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#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; int sum = 0; for (int t = 0; t <= 100; t++) { for (int k = 0; k <= 100; k++) { if (a >= t && b >= 2 * t + k && c >= 2 * k) { sum = max(sum, 3 * t + 3 * k); } } } cout << sum << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 1e9; int main() { int te; scanf("%d", &te); while (te--) { int a, b, c; scanf("%d%d%d", &a, &b, &c); int c2 = 3 * min(b, c / 2); int g2 = min(b, c / 2); b -= g2; int c1 = 3 * min(a, b / 2); printf("%d\n", c1 + c2); } return 0; }
#include <bits/stdc++.h> using namespace std; long long fast_exp(long long base, long long exp) { long long res = 1; while (exp > 0) { if (exp % 2 == 1) res = (res * base) % 1000000007; base = (base * base) % 1000000007; exp /= 2; } return res % 1000000007; } long long fib(long long n) { if (n < 2) return n; long long a = 0, b = 1, ans; int i = 1; while (i < n) { ans = (a + b) % 1000000007; a = b; b = ans; i++; } return ans; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; long long ans = 0; if (b < c / 2) { ans += 3 * b; cout << ans << "\n"; } else { ans += 3 * (c / 2); b -= c / 2; int add = min(a, b / 2); ans += 3 * add; cout << ans << "\n"; } } }
#include <bits/stdc++.h> using namespace std; int t, a, b, c; int main() { ios_base::sync_with_stdio(); cin.tie(0); cout.tie(0); cin >> t; while (t--) { cin >> a >> b >> c; int x = min(b, c / 2); b -= x; int y = min(a, b / 2); cout << 3 * (x + y) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 1e9 + 7; const int N = 1e6 + 5; long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } long long lcm(long long a, long long b) { return a * b / gcd(a, b); } inline long long qsm(long long x, long long y) { long long res = 1; while (y) { if (y & 1) res = res * x % mod; x = x * x % mod; y >>= 1; } return res; } int n, m, k, rt; int main() { int T; scanf("%d", &T); while (T--) { int ans = 0, a, b, c; scanf("%d%d%d", &a, &b, &c); ans += min(c / 2, b); b -= min(c / 2, b); ans += min(b / 2, a); printf("%d\n", ans * 3); } return 0; }
#include <bits/stdc++.h> using namespace std; int t, a, b, c, ans; int main() { scanf("%d", &t); while (t--) { ans = 0; scanf("%d%d%d", &a, &b, &c); c /= 2; if (b >= c) { ans += c * 3; b -= c; b /= 2; if (a >= b) ans += b * 3; else ans += a * 3; } else ans += b * 3; printf("%d\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; int n, a, b, c, minimal, minimal2, ans, ans1; int main() { cin >> n; while (n > 0) { cin >> a >> b >> c; n--; int b1 = b, c1 = c; minimal = min(a, b / 2); b -= minimal * 2; ans += minimal + (minimal * 2); minimal2 = min(b, c / 2); ans += minimal2 + (minimal2 * 2); minimal = min(b1, c1 / 2); ans1 += minimal + (minimal * 2); b1 -= minimal; minimal2 = min(a, b1 / 2); ans1 += minimal2 + (minimal2 * 2); (ans > ans1) ? cout << ans << endl : cout << ans1 << endl; ans = 0; ans1 = 0; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t, a, b, c; cin >> t; while (t--) { cin >> a >> b >> c; int ans = 0; if (c / 2 <= b) ans += c / 2 * 2 + c / 2, b -= c / 2; else { cout << b * 3 << endl; continue; } if (b / 2 <= a) cout << ans + b / 2 * 2 + b / 2 << endl; else cout << ans + a * 3 << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { int t, a, b, c; cin >> t; int ans[t]; for (int i = 0; i < t; i++) { cin >> a >> b >> c; ans[i] = ((min(c / 2, b)) * 3 + (min(a, (b - min(c / 2, b)) / 2)) * 3); } for (int z = 0; z < t; z++) { cout << ans[z] << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t, a, b, c, sum, i, j, k; cin >> t; for (i = 0; i < t; i++) { sum = 0; cin >> a >> b >> c; while (c >= 2 && b >= 1) { sum += 3; c -= 2; b -= 1; } while (b >= 2 && a >= 1) { sum += 3; a -= 1; b -= 2; } cout << sum << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int n; cin >> n; for (int i = 0; i < n; i++) { int a, b, c; cin >> a >> b >> c; int count = 0; int mn = min(b, c / 2); count += (mn * 3); b -= mn; c -= (2 * mn); mn = min(a, b / 2); count += (mn * 3); cout << count << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; int maxn = 1000; while (t--) { int sum = 0, sum2 = 0; int a, b, c; cin >> a >> b >> c; int e = a, f = b, g = c; while (a >= 1 && b >= 2) { sum += 3; b -= 2; a -= 1; } while (b >= 1 && c >= 2) { sum += 3; b -= 1; c -= 2; } while (f >= 1 && g >= 2) { sum2 += 3; g -= 2; f -= 1; } while (e >= 1 && f >= 2) { sum2 += 3; e -= 1; f -= 2; } if (sum >= sum2) cout << sum << endl; else cout << sum2 << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int test, x, y, z; cin >> test; while (test--) { int ans = 0; cin >> x >> y >> z; ans += min(y, z / 2); y -= ans; ans += min(x, y / 2); cout << ans * 3 << endl; } }
