lg[i >> 1] + 1; st[id[i]][0] = w[i]; } for (int k = 1; k <= lg[n]; ++k) { for (int u = 1; u <= n; ++u) { if (u + (1 << k) - 1 > n) break; int p = u + (1 << (k - 1)); st[u][k] = max(st[u][k - 1], st[p][k - 1]); } } } long long inline qry(int l, int r) { int k = lg[r - l + 1] - 1, len = 1 << k; return max(st[l][k], st[r - len + 1][k]); } }; sparse_table st; void inline dijkstra() { memset(vis, 0, sizeof(vis)); memset(dis, inf, sizeof(dis)); for (int u = 1; u <= k; ++u) { fm[u] = u; h.push(make_pair(dis[u] = 0, u)); } for (; h.sz;) { int u = h.get().second; for (int i = g.hd[u]; i; i = g.e[i].nxt) { int v = g.e[i].to; long long w = g.e[i].w; if (vis[v]) continue; if (dis[v] > dis[u] + w) { fm[v] = fm[u]; h.push(make_pair(dis[v] = dis[u] + w, v)); } } } } void inline kruskal() { for (int i = 1; i <= g.sz; ++i) { int u = g.e[i].fm, v = g.e[i].to; g.e[i].w += dis[u] + dis[v]; } sort(g.e + 1, g.e + g.sz + 1); uf.init(); for (int i = 1; i <= g.sz; ++i) { int u = fm[g.e[i].fm], v = fm[g.e[i].to]; long long w = g.e[i].w; if (uf.unite(u, v)) { tr.connect(u, v, w); } } } void dfs1(int u = rt) { siz[u] = 1; for (int i = tr.hd[u]; i; i = tr.e[i].nxt) { int v = tr.e[i].to; long long w = tr.e[i].w; if (v == pr[u]) continue; pr[v] = u; ::w[v] = w; dep[v] = dep[u] + 1; dfs1(v); siz[u] += siz[v]; if (siz[hs[u]] < siz[v]) { hs[u] = v; } } } void dfs2(int u = rt, int tp = rt) { id[u] = ++t; top[u] = tp; if (!hs[u]) return; dfs2(hs[u], tp); for (int i = tr.hd[u]; i; i = tr.e[i].nxt) { int v = tr.e[i].to; if (v == pr[u] || v == hs[u]) continue; dfs2(v, v); } } long long inline qry(int u, int v) { long long res = 0; for (; top[u] != top[v]; v = pr[top[v]]) { if (dep[top[u]] > dep[top[v]]) { swap(u, v); } res = max(res, st.qry(id[top[v]], id[v])); } if (dep[u] > dep[v]) { swap(u, v); } if (id[u] + 1 <= id[v]) { res = max(res, st.qry(id[u] + 1, id[v])); } return res; } void inline init() { dijkstra(); kruskal(); dfs1(); dfs2(); st.init(); } int main() { read(n), read(m), read(k), read(q); for (int i = 1; i <= m; ++i) { int u, v, w; read(u), read(v), read(w); g.connect(u, v, w); } init(); for (int i = 1; i <= q; ++i) { int u, v; read(u), read(v); write(qry(u, v)); } (fwrite(puf, 1, p - puf, stdout), p = puf); }
#include <bits/stdc++.h> using namespace std; const int A = 1e5 + 11; const int B = 1e6 + 11; const int mod = 1e9 + 7; const int inf = 0x3f3f3f3f; inline int read() { char c = getchar(); int x = 0, f = 1; for (; !isdigit(c); c = getchar()) if (c == '-') f = -1; for (; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48); return x * f; } struct edgexx { int v, nxt, w; } edge[B]; struct edgex { int v, nxt; } edge_[B]; struct node { long long d; int id; bool operator<(const node &a) const { return d > a.d; } }; struct xxs { int u, v; long long w; bool operator<(const xxs &e) const { return w < e.w; } } e[B]; int n, cnt, js, k, c, t, head[B], m, q, head2[B], fa[B], u_fa[B]; long long dis[B], wnd[B]; int sz[B], son[B], top[B], dep[B]; priority_queue<node> pq; void add1(int u, int v, int w) { edge[++cnt].nxt = head[u]; edge[cnt].v = v; edge[cnt].w = w; head[u] = cnt; } void add2(int u, int v) { edge_[++js].nxt = head2[u]; edge_[js].v = v; head2[u] = js; } int find(int x) { if (x == u_fa[x]) return x; return u_fa[x] = find(u_fa[x]); } void dfs1(int u, int f) { sz[u] = 1; dep[u] = dep[fa[u] = f] + 1; for (int i = head2[u]; i; i = edge_[i].nxt) { int v = edge_[i].v; if (v == f) continue; dfs1(v, u); sz[u] += sz[v]; if (sz[v] > sz[son[u]]) son[u] = v; } } void dfs2(int u, int topf) { top[u] = topf; if (son[u]) dfs2(son[u], topf); for (int i = head2[u]; i; i = edge_[i].nxt) { int v = edge_[i].v; if (v == fa[u] || v == son[u]) continue; dfs2(v, v); } } int lca(int u, int v) { while (top[u] != top[v]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); u = fa[top[u]]; } return dep[u] < dep[v] ? u : v; } int main() { cin >> n >> m >> k >> q; for (int i = 1; i <= m; i++) { int x = read(), y = read(), z = read(); add1(x, y, z); add1(y, x, z); e[i] = (xxs){x, y, z}; } memset(dis, 0x3f, sizeof(dis)); for (int i = 1; i <= k; i++) pq.push((node){dis[i] = 0, i}); while (!pq.empty()) { long long d = pq.top().d; int u = pq.top().id; pq.pop(); if (d != dis[u]) continue; for (int i = head[u]; i; i = edge[i].nxt) { int v = edge[i].v; if (dis[v] > d + edge[i].w) pq.push((node){dis[v] = d + edge[i].w, v}); } } for (int i = 1; i <= m; i++) e[i].w += dis[e[i].u] + dis[e[i].v]; sort(e + 1, e + 1 + m); for (int i = 1; i <= 2 * n; i++) u_fa[i] = i; cnt = n; for (int i = 1; i <= m; i++) { int u = e[i].u, v = e[i].v; long long w = e[i].w; u = find(u); v = find(v); if (u == v) continue; u_fa[u] = u_fa[v] = ++cnt; wnd[cnt] = w; add2(cnt, u); add2(cnt, v); } dfs1(cnt, 0); dfs2(cnt, cnt); while (q--) { int u = read(), v = read(); printf("%lld\n", wnd[lca(u, v)]); } return 0; }