#include <bits/stdc++.h> using namespace std; int t, a, b, c; int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); if (fopen("test.inp", "r")) freopen("test.inp", "r", stdin), freopen("test.out", "w", stdout); cin >> t; while (t--) { cin >> a >> b >> c; int res = 0; for (int i = 0; i <= 100; i++) for (int j = 0; j <= 100; j++) if (i <= a && i * 2 + j <= b && j * 2 <= c) { res = max(res, i + i * 2 + j + j * 2); } cout << res << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int q; cin >> q; while (q--) { int a, b, c; cin >> a >> b >> c; int ans = 0; while (b >= 1 && c >= 2) { ans += 3; b--; c -= 2; } while (a >= 1 && b >= 2) { ans += 3; a--; b -= 2; } cout << ans << endl; } }
#include <bits/stdc++.h> using namespace std; int T, a, b, c, sum; int main() { scanf("%d", &T); while (T--) { sum = 0; scanf("%d%d%d", &a, &b, &c); int num = c / 2; if (b >= num) { sum += num * 2; sum += num; b -= num; num = b / 2; if (a >= num) { sum += num * 2; sum += num; } else { sum += a * 2; sum += a; } } else { sum += b * 2; sum += b; } printf("%d\n", sum); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { cin.tie(nullptr)->sync_with_stdio(false); int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; int total = 0; total += 3 * (min(b, c / 2)); b -= total / 3; total += 3 * min(a, b / 2); cout << total << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100005; void solve() { long long a, b, c; cin >> a >> b >> c; long long x = min(2 * b, c); long long ans = 0; if (x == c) { long long y = c / 2; b = b - y; ans += 3 * y; } else { ans = ans + 3 * b; b = 0; } if (b > 0) { long long z = min(2 * a, b); if (z == b) { long long p = b / 2; ans = ans + 3 * p; } else { ans = ans + 3 * a; a = 0; } } cout << ans << endl; } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t = 1; cin >> t; while (t--) { solve(); } }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(0); cin.tie(0); int t; cin >> t; for (int _i = 0; _i < t; ++_i) { int a, b, c; int ans = 0; cin >> a >> b >> c; for (int x = 0; x <= a; ++x) { for (int y = 0; 2 * y <= c; ++y) { if (2 * x + y <= b) ans = max(ans, 3 * (x + y)); } } cout << ans << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int a, b, c, t; int main() { cin >> t; while (t--) { cin >> a >> b >> c; int maxim = 0; for (int i = 0; i <= a; ++i) { for (int j = 0; j <= b; ++j) { int aa = a, bb = b, cc = c, contor = 0; aa -= i; bb -= 2 * i; if (aa < 0 || bb < 0) continue; contor = i * 3; bb -= j; cc -= 2 * j; if (bb < 0 || cc < 0) continue; contor += j * 3; maxim = max(contor, maxim); } } cout << maxim << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; void solve() { int a, b, c; cin >> a >> b >> c; int ans = 0; for (int x = 0; x < a + 1; x++) { for (int y = 0; y < c / 2 + 1; y++) { if (2 * x + y <= b) ans = max(3 * x + 3 * y, ans); } } cout << ans << "\n"; } int main() { int t = 1; cin >> t; while (t--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; for (int i = 0; i < t; i++) { int a, b, c; cin >> a >> b >> c; if (b == 0) { cout << "0\n"; } else if (a == 0) { if (b > c / 2) { cout << ((c / 2) * 3) << "\n"; } else if (b <= c / 2) { cout << (b * 3) << "\n"; } } else if (c == 0) { if (a > b / 2) { cout << ((b / 2) * 3) << "\n"; } else if (a <= b / 2) { cout << (a * 3) << "\n"; } } else { int ans = 0; if (b > c / 2) { ans += (c / 2) * 3; b -= c / 2; } else if (b <= c / 2) { ans += (b * 3); b = 0; } if (a > b / 2) { ans += (((b / 2) * 3)); } else if (a <= b / 2) { ans += (a * 3); } cout << ans << '\n'; } } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int t; cin >> t; while (t--) { int a, b, c, i, j, s = 0; cin >> a >> b >> c; if (2 * b <= c) { s = s + 3 * b; } else { s += 3 * (c / 2); b = b - (c / 2); if (2 * a <= b) { s += 3 * a; } else { s += 3 * (b / 2); } } cout << s << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; void solve() { long long a, b, c, s = 0; cin >> a >> b >> c; if ((2 * b) <= c) { s = 3 * b; } else { b = b - c / 2; s = s + (3 * (c / 2)); if ((2 * a) <= b) { s = s + 3 * a; } else { a = a - b / 2; s = s + (3 * (b / 2)); } } cout << s << "\n"; } signed main() { long long t = 1; cin >> t; while (t--) { solve(); } }
#include <bits/stdc++.h> using namespace std; using ll = long long; int arr[101][101][101]; int fboii(int a, int b, int c) { if (arr[a][b][c] != -1) { return arr[a][b][c]; } int ans1 = 0, ans2 = 0; if (a >= 1 && b >= 2) { ans1 = 3 + fboii(a - 1, b - 2, c); } if (b >= 1 && c >= 2) { ans2 = 3 + fboii(a, b - 1, c - 2); } arr[a][b][c] = max(ans1, ans2); return max(ans1, ans2); } int main() { int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; for (int i = 0; i < 101; i++) { for (int j = 0; j < 101; j++) { for (int k = 0; k < 101; k++) { arr[i][j][k] = -1; } } } cout << fboii(a, b, c) << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { int t, a, b, c; cin >> t; while (t--) { cin >> a >> b >> c; int x = min(c / 2, b); b -= x; c -= 2 * x; int y = min(b / 2, a); cout << (x + y) * 3 << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long long t, a, b, c, count; cin >> t; while (t--) { count = 0; cin >> a >> b >> c; if (b == 0) { cout << 0 << "\n"; continue; } if (a == 0) { if (b >= (c / 2) && c > 0) { count += ((c / 2) + (2 * (c / 2))); c = c - (2 * (c / 2)); } else if (c > 0) { count += (3 * b); c = c - (2 * b); } cout << count << "\n"; continue; } if (c == 0) { if (a >= (b / 2) && b > 0) { count += ((b / 2) + (2 * (b / 2))); b = b - (2 * (b / 2)); } else if (b > 0) { count += (3 * a); b = b - (2 * a); } cout << count << "\n"; continue; } long long aa = a, bb = b, cc = c; if (a >= (b / 2)) { count += ((b / 2) + (2 * (b / 2))); b = b - (2 * (b / 2)); } else { count += (3 * a); b = b - (2 * a); } if (b >= (c / 2) && c > 0) { count += ((c / 2) + (2 * (c / 2))); c = c - (2 * (c / 2)); } else { if (c > 0) { count += (3 * b); c = c - (2 * b); } } long long count1 = count; count = 0; if (bb >= (cc / 2)) { count += ((cc / 2) + (2 * (cc / 2))); bb = bb - (cc / 2); } else { count += (3 * bb); bb = bb - (cc / 2); } if (aa >= (bb / 2) && bb > 0) { count += ((bb / 2) + (2 * (bb / 2))); bb = bb - (2 * (bb / 2)); } else { if (bb > 0) { count += (3 * aa); bb = bb - (2 * aa); } } long long count2 = count; cout << max(count1, count2) << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t, k, a, b, c, req, x; cin >> t; for (k = 0; k < t; k++) { cin >> a >> b >> c; req = 0; x = min(b, c / 2); if (b >= x) { req += (x * 2) + x; c -= (x * 2); b -= x; } x = min(a, b / 2); if (a >= x) { req += (x * 2) + x; b -= (x * 2); a -= x; } cout << req << "\n"; } }
#include <bits/stdc++.h> using namespace std; int main() { int q, a, b, c, num1, num2; cin >> q; while (q--) { cin >> a >> b >> c; num1 = min(a, b / 2); num2 = min(b, c / 2); int sum = 0; sum += num2; sum += min(a, (b - num2) / 2); cout << sum * 3 << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { cin.tie(0); ios::sync_with_stdio(false); int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; int ans = min(b, c / 2); c -= 2 * ans; b -= ans; ans += min(a, b / 2); cout << ans * 3 << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { int a, b, c, t, res; cin >> t; for (int i = 0; i < t; i++) { cin >> a >> b >> c; res = 0; while (b - 1 >= 0 && c - 2 >= 0) { res += 3; c -= 2; b--; } while (b - 2 >= 0 && a - 1 >= 0) { res += 3; a--; b -= 2; } cout << res << endl; } }
#include <bits/stdc++.h> using namespace std; signed main() { cin.tie(0); ios::sync_with_stdio(false); long long n; cin >> n; long long a, b, c; for (long long i = 0; i < n; i++) { cin >> a >> b >> c; long long ans = 0; ans += min(b, c / 2); b -= ans; ans += min(a, b / 2); cout << ans * 3 << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t, a, b, c; cin >> t; while (t--) { cin >> a >> b >> c; int x = c / 2, sum = 0; sum += 3 * min(x, b); b -= min(x, b); int y = b / 2; sum += min(a, y) * 3; cout << sum << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; int m, ans = 0; m = min(b, c / 2); ans += m * 3; b = b - m; c -= 2 * m; m = min(a, b / 2); ans += m * 3; cout << ans << endl; } }
#include <bits/stdc++.h> using namespace std; inline int read() { register int x = 0, c = getchar(); while (!isdigit(c)) c = getchar(); while (isdigit(c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getchar(); return x; } int main(void) { int T; T = read(); while (T--) { int a, b, c, ans = 0; a = read(), b = read(), c = read(); ans += min(b, c >> 1) * 3; b -= min(b, c >> 1); ans += min(b >> 1, a) * 3; printf("%d\n", ans); } }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; int n = 0; while (b > 0 && c > 1) { int p = c / 2; int q = b; if (p > q) { b = 0; n += 3 * q; break; } else { c = 0; n += 3 * p; b -= p; } } while (a > 0 && b > 1) { int p = b / 2; int q = a; if (p > q) { a = 0; n += 3 * q; break; } else { b = 0; n += 3 * p; a -= p; } } cout << n << endl; } }
#include <bits/stdc++.h> using namespace std; const long long int mod = 1000000007; long long int power(int x, int y) { long long int res = 1; while (y > 0) { if (y & 1) res = ((res % mod) * (x % mod)) % mod; y = y >> 1; x = ((x % mod) * (x % mod)) % mod; } return res; } int main() { ios::sync_with_stdio(false); int t; cin >> t; while (t--) { int a, b, c; cin >> a >> b >> c; int i = c / 2; int stone = 0; if (b - i > 0) { stone += i * 2 + i; b -= i; } else { stone += b * 2 + b; b = 0; } int j = b / 2; if (a - j > 0) stone += j * 2 + j; else stone += a * 2 + a; cout << stone << '\n'; } }