#include <bits/stdc++.h> using namespace std; const int N_MAX = 100002; const int M_MAX = 300002; const int Q_MAX = 300002; const int W_MAX = 1000000001; const long long INF = 1LL * M_MAX * W_MAX; int n, m, k, q; struct Edge { int u, v; long long w; int other(int node) { return this->u + this->v - node; } }; bool operator<(const Edge &a, const Edge &b) { return a.w < b.w; } Edge edges[M_MAX]; vector<Edge *> outEdges[N_MAX]; int qa[Q_MAX], qb[Q_MAX]; long long l[Q_MAX], r[Q_MAX], mid[Q_MAX]; int finish; vector<pair<long long, int> > mids; int root[N_MAX]; int find_root(int node) { if (root[node] == node) return node; return root[node] = find_root(root[node]); } void join(int u, int v) { u = find_root(u); v = find_root(v); if (u == v) return; root[u] = v; } long long d[N_MAX]; set<pair<long long, int> > s; bool visited[N_MAX]; void dijkstra() { for (int i = 1; i <= k; i++) s.insert(make_pair(0, i)); while (!s.empty()) { pair<long long, int> f = *s.begin(); s.erase(s.begin()); if (visited[f.second] == true) continue; visited[f.second] = true; d[f.second] = f.first; for (Edge *e : outEdges[f.second]) if (visited[e->other(f.second)] == false) s.insert(make_pair(f.first + e->w, e->other(f.second))); } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (int i = 1; i <= m; i++) { cin >> edges[i].u >> edges[i].v >> edges[i].w; outEdges[edges[i].u].push_back(&edges[i]); outEdges[edges[i].v].push_back(&edges[i]); } for (int i = 1; i <= q; i++) cin >> qa[i] >> qb[i]; for (int i = 1; i <= n; i++) d[i] = INF; dijkstra(); long long mx = -1; for (int i = 1; i <= m; i++) { edges[i].w += d[edges[i].u] + d[edges[i].v]; mx = max(mx, edges[i].w); } for (int i = 1; i <= q; i++) { l[i] = 0; r[i] = mx; } sort(edges + 1, edges + m + 1); while (finish < q) { mids.clear(); for (int i = 1; i <= q; i++) if (l[i] < r[i]) { mid[i] = (l[i] + r[i]) / 2; mids.push_back(make_pair(mid[i], i)); } sort(mids.begin(), mids.end()); int pos = 0; for (int i = 1; i <= n; i++) root[i] = i; for (int i = 0; i < mids.size(); i++) { while (pos < m && edges[pos + 1].w <= mids[i].first) { pos++; join(edges[pos].u, edges[pos].v); } if (find_root(qa[mids[i].second]) == find_root(qb[mids[i].second])) r[mids[i].second] = mids[i].first; else l[mids[i].second] = mids[i].first + 1; if (l[mids[i].second] >= r[mids[i].second]) finish++; } } for (int i = 1; i <= q; i++) cout << l[i] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; vector<pair<long long, long long> > Next[200005]; vector<pair<long long, long long> > use[200005]; priority_queue<pair<long long, long long>, vector<pair<long long, long long> >, greater<pair<long long, long long> > > all; priority_queue<pair<long long, pair<long long, long long> >, vector<pair<long long, pair<long long, long long> > >, greater<pair<long long, pair<long long, long long> > > > mst; bool have[200005] = {0}; long long con[200005]; long long Father[200005]; long long who[25][200005]; long long big[25][200005]; long long deg[200005]; pair<long long, pair<long long, long long> > t2; pair<long long, long long> t; long long Find(long long here) { if (Father[here] == here) return here; Father[here] = Find(Father[here]); return Father[here]; } void F(long long here, long long d) { long long i, j; have[here] = 1; deg[here] = d; for (j = 1; (1 << j) <= d; j++) { who[j][here] = who[j - 1][who[j - 1][here]]; big[j][here] = max(big[j - 1][here], big[j - 1][who[j - 1][here]]); } for (auto i : use[here]) { if (!have[i.first]) { who[0][i.first] = here; big[0][i.first] = i.second; F(i.first, d + 1); } } } long long LCA(long long a, long long b) { long long i; if (a == b) return 0; if (deg[a] > deg[b]) for (i = 20; i >= 0; i--) if (deg[a] - (1 << i) >= deg[b]) return max(LCA(who[i][a], b), big[i][a]); if (deg[a] < deg[b]) for (i = 20; i >= 0; i--) if (deg[b] - (1 << i) >= deg[a]) return max(LCA(a, who[i][b]), big[i][b]); if (who[0][a] == who[0][b]) return max(big[0][a], big[0][b]); for (i = 20; i >= 0; i--) if ((1 << i) <= max(deg[a], deg[b]) && who[i][a] != who[i][b]) return max(max(big[i][a], big[i][b]), LCA(who[i][a], who[i][b])); } int main() { long long N, M, K, Q, tt, i, a, b; scanf("%lld %lld %lld %lld", &N, &M, &K, &Q); for (i = 0; i < M; i++) { scanf("%lld %lld %lld", &a, &b, &tt); Next[a].push_back(make_pair(b, tt)); Next[b].push_back(make_pair(a, tt)); } for (i = 1; i <= K; i++) all.push(make_pair(0, i)); while (!all.empty()) { t = all.top(); all.pop(); if (have[t.second]) continue; have[t.second] = 1; con[t.second] = t.first; for (auto i : Next[t.second]) all.push(make_pair(t.first + i.second, i.first)); } for (i = 1; i <= N; i++) { have[i] = 0; Father[i] = i; for (auto &j : Next[i]) { j.second += con[i]; j.second += con[j.first]; mst.push(make_pair(j.second, make_pair(i, j.first))); } } while (!mst.empty()) { t2 = mst.top(); mst.pop(); if (Find(t2.second.first) != Find(t2.second.second)) { Father[Find(t2.second.first)] = Find(t2.second.second); use[t2.second.first].push_back(make_pair(t2.second.second, t2.first)); use[t2.second.second].push_back(make_pair(t2.second.first, t2.first)); } } F(1, 0); while (Q--) { scanf("%lld %lld", &a, &b); printf("%lld\n", LCA(a, b)); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long inf = 1e18; const long long INF = 1e18; const int md = 1e9 + 7; const int N = 3e5 + 1; struct edge { int v, u; long long w; edge() {} edge(int v, long long w, int u = -1) : v(v), w(w), u(u) {} }; vector<edge> g[N]; int p[N]; long long ANS[N]; vector<pair<int, int>> Q[N]; void make(int v) { p[v] = v; } void add_q(int a, int b, int num) { Q[a].push_back({b, num}); Q[b].push_back({a, num}); } int fin(int v) { if (p[v] == v) return v; return p[v] = fin(p[v]); } void un(int a, int b, long long W) { a = fin(a), b = fin(b); if (a == b) return; if ((int)(Q[a]).size() < (int)(Q[b]).size()) swap(a, b); for (auto u : Q[b]) { if (fin(u.first) == a) ANS[u.second] = W; else Q[a].push_back(u); } p[b] = a; } signed main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); int n, m, k, q; cin >> n >> m >> k >> q; vector<edge> edges(m); for (int f = 0; f < m; ++f) { int u, v, w; cin >> u >> v >> w; --u, --v; g[v].push_back(edge{u, w}); g[u].push_back(edge{v, w}); edges[f] = edge{u, w, v}; } vector<long long> d(n, inf); auto cmp = [&](int a, int b) { return d[a] < d[b]; }; priority_queue<pair<long long, int>> DJ; for (int f = 0; f < k; ++f) { d[f] = 0; DJ.push({d[f], f}); } while (!DJ.empty()) { int head = DJ.top().second; DJ.pop(); for (auto u : g[head]) { if (d[u.v] > d[head] + u.w) { d[u.v] = d[head] + u.w; DJ.push({-d[u.v], u.v}); } } } for (int f = 0; f < m; ++f) edges[f].w += d[edges[f].u] + d[edges[f].v]; vector<int> perm(m); for (int i = 0; i < m; ++i) perm[i] = i; sort(perm.begin(), perm.end(), [&](int a, int b) { return edges[a].w < edges[b].w; }); for (int f = 0; f < n; ++f) make(f); for (int i = 0; i < q; ++i) { int a, b; cin >> a >> b; --a, --b; add_q(a, b, i); } for (int f = 0; f < m; ++f) { int curr = perm[f]; un(edges[curr].u, edges[curr].v, edges[curr].w); } for (int f = 0; f < q; ++f) cout << ANS[f] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; struct Edge { int u, v; long long w; } e[300010]; struct Query { int a, b; long long ans; Query() { ans = -1; } } q[300010]; struct data { int u; long long s; data(){}; data(int a, long long b) { u = a, s = b; } bool operator<(const data &a) const { return s > a.s; } }; int n, m, k, Q; int fa[100010]; int cnt, head[100010], nxt[300010 << 1], to[300010 << 1], w[300010 << 1]; long long dis[100010]; vector<int> g[100010]; priority_queue<data> que; void adde(int u, int v, int wi) { to[++cnt] = v; w[cnt] = wi; nxt[cnt] = head[u]; head[u] = cnt; } void dijkstra() { memset(dis, 127, sizeof(dis)); for (int i = 1; i <= k; i++) que.push(data(i, 0)), dis[i] = 0; while (!que.empty()) { data now = que.top(); que.pop(); for (int i = head[now.u]; i; i = nxt[i]) { int v = to[i]; if (dis[now.u] + w[i] <= dis[v]) { dis[v] = dis[now.u] + w[i]; que.push(data(v, dis[v])); } } } } bool cmp(Edge a, Edge b) { return a.w < b.w; } int find(int x) { return x == fa[x] ? x : (fa[x] = find(fa[x])); } int main() { scanf("%d%d%d%d", &n, &m, &k, &Q); for (int i = 1; i <= m; i++) { scanf("%d%d%lld", &e[i].u, &e[i].v, &e[i].w); adde(e[i].u, e[i].v, e[i].w), adde(e[i].v, e[i].u, e[i].w); } for (int i = 1; i <= Q; i++) { scanf("%d%d", &q[i].a, &q[i].b); g[q[i].a].push_back(i), g[q[i].b].push_back(i); } dijkstra(); for (int i = 1; i <= m; i++) e[i].w = e[i].w + dis[e[i].u] + dis[e[i].v]; sort(e + 1, e + m + 1, cmp); for (int i = 1; i <= n; i++) fa[i] = i; for (int i = 1; i <= m; i++) { int a = find(e[i].u), b = find(e[i].v); if (a != b) { if (g[b].size() < g[a].size()) swap(a, b); fa[a] = b; for (int j = 0, size = g[a].size(); j < size; j++) { int x = find(q[g[a][j]].a), y = find(q[g[a][j]].b); if (x == y) { if (q[g[a][j]].ans == -1) q[g[a][j]].ans = e[i].w; } else g[b].push_back(g[a][j]); } } } for (int i = 1; i <= Q; i++) printf("%lld\n", q[i].ans); return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { for (auto i = begin(v); i != end(v); i++) os << *i << (i == end(v) - 1 ? "" : " "); return os; } template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto i = begin(v); i != end(v); i++) is >> *i; return is; } int n, m, k, q; vector<pair<int, int>> edg[101000]; vector<long long> best_dists(101000, 10000000000000000LL); set<int> markers[101000]; int dsu[101000]; int drank[101000]; vector<long long> ans(301000, 10000000000000000LL); struct Edg { int u, v; long long w; }; int dsu_find(int a) { if (dsu[a] == a) return a; return dsu_find(dsu[a]); } void dsu_union(int a, int b, long long curr_ans) { a = dsu_find(a); b = dsu_find(b); if (a == b) return; if (drank[a] >= drank[b]) { dsu[b] = a; drank[a] = max(drank[a], drank[b] + 1); } else { dsu[a] = b; swap(a, b); drank[a] = max(drank[a], drank[b] + 1); } for (int x : markers[b]) { if (markers[a].find(x) != markers[a].end()) { ans[x] = curr_ans; } else { markers[a].insert(x); } } } int main() { cin.tie(NULL); ios_base::sync_with_stdio(false); cout.tie(NULL); cin >> n >> m >> k >> q; vector<Edg> edges; for (int i = 0; i < m; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; edg[u].push_back({v, w}); edg[v].push_back({u, w}); edges.push_back(Edg{u, v, w}); } set<pair<long long, int>> ss; for (int i = 0; i < k; i++) { ss.insert({0, i}); best_dists[i] = 0; } while (ss.size() > 0) { auto curr = *ss.begin(); ss.erase(curr); for (auto x : edg[curr.second]) { long long new_dist = curr.first + x.second; if (new_dist < best_dists[x.first]) { ss.erase({best_dists[x.first], x.first}); best_dists[x.first] = new_dist; ss.insert({best_dists[x.first], x.first}); } } } for (int i = 0; i < m; i++) { edges[i].w += best_dists[edges[i].u] + best_dists[edges[i].v]; } sort(edges.begin(), edges.end(), [&](Edg& x, Edg& y) { return x.w < y.w; }); vector<pair<int, int>> qs(q); for (int i = 0; i < q; i++) { int a, b; cin >> a >> b; a--, b--; qs[i] = {a, b}; markers[a].insert(i); markers[b].insert(i); } for (int i = 0; i < n; i++) { dsu[i] = i; } for (int i = 0; i < m; i++) { dsu_union(edges[i].u, edges[i].v, edges[i].w); } for (int i = 0; i < q; i++) cout << ans[i] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; int lg(long long n) { assert(n > 0); int ans = -1; while (n) { ans++; n >>= 1; } return ans; } struct DSU { vector<int> fa, sz; DSU() {} DSU(int n) { fa.resize(n); iota(fa.begin(), fa.end(), 0); sz.assign(n, 1); } bool join(int x, int y) { int a = find(x), b = find(y); if (a != b) { if (sz[a] < sz[b]) swap(a, b); sz[a] += sz[b]; fa[b] = a; return true; } return false; } int find(int x) { if (x == fa[x]) return x; return fa[x] = find(fa[x]); } }; void solve() { int n, m, k, q; cin >> n >> m >> k >> q; vector<tuple<int, int, int>> edges(m); vector<vector<pair<int, int>>> adj(n); for (int i = 0; i < m; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; edges[i] = make_tuple(u, v, w); adj[u].emplace_back(v, w); adj[v].emplace_back(u, w); } const long long INF = 9e18; set<pair<long long, int>> qu; vector<long long> d(n, INF); for (int i = 0; i < k; i++) { d[i] = 0; qu.insert({0, i}); } while (!qu.empty()) { int v = qu.begin()->second; qu.erase(qu.begin()); for (auto [to, len] : adj[v]) { if (d[v] + len < d[to]) { qu.erase({d[to], to}); d[to] = d[v] + len; qu.insert({d[to], to}); } } } vector<tuple<long long, int, int>> newedge(m); for (int i = 0; i < m; i++) { auto [u, v, w] = edges[i]; newedge[i] = make_tuple(d[u] + d[v] + w, u, v); } sort(newedge.begin(), newedge.end()); vector<pair<int, int>> queries(q); vector<long long> ans(q); vector<vector<int>> tokens(n); vector<int> where(q * 2); for (int i = 0; i < q; i++) { int u, v; cin >> u >> v; u--, v--; queries[i] = make_pair(u, v); tokens[u].push_back(2 * i); tokens[v].push_back(2 * i + 1); where[2 * i] = u; where[2 * i + 1] = v; } DSU dsu(n); for (auto [w, u, v] : newedge) { u = dsu.find(u); v = dsu.find(v); if (u == v) continue; if (dsu.sz[u] < dsu.sz[v]) { swap(u, v); } for (int t : tokens[v]) { if (dsu.find(where[t ^ 1]) == u) { assert(ans[t / 2] == 0); ans[t / 2] = w; } tokens[u].push_back(t); } dsu.join(u, v); tokens[v].clear(); } for (int i = 0; i < q; i++) { cout << ans[i] << '\n'; } } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t = 1; while (t--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 10; int n, m, k, q; int fa[N]; long long dis[N]; long long ans[N]; vector<pair<int, int> > g[N], Q[N]; priority_queue<pair<long long, pair<int, int> > > h; int getfa(int x) { return x == fa[x] ? x : fa[x] = getfa(fa[x]); } void update(int x) { for (auto u : g[x]) if (dis[u.first] > dis[x] + u.second) { h.push(make_pair(-(dis[u.first] = dis[x] + u.second), make_pair(u.first, x))); } } void combine1(int x, int y) { update(x); x = getfa(x), y = getfa(y); fa[x] = y; } void combine(int x, int y, long long v) { x = getfa(x), y = getfa(y); if (x == y) return; if (Q[x].size() < Q[y].size()) swap(x, y); fa[y] = x; for (auto u : Q[y]) if (getfa(x) == getfa(u.first)) { if (!ans[u.second]) ans[u.second] = v; } else Q[x].push_back(u); } int main() { scanf("%d %d %d %d", &n, &m, &k, &q); for (int i = 1; i <= m; i++) { int x, y, z; scanf("%d %d %d", &x, &y, &z); g[x].push_back(make_pair(y, z)); g[y].push_back(make_pair(x, z)); } for (int i = 1; i <= q; i++) { int x, y; scanf("%d %d", &x, &y); Q[x].push_back(make_pair(y, i)); Q[y].push_back(make_pair(x, i)); } for (int i = 1; i <= n; i++) fa[i] = i; for (int i = k + 1; i <= n; i++) dis[i] = 1e18; for (int i = 1; i <= k; i++) update(i); while (!h.empty()) { auto x = h.top(); h.pop(); if (dis[x.second.first] != -x.first) continue; combine1(x.second.first, x.second.second); } for (int i = 1; i <= n; i++) for (auto u : g[i]) h.push( make_pair(-dis[i] - dis[u.first] - u.second, make_pair(u.first, i))); while (!h.empty()) { auto x = h.top(); h.pop(); combine(x.second.first, x.second.second, -x.first); } for (int i = 1; i <= q; i++) printf("%lld\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; const long long MAXN = 2e6 + 8, mod = 1e9 + 8, inf = 1ll << 50; struct E { int x, y, nt; long long v; bool operator<(const E& b) const { return v < b.v; } } e[MAXN]; int head[MAXN], cnt; inline void add(int x, int y, long long v) { e[++cnt].nt = head[x]; head[x] = cnt; e[cnt].v = v; e[cnt].x = x; e[cnt].y = y; } struct Node { int y, nt; } node[MAXN << 1]; int Nodehead[MAXN << 1], Nodecnt; inline void addNode(int x, int y) { node[++Nodecnt].nt = Nodehead[x]; node[Nodecnt].y = y; Nodehead[x] = Nodecnt; } int n, m, k, q; long long dis[MAXN]; bool vis[MAXN]; void dijkstra() { priority_queue<pair<long long, int>> que; for (int i = 1; i <= k; ++i) que.emplace(0, i); for (int i = k + 1; i <= n; ++i) dis[i] = inf; int x, y; long long v; while (!que.empty()) { x = que.top().second; que.pop(); if (vis[x]) continue; vis[x] = 1; for (int i = head[x]; i; i = e[i].nt) { y = e[i].y, v = e[i].v; if (dis[y] > dis[x] + v) { dis[y] = dis[x] + v; que.emplace(-dis[y], y); } } } } int deep[MAXN << 1], son[MAXN << 1], fa[MAXN << 1], tot[MAXN << 1]; void dfs1(int x, int f) { deep[x] = deep[f] + 1, tot[x] = 1, fa[x] = f; int max_son = -1; for (int i = Nodehead[x]; i; i = node[i].nt) { int y = node[i].y; if (tot[y]) continue; dfs1(y, x); tot[x] += tot[y]; if (max_son < tot[y]) son[x] = y, max_son = tot[y]; } } int top[MAXN << 1]; void dfs2(int x, int tp) { top[x] = tp; if (son[x]) dfs2(son[x], tp); else return; for (int i = Nodehead[x]; i; i = node[i].nt) { int y = node[i].y; if (top[y]) continue; dfs2(y, y); } } int lca(int x, int y) { while (top[x] ^ top[y]) { if (deep[top[x]] < deep[top[y]]) y = fa[top[y]]; else x = fa[top[x]]; } if (deep[x] > deep[y]) return y; return x; } int find(int x) { return x ^ fa[x] ? (fa[x] = find(fa[x])) : x; } long long val[MAXN << 1]; void kruskal() { int id = n; sort(e + 1, e + 1 + cnt); for (int i = 0; i < n * 2 + 2; ++i) fa[i] = i; for (int i = 1; i <= cnt; ++i) { int fx = find(e[i].x), fy = find(e[i].y); if (fx ^ fy) { val[++id] = e[i].v; fa[fx] = fa[fy] = id; addNode(id, fx); addNode(fx, id); addNode(id, fy); addNode(fy, id); } } dfs1(id, 0); dfs2(id, id); } int main() { cin >> n >> m >> k >> q; for (int i = 0; i < m; ++i) { int x, y; long long v; scanf("%d%d%lld", &x, &y, &v); add(x, y, v); add(y, x, v); } dijkstra(); for (int i = 1; i <= n; ++i) for (int j = head[i]; j; j = e[j].nt) { e[j].v += dis[e[j].x] + dis[e[j].y]; } kruskal(); while (q--) { int x, y; scanf("%d%d", &x, &y); printf("%lld\n", val[lca(x, y)]); } }
#include <bits/stdc++.h> using namespace std; bool vis[200010]; void dfs(vector<long long int> arr[], long long int i, long long int temp) { vis[i] = true; for (long long int u : arr[i]) { if (!vis[u] and u != temp) dfs(arr, u, temp); } } int main() { long long int t; cin >> t; while (t--) { long long int n, m, a, b, u, v; cin >> n >> m >> a >> b; vector<long long int> arr[n + 1]; for (long long int i = 0; i < m; i++) { cin >> u >> v; arr[u].push_back(v); arr[v].push_back(u); } memset(vis, false, sizeof(vis)); dfs(arr, a, b); unordered_set<long long int> us1; for (long long int i = 1; i <= n; i++) { if (vis[i]) us1.insert(i); } us1.erase(a); memset(vis, false, sizeof(vis)); dfs(arr, b, a); unordered_set<long long int> us2; for (long long int i = 1; i <= n; i++) { if (vis[i]) us2.insert(i); } us2.erase(b); long long int ans1 = 0, ans2 = 0; for (auto val : us1) { if (us2.find(val) == us2.end()) ans1++; } for (auto val : us2) { if (us1.find(val) == us1.end()) ans2++; } cout << ans1 * ans2 << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; namespace gao { inline int read() { char c = getchar(); int x = 0, f = 1; while (c > '9' || c < '0') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); } return x * f; } struct node { int t, nt; } e[1000005 << 1]; int f[1000005], c[1000005], head[1000005], sz[1000005], n, tot, a, b, m, n2; long long ans; inline void add2(int u, int v) { e[++tot].t = v; e[tot].nt = head[u]; head[u] = tot; } inline void add(int u, int v) { add2(u, v), add2(v, u); } inline void dfs(int u, int fa) { f[u] = fa; sz[u] = c[u]; for (int i = head[u]; i; i = e[i].nt) { int v = e[i].t; if (v == fa) continue; dfs(v, u); sz[u] += sz[v]; } } inline void calc() { dfs(a, 0); int u = b; while (f[u] != a) u = f[u]; ans = 1ll * (n2 - sz[u] - 1) * (sz[b] - 1); printf("%lld\n", ans); } inline void clear() { for (int i = 1; i <= n; i++) head[i] = sz[i] = c[i] = f[i] = 0; n = tot = 0; } } // namespace gao namespace gao2 { struct node { int t, nt; } e[1000005 << 1]; int n, f[1000005], head[1000005], tot, dfn[1000005], low[1000005], st[1000005], tp, cnt; inline void add(int u, int v) { e[++tot].t = v; e[tot].nt = head[u]; head[u] = tot; } inline void tarjan(int u, int fa) { dfn[u] = low[u] = ++cnt; st[++tp] = u; for (int i = head[u]; i; i = e[i].nt) { int v = e[i].t; if (v == fa) continue; if (!dfn[v]) { tarjan(v, u); low[u] = min(low[u], low[v]); if (low[v] >= dfn[u]) { gao::n++; gao::add(u, gao::n); while (tp > 0) { gao::add(gao::n, st[tp]); tp--; if (st[tp + 1] == v) break; } } } else low[u] = min(low[u], dfn[v]); } } inline void solve() { gao::n = n; for (int i = 1; i <= n; i++) gao::c[i] = 1; for (int i = 1; i <= n; i++) { if (!dfn[i]) tarjan(i, 0); } } inline void clear() { for (int i = 1; i <= n; i++) head[i] = dfn[i] = low[i] = st[i] = 0; n = tot = cnt = tp = 0; } } // namespace gao2 int T, n, a, b, m; inline int read() { char c = getchar(); int x = 0, f = 1; while (c > '9' || c < '0') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); } return x * f; } signed main() { T = read(); while (T--) { gao::clear(); gao2::clear(); n = read(), m = read(), gao::a = read(), gao::b = read(); for (int i = 1; i <= m; i++) { int u = read(), v = read(); gao2::add(u, v), gao2::add(v, u); } gao2::n = n; gao::n2 = n; gao2::solve(); gao::calc(); } }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { if (a > b) swap(a, b); if (a == 0) return