#include <bits/stdc++.h> using namespace std; struct Edge { int x, y; long long val; } e[3 * 100055]; bool cmp(Edge x1, Edge x2) { return x1.val < x2.val; } int head[100055], to[6 * 100055], nex[6 * 100055]; long long w[6 * 100055]; int edge; inline void addEdge(int x, int y, long long z) { to[++edge] = y, w[edge] = z, nex[edge] = head[x], head[x] = edge; to[++edge] = x, w[edge] = z, nex[edge] = head[y], head[y] = edge; } int n, m, k, q; void init() { for (int i = 1; i <= n; i++) head[i] = 0; edge = 0; } bool vis[100055]; long long d[100055]; struct node { int x; long long val; node(int x, long long val) : x(x), val(val) {} friend bool operator<(node x1, node x2) { return x1.val > x2.val; } }; priority_queue<node> que; int pre[100055]; int findd(int x) { if (pre[x] == x) return x; return pre[x] = findd(pre[x]); } long long f[100055][18]; int g[100055][18]; int dep[100055]; int N; void dfs(int u, int fa) { for (int i = 1; i <= N; i++) { g[u][i] = g[g[u][i - 1]][i - 1]; f[u][i] = max(f[u][i - 1], f[g[u][i - 1]][i - 1]); } for (int i = head[u]; i; i = nex[i]) { int v = to[i]; if (v == fa) continue; dep[v] = dep[u] + 1; g[v][0] = u; f[v][0] = w[i]; dfs(v, u); } } inline long long lca(int x, int y) { if (dep[x] > dep[y]) swap(x, y); long long ans = 0; for (int i = N; i >= 0; i--) { if (dep[g[y][i]] >= dep[x]) { ans = max(ans, f[y][i]); y = g[y][i]; } } if (x == y) return ans; for (int i = N; i >= 0; i--) { if (g[x][i] != g[y][i]) { ans = max(f[x][i], ans); ans = max(f[y][i], ans); x = g[x][i]; y = g[y][i]; } } if (x != y) ans = max(ans, f[x][0]), ans = max(ans, f[y][0]); return ans; } int main() { cin >> n >> m >> k >> q; int x, y, z; for (int i = 1; i <= m; i++) { scanf("%d%d%d", &x, &y, &z); addEdge(x, y, z); e[i].x = x, e[i].y = y, e[i].val = z; } for (int i = k + 1; i <= n; i++) d[i] = 0x7f7f7f7f7f7f7f7f; for (int i = 1; i <= k; i++) que.push(node(i, 0)); while (que.size()) { int u = que.top().x; que.pop(); if (vis[u]) continue; vis[u] = true; for (int i = head[u]; i; i = nex[i]) { int v = to[i]; if (d[v] > d[u] + w[i]) { d[v] = d[u] + w[i]; que.push(node(v, d[v])); } } } for (int i = 1; i <= m; i++) e[i].val += (d[e[i].x] + d[e[i].y]); sort(e + 1, e + 1 + m, cmp); init(); for (int i = 1; i <= n; i++) pre[i] = i; for (int i = 1; i <= m; i++) { x = e[i].x; int xx = findd(x); y = e[i].y; int yy = findd(y); if (xx != yy) { pre[xx] = yy; addEdge(x, y, e[i].val); } } N = ceil(log2(n)); dep[1] = 1; dfs(1, 0); while (q--) { scanf("%d%d", &x, &y); printf("%lld\n", lca(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; const int ONE = 2000005; const long long INF = 1ll << 60; int get() { int res = 1, Q = 1; char c; while ((c = getchar()) < 48 || c > 57) if (c == '-') Q = -1; if (Q) res = c - 48; while ((c = getchar()) >= 48 && c <= 57) res = res * 10 + c - 48; return res * Q; } int n, m, k, Q; int nxt[ONE], first[ONE], go[ONE], tot; long long w[ONE]; int x, y, num; long long val; struct power { int x, y; long long val; friend bool operator<(const power &a, const power &b) { return a.val < b.val; } } a[ONE]; void Add(int u, int v, long long e) { nxt[++tot] = first[u], first[u] = tot, go[tot] = v, w[tot] = e; nxt[++tot] = first[v], first[v] = tot, go[tot] = u, w[tot] = e; } long long dist[ONE]; bool vis[ONE]; priority_queue<pair<long long, int>> q; void Dijkstra() { for (int i = 1; i <= k; i++) q.emplace(0, i); for (int i = k + 1; i <= n; i++) dist[i] = INF; while (!q.empty()) { int u = q.top().second; q.pop(); if (vis[u]) continue; vis[u] = 1; for (int e = first[u]; e; e = nxt[e]) { int v = go[e]; if (dist[v] > dist[u] + w[e]) dist[v] = dist[u] + w[e], q.emplace(-dist[v], v); } } } int siz[ONE], son[ONE], top[ONE], fat[ONE], Dep[ONE]; void Dfs1(int u, int fa) { siz[u] = 1, fat[u] = fa, Dep[u] = Dep[fa] + 1; for (int e = first[u]; e; e = nxt[e]) { int v = go[e]; if (v == fa) continue; Dfs1(v, u); siz[u] += siz[v]; if (siz[v] > siz[son[u]]) son[u] = v; } } void Dfs2(int u, int fa) { if (int v = son[u]) top[v] = top[u], Dfs2(v, u); for (int e = first[u]; e; e = nxt[e]) { int v = go[e]; if (v == fa || v == son[u]) continue; Dfs2(top[v] = v, u); } } int LCA(int u, int v) { while (top[u] != top[v]) { int &x = Dep[top[u]] > Dep[top[v]] ? u : v; x = fat[top[x]]; } return Dep[u] < Dep[v] ? u : v; } int f[ONE]; int Find(int x) { if (f[x] == x) return x; return f[x] = Find(f[x]); } int now; long long value[ONE]; void Kruskal() { num = 0; for (int u = 1; u <= n; u++) for (int e = first[u]; e; e = nxt[e]) a[++num] = (power){u, go[e], w[e] + dist[u] + dist[go[e]]}; sort(a + 1, a + num + 1); tot = 0; for (int i = 1; i <= (n << 1) + 1; i++) f[i] = i, first[i] = 0; now = n; for (int i = 1; i <= num; i++) { int fx = Find(a[i].x), fy = Find(a[i].y); if (fx != fy) { value[++now] = a[i].val; f[fx] = f[fy] = now; Add(now, fx, 0), Add(now, fy, 0); } } } int main() { cin >> n >> m >> k >> Q; for (int i = 1; i <= m; i++) { scanf("%d %d %lld", &x, &y, &val); Add(x, y, val); } Dijkstra(); Kruskal(); top[now] = now; Dfs1(now, 0); Dfs2(now, 0); while (Q--) { scanf("%d %d", &x, &y); printf("%lld\n", value[LCA(x, y)]); } }
#include <bits/stdc++.h> using namespace std; struct dataEdge { long long u, v, w; dataEdge(){}; dataEdge(long long u, long long v, long long w) : u(u), v(v), w(w){}; bool operator<(const dataEdge &a) const { return w < a.w; } }; struct dataHeap { long long u, type, val; dataHeap(){}; dataHeap(long long u, long long type, long long val) : u(u), type(type), val(val){}; bool operator>(const dataHeap &u) const { return val > u.val; } }; const long long N = 3e5 + 4, oo = 1e17 + 4; long long n, m, k, QQues; vector<pair<long long, long long> > adj[N]; vector<dataEdge> Edge; long long par[N]; vector<long long> lsNode; long long getRoot(long long u) { return (par[u] < 0) ? u : (par[u] = getRoot(par[u])); } bool Merge(long long u, long long v) { u = getRoot(u); v = getRoot(v); if (u == v) return false; if (par[u] > par[v]) swap(u, v); par[u] += par[v]; par[v] = u; return true; } long long d[N][2], root[N][2]; priority_queue<dataHeap, vector<dataHeap>, greater<dataHeap> > pq; void Dijkstra0() { for (long long u = 1; u <= (long long)n; ++u) d[u][0] = d[u][1] = oo, root[u][0] = root[u][1] = -1; for (long long u = 1; u <= (long long)k; ++u) { d[u][0] = 0; root[u][0] = u; pq.push(dataHeap(u, 0, d[u][0])); } while (pq.size()) { long long u = pq.top().u, type = pq.top().type, val = pq.top().val; pq.pop(); if (d[u][type] != val) continue; for (pair<long long, long long> foo : adj[u]) { long long v = foo.second, cost = foo.first; if (d[v][0] > val + cost) { d[v][0] = val + cost; root[v][0] = root[u][type]; pq.push(dataHeap(v, 0, d[v][0])); } } } } void Dijkstra1() { for (long long u = 1; u <= (long long)n; ++u) pq.push(dataHeap(u, 0, d[u][0])); while (pq.size()) { long long u = pq.top().u, type = pq.top().type, val = pq.top().val; pq.pop(); if (d[u][type] != val) continue; for (pair<long long, long long> foo : adj[u]) { long long v = foo.second, cost = foo.first; if (d[v][1] > val + cost && getRoot(root[v][0]) != getRoot(root[u][type])) { d[v][1] = val + cost; root[v][1] = root[u][type]; pq.push(dataHeap(v, 1, d[v][1])); } } } } dataEdge Trace[N]; vector<dataEdge> Tree, CC; long long Time, debug, best[N]; void sol() { for (long long u = 1; u <= (long long)n; ++u) { par[u] = -1; if (u <= k) lsNode.push_back(u); } while (true) { if ((long long)lsNode.size() == 1) return; Dijkstra0(); Dijkstra1(); for (long long u = 1; u <= (long long)n; ++u) best[u] = oo, Trace[u] = dataEdge(-1, -1, -1); for (long long u = 1; u <= (long long)k; ++u) { long long v = root[u][1], w = d[u][1], topo_u = getRoot(u), topo_v = getRoot(v); if (v == -1) continue; if (best[topo_u] > d[u][1]) { best[topo_u] = d[u][1]; Trace[topo_u] = dataEdge(u, v, w); } if (best[topo_v] > d[u][1]) { best[topo_v] = d[u][1]; Trace[topo_v] = dataEdge(u, v, w); } } CC.clear(); for (long long topo : lsNode) { long long u = Trace[topo].u, v = Trace[topo].v, w = Trace[topo].w; if (u != -1) CC.push_back(dataEdge(u, v, w)); } sort(CC.begin(), CC.end()); for (dataEdge foo : CC) { long long u = foo.u, v = foo.v; if (Merge(u, v)) Tree.push_back(foo); } lsNode.clear(); for (long long u = 1; u <= (long long)k; ++u) if (par[u] < 0) lsNode.push_back(u); } } long long Low[N], High[N], ans[N]; vector<long long> needCheck[N]; pair<long long, long long> ques[N]; void Answer_Query() { assert((long long)Tree.size() == k - 1); sort(Tree.begin(), Tree.end()); for (long long i = 1; i <= (long long)QQues; ++i) cin >> ques[i].first >> ques[i].second; for (long long i = 1; i <= (long long)QQues; ++i) Low[i] = 0, High[i] = k - 1, ans[i] = -1; while (true) { bool isEnd = true; for (long long i = 1; i <= (long long)QQues; ++i) if (Low[i] <= High[i]) { long long mid = (Low[i] + High[i]) / 2; needCheck[mid].push_back(i); isEnd = false; } if (isEnd) break; for (long long u = 1; u <= (long long)n; ++u) par[u] = -1; for (long long i = 0; i < (long long)Tree.size(); ++i) { long long u = Tree[i].u, v = Tree[i].v, w = Tree[i].w; Merge(u, v); for (long long id : needCheck[i]) { long long u = ques[id].first, v = ques[id].second; u = getRoot(u); v = getRoot(v); if (u == v) { High[id] = i - 1; ans[id] = w; } else Low[id] = i + 1; } needCheck[i].clear(); } } for (long long i = 1; i <= (long long)QQues; ++i) cout << ans[i] << '\n'; } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); if (fopen("input.txt", "r")) { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); } cin >> n >> m >> k >> QQues; long long u, v, w; for (long long i = 1; i <= (long long)m; ++i) { cin >> u >> v >> w; adj[u].push_back(pair<long long, long long>(w, v)); adj[v].push_back(pair<long long, long long>(w, u)); Edge.push_back(dataEdge(u, v, w)); } sol(); Answer_Query(); return 0; }