b; return gcd(b % a, a); } long long powerMod(long long x, long long y) { long long res = 1; x %= 998244353; while (y > 0) { if (y & 1) res = (res * x) % 998244353; y = y >> 1; x = (x * x) % 998244353; } return res % 998244353; } string binary(long long s) { string res = ""; while (s != 0) { res += (char)('0' + s % 2); s /= 2; } reverse(res.begin(), res.end()); return res; } vector<int> parent; vector<set<int> > adj; vector<bool> vi; set<int> ea, emplace_back; int n, a, b; int find(int a) { return a == parent[a] ? a : parent[a] = find(parent[a]); } void join(int a, int b) { parent[find(b)] = find(a); } void dfs(int p, int node) { for (int i : adj[node]) { parent[i] = p; if (!vi[i]) { vi[i] = true; dfs(p, i); } } } int main() { ios::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL); ; int i, j, k, l, m, p, s, t; cin >> t; while (t--) { cin >> n >> m >> a >> b; --a; --b; parent.resize(n); vi.resize(n, false); adj.resize(n); for (i = 0; i < n; i++) parent[i] = i; for (i = 0; i < m; i++) { cin >> j >> k; --j, --k; if (j == a || k == a || j == b || k == b) { if ((j == a && k == b) || (j == b && k == a)) ; else if (j == a) ea.insert(k); else if (j == b) emplace_back.insert(k); else if (k == a) ea.insert(j); else if (k == b) emplace_back.insert(j); continue; } adj[j].insert(k); adj[k].insert(j); } for (i = 0; i < n; i++) { if (!vi[i]) { vi[i] = true; dfs(i, i); } } set<int> da, db; for (int i : ea) { da.insert(find(i)); } for (int i : emplace_back) { db.insert(find(i)); } vector<int> rem; for (int i : da) { if (db.find(i) != db.end()) { rem.emplace_back(i); } } for (int i : rem) { da.erase(i); db.erase(i); } vector<int> cnt(n, 0); for (i = 0; i < n; i++) { cnt[find(i)]++; } long long aa = 0LL, bb = 0LL; for (int i : da) { aa += cnt[i]; } for (int i : db) { bb += cnt[i]; } cout << (aa * bb) << "\n"; adj.clear(); ea.clear(); emplace_back.clear(); vi.clear(); parent.clear(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 200200; int n, m, a, b; vector<int> adj[N]; int sz[N], mark[N], tin[N], timer, found_b; int qnt_a, qnt_b; void dfs(int v) { found_b |= (v == b); mark[v] = tin[v] = ++timer; sz[v] = 1; for (int u : adj[v]) { if (mark[u]) { tin[v] = min(tin[v], mark[u]); } else { int bef = found_b; dfs(u); if (v == a && bef == 0 && found_b == 1) { qnt_a -= sz[u]; } sz[v] += sz[u]; tin[v] = min(tin[v], tin[u]); if (v == b && tin[u] >= mark[v]) { qnt_b += sz[u]; } } } if (v == a) { qnt_a += sz[a] - 1; } } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int tot_cas; cin >> tot_cas; for (int cas = 1; cas <= tot_cas; cas++) { cin >> n >> m >> a >> b; for (int i = 1; i <= n; i++) { adj[i].clear(); mark[i] = tin[i] = sz[i] = 0; } for (int i = 0; i < m; i++) { int a, b; cin >> a >> b; adj[a].push_back(b); adj[b].push_back(a); } timer = found_b = qnt_a = qnt_b = 0; dfs(a); cout << 1ll * qnt_a * qnt_b << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e5 + 5; const int maxm = 5e5 + 5; struct edge { int to, next; } G[maxm << 1]; int tot, head[maxn]; void addEdge(int u, int v) { G[tot] = {v, head[u]}; head[u] = tot++; } int T, n, m, a, b, visa[maxn], visb[maxn]; void bfs1() { for (int i = 1; i <= n; i++) visa[i] = 0; queue<int> q; q.push(a); visa[a] = 1; int u, v, i; while (!q.empty()) { u = q.front(); q.pop(); for (int i = head[u]; i != -1; i = G[i].next) { v = G[i].to; if (visa[v]) continue; visa[v] = 1; if (v != b) q.push(v); } } } void bfs2() { for (int i = 1; i <= n; i++) visb[i] = 0; queue<int> q; q.push(b); visb[b] = 1; int u, v, i; while (!q.empty()) { u = q.front(); q.pop(); for (int i = head[u]; i != -1; i = G[i].next) { v = G[i].to; if (visb[v]) continue; visb[v] = 1; if (v != a) q.push(v); } } } int main() { for (cin >> T; T--;) { cin >> n >> m >> a >> b; tot = 0; for (int i = 1; i <= n; i++) { head[i] = -1; visa[i] = visb[i] = 0; } int u, v; for (int i = 1; i <= m; i++) { cin >> u >> v; addEdge(u, v); addEdge(v, u); } bfs1(); bfs2(); long long A = 0, B = 0; for (int i = 1; i <= n; i++) { A += visa[i] && !visb[i]; B += visb[i] && !visa[i]; } cout << A * B << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int t; cin >> t; while (t--) { int n, m, a, b; cin >> n >> m >> a >> b; std::vector<int> gra[n + 1], grb[n + 1]; for (int i = 0; i < m; i++) { int l, r; cin >> l >> r; if ((l == a or r == a) and (l == b or r == b)) continue; else if (l == a or r == a) { gra[l].push_back(r); gra[r].push_back(l); } else if (l == b or r == b) { grb[l].push_back(r); grb[r].push_back(l); } else { gra[l].push_back(r); gra[r].push_back(l); grb[l].push_back(r); grb[r].push_back(l); } } int vis[n + 1]; memset(vis, 0, sizeof(vis)); queue<int> q; q.push(a); vis[a] = 1; long long int ca = 0; while (q.size()) { int i = q.front(); ca++; q.pop(); for (auto j : gra[i]) { if (!vis[j]) { vis[j] = 1; q.push(j); } } } memset(vis, 0, sizeof(vis)); q.push(b); vis[b] = 1; long long int cb = 0; while (q.size()) { int i = q.front(); cb++; q.pop(); for (auto j : grb[i]) { if (!vis[j]) { vis[j] = 1; q.push(j); } } } ca = n - ca - 1; cb = n - cb - 1; ca *= cb; cout << ca << '\n'; } return 0; }
#include <bits/stdc++.h> const long long mod = 1000000007; const long long mod1 = 998244353; using namespace std; long long n, m, a, b, sum = 0; vector<long long> v[200005]; bool visited[200005]; void dfs(long long x, long long y) { if (x == y) return; visited[x] = true, sum++; for (long long i = 0; i < v[x].size(); i++) { if (!visited[v[x][i]]) { dfs(v[x][i], y); } } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long t; cin >> t; while (t--) { cin >> n >> m >> a >> b; for (long long i = 0; i <= n + 1; i++) v[i].clear(), visited[i] = false; for (long long i = 0; i < m; i++) { long long x, y; cin >> x >> y; v[x].push_back(y); v[y].push_back(x); } dfs(a, b); long long xz = sum; sum = 0; for (long long i = 0; i <= n; i++) visited[i] = false; dfs(b, a); long long yz = sum; sum = 0; long long z = xz + yz - n; xz -= z + 1, yz -= z + 1; cout << xz * yz << endl; } }
#include <bits/stdc++.h> using namespace std; const long long MOD = 1000000007; void dfs(int u, int r, vector<vector<int>> &adj, vector<int> &color) { color[u] = 1; for (auto v : adj[u]) { if (color[v] == 0 && v != r) { dfs(v, r, adj, color); } } color[u] = 2; } void sherlock(int t) { int n, m, a, b; cin >> n >> m >> a >> b; vector<vector<int>> adj(n + 1); int u, v; for (int i = 0; i < m; i++) { cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } vector<int> colora(n + 1), colorb(n + 1); dfs(a, b, adj, colora); dfs(b, a, adj, colorb); int x = 0, y = 0; for (int i = 1; i <= n; i++) { if (colora[i] == 2 && colorb[i] == 0) x++; if (colora[i] == 0 && colorb[i] == 2) y++; } cout << (x - 1) * 1LL * (y - 1) << endl; return; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int tt; cin >> tt; for (int t = 1; t <= tt; t++) sherlock(t); return 0; }
#include <bits/stdc++.h> #pragma optimize("O3") using namespace std; const long long MOD = 1e9 + 7; const long long INF = 2 * 1e12 + 7; const int base = 2e5 + 1; const int MAX = 1e4 + 2; const double EPS = 1e-9; const double PI = acos(-1.); const int MAXN = 2 * 1e6 + 1; int main() { int t; cin >> t; while (t--) { int n, m, a, b; cin >> n >> m >> a >> b; vector<vector<int> > g(n + 1), from(n + 1); vector<int> was(n + 1, 0), can(n + 1, 1), was2(n + 1, 0), p(n + 1), used(n + 1, 0); for (long long i = (0); i < (m); ++i) { int v, u; cin >> v >> u; g[v].push_back(u); g[u].push_back(v); } queue<int> q; q.push(a); was[a] = 1; while (!q.empty()) { int v = q.front(); q.pop(); if (v == b) continue; for (auto u : g[v]) { if (!was[u]) { was[u] = 1; q.push(u); p[u] = v; } from[u].push_back(v); } } stack<int> s; s.push(b); was2[b] = 1; while (!s.empty()) { int v = s.top(); s.pop(); if (v == a) continue; can[v] = 0; for (auto u : from[v]) { if (!was2[u]) { was2[u] = 1; s.push(u); } } } can[a] = 1; can[b] = 1; long long c1 = -1, c2 = -1; s.push(a); used[a] = 1; while (!s.empty()) { int v = s.top(); s.pop(); c1++; for (auto u : g[v]) { if (!can[u] || u == b) continue; if (!used[u]) { used[u] = 1; s.push(u); } } } s.push(b); used[b] = 1; while (!s.empty()) { int v = s.top(); s.pop(); c2++; for (auto u : g[v]) { if (!can[u] || u == a) continue; if (!used[u]) { used[u] = 1; s.push(u); } } } cout << c1 * c2 << '\n'; } return 0; }
#include <bits/stdc++.h> const long long maxn = 2e6 + 9, inf = 0x3f3f3f3f; long long Read() { long long x(0), f(1); char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') { x = (x << 3ll) + (x << 1ll) + c - '0'; c = getchar(); } return x * f; } long long T, n, m; struct node { long long to, nxt; } dis[maxn]; long long num, tim, N, tot, a, b, flag; long long visit[maxn], dfn[maxn], low[maxn], head[maxn], ge[maxn]; void Add(long long u, long long v) { dis[++num] = (node){v, head[u]}; head[u] = num; } void Dfs(long long u, long long ff) { flag |= (u == ff); visit[u] = 1; ++tot; for (long long i = head[u]; i; i = dis[i].nxt) { long long v(dis[i].to); if (!visit[v]) Dfs(v, ff); } } void solve() { for (long long i = 1; i <= n; ++i) visit[i] = 0; visit[a] = 1; long long N(0), Tmp, flag1(0); for (long long i = head[a]; i; i = dis[i].nxt) { long long v(dis[i].to); if (!visit[v]) { flag = 0; tot = 0; Dfs(v, b); N += tot; if (flag) Tmp = tot, flag1 = 1; } } if (flag1) { long long N1(N - Tmp); N = flag1 = 0; for (long long i = 1; i <= n; ++i) visit[i] = 0; visit[b] = 1; for (long long i = head[b]; i; i = dis[i].nxt) { long long v(dis[i].to); if (!visit[v]) { flag = 0; tot = 0; Dfs(v, a); N += tot; if (flag) Tmp = tot, flag1 = 1; } } if (flag1) { long long N2(N - Tmp); printf("%lld\n", N1 * N2); } else puts("0"); } else puts("0"); } int main() { T = Read(); while (T--) { n = Read(); m = Read(); a = Read(); b = Read(); num = tim = 0; for (long long i = 1; i <= n; ++i) head[i] = dfn[i] = low[i] = ge[i] = 0; for (long long i = 1; i <= m; ++i) { long long u(Read()), v(Read()); Add(u, v); Add(v, u); } solve(); } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") using namespace std; template <class T> ostream& operator<<(ostream& os, vector<T> V) { os << "[ "; for (auto v : V) os << v << " "; return os << "]"; } template <class L, class R> ostream& operator<<(ostream& os, pair<L, R> P) { return os << "(" << P.first << "," << P.second << ")"; } template <typename Arg1> void __f(const