#include <bits/stdc++.h> using namespace std; struct UnionFind { vector<int> par; vector<int> sz; UnionFind(int n = 0) { if (n > 0) initialize(n); } void initialize(int n) { par.resize(n); sz.resize(n); for (int i = 0; i < n; i++) { par[i] = i; sz[i] = 1; } } int find(int x) { if (par[x] == x) { return x; } else { return par[x] = find(par[x]); } } bool unite(int x, int y) { x = find(x); y = find(y); if (x == y) return false; if (sz[x] > sz[y]) swap(x, y); par[x] = y; sz[y] += sz[x]; return true; } bool same(int x, int y) { return find(x) == find(y); } int size(int x) { return sz[find(x)]; } }; struct UnionFind_P { vector<int> par; vector<int> rank; vector<int64_t> time; vector<vector<pair<int64_t, int>>> sz; const int64_t INF = 1e18; void initialize(int n) { par.resize(n); rank.resize(n); time.resize(n); sz.resize(n); for (int i = 0; i < n; i++) { par[i] = i; rank[i] = 0; time[i] = INF; sz[i].push_back({-1, 1}); } } int find(int x, int64_t t) { if (time[x] > t) { return x; } else { return find(par[x], t); } } int size(int x, int64_t t) { x = find(x, t); return (*(lower_bound(sz[x].begin(), sz[x].end(), make_pair(t + 1, 0)) - 1)) .second; } void unite(int x, int y, int64_t t) { x = find(x, t); y = find(y, t); if (x == y) return; int new_sz = sz[x].back().second + sz[y].back().second; if (sz[x].back().second > sz[y].back().second) swap(x, y); par[x] = y; time[x] = t; sz[y].push_back({t, new_sz}); } bool same(int x, int y, int64_t t) { return find(x, t) == find(y, t); } }; int main() { int N, M, K, Q; cin >> N >> M >> K >> Q; vector<pair<int64_t, int64_t>> edges[100000]; for (int i = 0; i < M; i++) { int a, b, c; scanf("%d %d %d", &a, &b, &c); a--; b--; edges[a].emplace_back(b, c); edges[b].emplace_back(a, c); } vector<pair<int64_t, int64_t>> dist(N); bitset<100000> done; pair<int64_t, int64_t> INFP = {1e18, 1e18}; priority_queue<vector<int64_t>, vector<vector<int64_t>>, greater<vector<int64_t>>> que; for (int i = 0; i < K; i++) { dist[i] = {0, i}; que.push({0, i, i}); } for (int i = K; i < N; i++) dist[i] = INFP; while (que.size()) { auto p = que.top(); que.pop(); int64_t d = p[0], i = p[1], s = p[2]; done[i] = 1; if (dist[i].first < d) continue; for (auto& e : edges[i]) { int64_t j = e.first, d2 = d + e.second; if (dist[j].first > d2) { dist[j] = {d2, s}; que.push({d2, j, s}); } } } vector<vector<int64_t>> es; for (int i = 0; i < N; i++) for (auto& e : edges[i]) { int j = e.first, c = e.second; es.push_back( {dist[i].first + dist[j].first + c, dist[i].second, dist[j].second}); } sort(es.begin(), es.end()); UnionFind_P uf; uf.initialize(N); for (auto& e : es) uf.unite(e[1], e[2], e[0]); for (int i = 0; i < Q; i++) { int a, b; scanf("%d %d", &a, &b); a--; b--; int64_t ok = 1e18, ng = -1; while (ok - ng > 1) { int64_t mid = (ok + ng) / 2; (uf.same(a, b, mid) ? ok : ng) = mid; } printf("%lld\n", ok); } return 0; }
#include <bits/stdc++.h> template <typename Arg1> void __f(const char* name, Arg1&& arg1) { std::cerr << name << " : " << arg1 << std::endl; } template <typename Arg1, typename... Args> void __f(const char* names, Arg1&& arg1, Args&&... args) { const char* comma = strchr(names + 1, ','); std::cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } using namespace std; const int N = 200001; const int LN = 20; struct T { int u, v; int64_t c; bool operator<(const T& a) const { return c > a.c; } }; struct E { int u; int64_t c; bool operator<(const E& a) const { return c < a.c; } } d[N]; unordered_map<int, unordered_map<int, int64_t>> mp; vector<E> gr[N], tr[N]; E st[N][LN]; int p[N], dep[N]; bool v[N]; void dfs(int node, int p, int64_t c, int depth) { dep[node] = depth; st[node][0].u = p; st[node][0].c = c; for (E it : tr[node]) if (it.u != p) dfs(it.u, node, it.c, depth + 1); } void initLca(int n) { for (int j = 1; j < LN; j++) { for (int i = 1; i <= n; i++) { st[i][j].u = st[st[i][j - 1].u][j - 1].u; st[i][j].c = max(st[i][j - 1].c, st[st[i][j - 1].u][j - 1].c); } } } int64_t lca(int u, int v) { int64_t ans = 0; if (dep[u] < dep[v]) swap(u, v); for (int i = LN - 1; i >= 0; i--) { if (dep[st[u][i].u] >= dep[v]) { ans = max(ans, st[u][i].c); u = st[u][i].u; } } if (u == v) return ans; for (int i = LN - 1; i >= 0; i--) { if (st[u][i].u != st[v][i].u) { ans = max(ans, max(st[u][i].c, st[v][i].c)); u = st[u][i].u; v = st[v][i].u; } } return max(ans, max(st[u][0].c, st[v][0].c)); } int par(int node) { return (p[node] < 0 ? node : p[node] = par(p[node])); } void merge(int u, int v, int64_t d) { int pu = par(u); int pv = par(v); if (pu != pv) { if (p[pu] < p[pv]) { p[pu] += p[pv]; p[pv] = pu; } else { p[pv] += p[pu]; p[pu] = pv; } tr[u].push_back({v, d}); tr[v].push_back({u, d}); } } int main() { ios_base::sync_with_stdio(false); memset(p, -1, sizeof p); int n, m, k, q; cin >> n >> m >> k >> q; for (int i = 0, u, v, c; i < m; i++) { cin >> u >> v >> c; gr[u].push_back({v, c}); gr[v].push_back({u, c}); } priority_queue<T> Q; for (int i = 1; i <= k; i++) Q.push({i, i, 0}); while (!Q.empty()) { int node = Q.top().u; int v = Q.top().v; int64_t c = Q.top().c; Q.pop(); if (::v[node]) { int64_t& x = mp[d[node].u][v]; if (x) x = min(x, c + d[node].c); else x = c + d[node].c; continue; } ::v[node] = true; d[node] = {v, c}; for (E it : gr[node]) Q.push({it.u, v, it.c + c}); } for (int i = 1; i <= k; i++) for (auto it : mp[i]) Q.push({i, it.first, it.second}); while (!Q.empty()) { merge(Q.top().u, Q.top().v, Q.top().c); Q.pop(); } dfs(1, 0, 0, 1); initLca(k); while (q--) { int u, v; cin >> u >> v; cout << lca(u, v) << endl; } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O3") 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 int maxn = 3e5 + 5; const long long inf = 1e18 + 9; int n, m, k, q; vector<pair<int, int> > g[maxn]; pair<long long, pair<int, int> > edges[maxn]; pair<int, int> query[maxn]; struct data { int id; long long val; bool operator<(const data& other) const { return val > other.val; } }; long long d[maxn]; int lab[maxn]; int low[maxn], high[maxn]; vector<int> vec[maxn]; void read_input() { cin >> n >> m >> k >> q; for (int i = 1; i <= m; ++i) { int u, v, w; cin >> u >> v >> w; edges[i] = make_pair(w, pair<int, int>(u, v)); g[u].push_back(pair<int, int>(v, w)); g[v].push_back(pair<int, int>(u, w)); } for (int i = 1; i <= q; ++i) { int u, v; cin >> u >> v; query[i] = pair<int, int>(u, v); } } void dijkstra() { priority_queue<data> pq; fill(d + 1, d + n + 1, inf); for (int i = 1; i <= k; ++i) { d[i] = 0; pq.push({i, 0}); } while (!pq.empty()) { data tp = pq.top(); pq.pop(); if (tp.val != d[tp.id]) continue; int u = tp.id; for (auto& to : g[u]) { int v = to.first, w = to.second; if (d[v] > d[u] + w) { d[v] = d[u] + w; pq.push({v, d[v]}); } } } } int find_set(int u) { return lab[u] < 0 ? u : lab[u] = find_set(lab[u]); } void union_sets(int u, int v) { if (lab[u] < lab[v]) swap(u, v); lab[v] += lab[u]; lab[u] = v; } void solve() { dijkstra(); for (int i = 1; i <= m; ++i) { int u = edges[i].second.first, v = edges[i].second.second; edges[i].first += d[u] + d[v]; } sort(edges + 1, edges + m + 1); for (int i = 1; i <= q; ++i) { low[i] = 1; high[i] = m; } while (true) { bool stop = true; for (int i = 1; i <= q; ++i) if (low[i] <= high[i]) { stop = false; int mid = (low[i] + high[i]) / 2; vec[mid].push_back(i); } if (stop) break; fill(lab + 1, lab + n + 1, -1); for (int i = 1; i <= m; ++i) { int u = edges[i].second.first, v = edges[i].second.second; u = find_set(u); v = find_set(v); if (u != v) union_sets(u, v); while ((int)vec[i].size()) { int id = vec[i].back(); vec[i].pop_back(); if (find_set(query[id].first) == find_set(query[id].second)) high[id] = i - 1; else low[id] = i + 1; } } } for (int i = 1; i <= q; ++i) cout << edges[low[i]].first << '\n'; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); read_input(); solve(); }
#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]; for (int j = 0; j < (int)qr[u].size(); j++) { if (rs[qr[u][j].second]) continue; if (mp[x][qr[u][j].first]) rs[qr[u][j].second] = w; } 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> struct disjoint_set { std::vector<int> p; disjoint_set(int n) : p(n, -1) {} int root(int u) { return p[u] < 0 ? u : p[u] = root(p[u]); } bool merge(int u, int v) { if ((u = root(u)) == (v = root(v))) return false; if (p[u] > p[v]) std::swap(u, v); p[u] += p[v]; p[v] = u; return true; } void reset() { std::fill(p.begin(), p.end(), -1); } }; class FCheapRobot { public: void solve(std::istream& in, std::ostream& out) { int n, m, k, q; in >> n >> m >> k >> q; using ll = long long; std::vector<std::vector<std::pair<int, int>>> g(n); std::vector<std::tuple<int, int, ll>> edges; for (int i = 0; i < m; ++i) { int u, v, w; in >> u >> v >> w; --u, --v; g[u].emplace_back(v, w); g[v].emplace_back(u, w); edges.emplace_back(u, v, w); } using node = std::pair<ll, int>; std::priority_queue<node, std::vector<node>, std::greater<node>> pq; std::vector<ll> dist(n, std::numeric_limits<ll>::max()); for (int i = 0; i < k; ++i) pq.emplace(dist[i] = 0, i); while (!pq.empty()) { int u; ll d; std::tie(d, u) = pq.top(); pq.pop(); if (dist[u] < d) continue; for (auto e : g[u]) if (dist[e.first] > d + e.second) pq.emplace(dist[e.first] = d + e.second, e.first); } for (auto& e : edges) { int u, v; ll w; std::tie(u, v, w) = e; w += dist[u] + dist[v]; e = std::make_tuple(u, v, w); } std::sort(edges.begin(), edges.end(), [](const std::tuple<int, int, ll>& a, const std::tuple<int, int, ll>& b) { return std::get<2>(a) < std::get<2>(b); }); std::vector<int> u(q), v(q), ord; for (int i = 0; i < q; ++i) in >> u[i] >> v[i], --u[i], --v[i]; std::vector<int> lo(q), hi(q, m - 1), mid(q); disjoint_set ds(n); while (true) { ord.clear(); for (int