char* name, Arg1&& arg1) { cerr << name << " : " << arg1 << endl; } template <typename Arg1, typename... Args> void __f(const char* names, Arg1&& arg1, Args&&... args) { const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } const long long INF = 0x3f3f3f3f; const long long M = 1e9 + 7; const long long N = 2e5 + 5; vector<long long> g[N]; long long n, m, a, b; bool d[N]; long long ctr; bool va, vb; void dfs(long long z) { if (z == a) { va = true; return; } if (z == b) { vb = true; return; } ctr++; for (long long y : g[z]) { if (!d[y]) { if (y != a && y != b) d[y] = true; dfs(y); } } } signed main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cout << fixed << setprecision(15); long long t; cin >> t; while (t--) { cin >> n >> m >> a >> b; for (long long i = 1; i <= n; ++i) g[i].clear(); for (long long i = 0; i < m; ++i) { long long u, v; cin >> u >> v; g[u].push_back(v); g[v].push_back(u); } memset(d, 0, sizeof(d)); long long na = 0, nb = 0; for (long long i = 1; i <= n; ++i) { if (i == a || i == b) continue; if (d[i]) continue; ctr = 0; va = vb = false; d[i] = true; dfs(i); if (va && !vb) na += ctr; if (vb && !va) nb += ctr; } cout << na * nb << '\n'; } }
#include <bits/stdc++.h> using namespace std; const int N = 2000 * 100 + 17; vector<long long> adj[N]; long long t, n, m, a, b; bool mark[N], vis[N]; void dfs1(int st, int p) { mark[st] = true; for (auto v : adj[st]) if (mark[v] == false && v != p) dfs1(v, p); } void dfs2(int st, int p) { vis[st] = true; for (auto v : adj[st]) if (vis[v] == false && v != p) dfs2(v, p); } long long solve() { long long res = 0; for (int i = 1; i <= n; i++) if (mark[i]) res++; return n - res - 1; } long long sov() { long long res = 0; for (int i = 1; i <= n; i++) if (vis[i]) res++; return n - res - 1; } void cl() { for (int i = 1; i <= n; i++) { adj[i].clear(); mark[i] = false; vis[i] = false; } } void input() { cin >> t; while (t--) { cin >> n >> m >> a >> b; long long x, y; for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } dfs1(a, b); dfs2(b, a); x = sov(), y = solve(); cout << x * y << endl; cl(); } } int main() { input(); return 0; }
#include <bits/stdc++.h> int dr[] = {2, 2, -2, -2, 1, -1, 1, -1}; int dc[] = {1, -1, 1, -1, 2, 2, -2, -2}; int dr1[] = {0, 0, 0, 1, 1, 1, -1, -1, -1}; int dc1[] = {-1, 0, 1, -1, 0, 1, -1, 0, 1}; int dr2[] = {0, 0, 1, -1}; int dc2[] = {1, -1, 0, 0}; using namespace std; vector<long long int> adj[300005]; long long int mark[300005], cnt; void dfs(long long int u) { mark[u] = 1; cnt++; for (long long int i = 0; i < adj[u].size(); i++) { long long int p = adj[u][i]; if (mark[p]) continue; dfs(p); } } int main() { long long int tc, n, m, x, y, i, j, a, b; cin >> tc; while (tc--) { cin >> n >> m >> a >> b; for (i = 1; i <= m; i++) { cin >> x >> y; adj[x].push_back(y); adj[y].push_back(x); } for (i = 1; i <= n; i++) mark[i] = 0; mark[b] = 1; cnt = 0; dfs(a); long long int xa = n - cnt - 1; for (i = 1; i <= n; i++) mark[i] = 0; mark[a] = 1; cnt = 0; dfs(b); long long int xb = n - cnt - 1; cout << xa * xb << endl; for (i = 1; i <= n; i++) adj[i].clear(); } return 0; }
#include <bits/stdc++.h> using namespace std; long long int fast_expo(long long int x, long long int p) { if (p == 0) return 1; else if (p % 2 == 0) { long long int t = fast_expo(x, p / 2) % 998244353; return (t * t) % 998244353; } else return (x * (fast_expo(x, p - 1)) % 998244353) % 998244353; } vector<int> adj[200005]; int vis[200005]; int ans; void dfs(int u, int no) { vis[u] = 1; ans++; for (auto v : adj[u]) { if (!vis[v] && v != no) dfs(v, no); } } int main() { int t; cin >> t; while (t--) { int n, m, a, b; cin >> n >> m >> a >> b; for (int i = 0; i <= n; i++) adj[i].clear(), vis[i] = 0; int u, v; for (int i = 0; i < m; i++) { cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } ans = 0; dfs(a, b); long long int val1 = n - 1 - ans; for (int i = 0; i <= n; i++) { vis[i] = 0; } ans = 0; dfs(b, a); long long int val2 = n - 1 - ans; cout << val1 * val2 << '\n'; } }
#include <bits/stdc++.h> using namespace std; double _eps = 1e-6; long long gcd(long long a, long long b) { if (b == 0) return a; return gcd(b, a % b); } vector<int> adj[2 * 100000 + 10]; vector<int> path; bool vis[2 * 100000 + 10]; bool mark[2 * 100000 + 10]; void dfs(int v, int d) { if (v == d) { for (int x : path) mark[x] = 1; return; } if (!vis[v]) { vis[v] = 1; path.push_back(v); for (int x : adj[v]) dfs(x, d); path.pop_back(); } } int mx = 0; void df(int v) { if (!vis[v] && !mark[v]) { vis[v] = 1; mx++; for (int x : adj[v]) df(x); } } int main() { int T; cin >> T; for (int caseno = 1; caseno <= T; caseno++) { int a, b; int n, m; cin >> n >> m >> a >> b; for (int i = 1; i <= n; ++i) adj[i].clear(); for (int i = 0; i < m; ++i) { int k, l; cin >> k >> l; adj[k].push_back(l); adj[l].push_back(k); } memset(vis, 0, sizeof(vis)); memset(mark, 0, sizeof(mark)); dfs(a, b); memset(vis, 0, sizeof(vis)); dfs(b, a); mark[a] = mark[b] = 0; memset(vis, 0, sizeof(vis)); mx = 0; mark[b] = 1; df(a); long long x = mx - 1; memset(vis, 0, sizeof(vis)); mark[a] = 1; mark[b] = 0; mx = 0; df(b); long long y = mx - 1; cout << x * y; puts(""); } return 0; }