i = 0; i < q; ++i) { if (lo[i] == hi[i]) continue; mid[i] = (lo[i] + hi[i]) / 2; ord.emplace_back(i); } if (ord.empty()) break; std::sort(ord.begin(), ord.end(), [&mid](int x, int y) { return mid[x] < mid[y]; }); ds.reset(); for (int i = 0, j = 0; i < (int)ord.size(); ++i) { ll w = std::get<2>(edges[mid[ord[i]]]); for (; j < m && std::get<2>(edges[j]) <= w; ++j) ds.merge(std::get<0>(edges[j]), std::get<1>(edges[j])); if (ds.root(u[ord[i]]) == ds.root(v[ord[i]])) hi[ord[i]] = mid[ord[i]]; else lo[ord[i]] = mid[ord[i]] + 1; } } for (int i = 0; i < q; ++i) out << std::get<2>(edges[lo[i]]) << '\n'; } }; int main() { std::ios_base::sync_with_stdio(0); std::istream& in(std::cin); std::ostream& out(std::cout); in.tie(0); FCheapRobot solver; solver.solve(in, out); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 10, mod = 1e9 + 7; vector<pair<int, int> > g[N]; long long dis[N]; int par[N], sz[N]; set<pair<long long, int> > s; void dijekstra() { while (s.size()) { auto x = *s.begin(); s.erase(s.begin()); long long d = x.first; int v = x.second; for (auto xx : g[v]) { int u = xx.first, w = xx.second; if (dis[u] > d + w) { par[u] = par[v]; s.erase({dis[u], u}); dis[u] = d + w; s.insert({dis[u], u}); } } } } int pr(int x) { if (par[x] == x) return x; return par[x] = pr(par[x]); } long long l[N], r[N], mid[N]; int a[N], b[N]; int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); 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].push_back({v, w}); g[v].push_back({u, w}); } for (int i = 0; i < n; i++) dis[i] = 1ll * mod * mod; for (int i = 0; i < k; i++) { s.insert({0, i}); dis[i] = 0; par[i] = i; } dijekstra(); vector<pair<long long, pair<int, int> > > e; for (int i = 0; i < n; i++) for (auto x : g[i]) { int v = x.first, w = x.second; if (par[i] < par[v]) e.push_back({w + dis[i] + dis[v], {par[i], par[v]}}); } sort(e.begin(), e.end()); for (int i = 0; i < q; i++) { scanf("%d%d", &a[i], &b[i]); a[i]--; b[i]--; l[i] = 0, r[i] = 1ll * n * mod; } bool go = true; while (go) { go = false; vector<pair<long long, int> > vec; for (int i = 0; i < q; i++) { if (r[i] - l[i] > 1) { mid[i] = (l[i] + r[i]) / 2; vec.push_back({mid[i], i}); go = true; } } sort(vec.begin(), vec.end()); for (int i = 0; i < k; i++) par[i] = i, sz[i] = 1; int cur = 0; for (auto x : vec) { while (cur < e.size() && e[cur].first <= x.first) { int u = e[cur].second.first, v = e[cur].second.second; u = pr(u); v = pr(v); if (sz[u] > sz[v]) swap(u, v); par[u] = v; sz[v] += sz[u]; cur++; } int id = x.second; if (pr(a[id]) == pr(b[id])) r[id] = mid[id]; else l[id] = mid[id]; } } for (int i = 0; i < q; i++) printf("%lld\n", r[i]); return 0; }
#include <bits/stdc++.h> struct Edge { Edge(int u, int v, long long w) : start(u), end(v), weight(w) {} int start, end; long long weight; bool operator<(const Edge &other) const { return (other.weight < weight); } }; const int MAXN = 2e5; const int LOGN = 18; std::vector<Edge> graph[MAXN]; std::priority_queue<Edge> dijkstra; int closestSpecial[MAXN]; long long distToClosest[MAXN]; std::vector<Edge> paths; int component[MAXN]; std::vector<Edge> specTree[MAXN]; int depth[MAXN]; int ancester[MAXN][LOGN]; long long weightToAnc[MAXN][LOGN]; void computeinfluence() { while (!dijkstra.empty()) { int special = dijkstra.top().start; int node = dijkstra.top().end; long long dist = dijkstra.top().weight; dijkstra.pop(); if (closestSpecial[node] != -1) continue; closestSpecial[node] = special; distToClosest[node] = dist; for (Edge &edge : graph[node]) dijkstra.emplace(special, edge.end, dist + edge.weight); } } int find(int node) { if (node != component[node]) component[node] = find(component[node]); return component[node]; } void merge(Edge &edge) { if (find(edge.start) != find(edge.end)) { component[find(edge.end)] = find(edge.start); specTree[edge.start].emplace_back(edge.start, edge.end, edge.weight); specTree[edge.end].emplace_back(edge.end, edge.start, edge.weight); } } void root(int node) { for (Edge &edge : specTree[node]) if (edge.end != ancester[node][0]) { ancester[edge.end][0] = node; weightToAnc[edge.end][0] = edge.weight; depth[edge.end] = depth[node] + 1; root(edge.end); } } int getanc(int node, int exp) { if (ancester[node][exp] == -1) ancester[node][exp] = getanc(getanc(node, exp - 1), exp - 1); return ancester[node][exp]; } long long getweighttoanc(int node, int exp) { if (weightToAnc[node][exp] == 0) weightToAnc[node][exp] = std::max(getweighttoanc(node, exp - 1), getweighttoanc(getanc(node, exp - 1), exp - 1)); return weightToAnc[node][exp]; } int lift(int node, int dist) { if (dist == 0) return node; int exp = 31 - __builtin_clz(dist); return lift(getanc(node, exp), dist - (1 << exp)); } long long liftw(int node, int dist) { if (dist == 0) return 0; int exp = 31 - __builtin_clz(dist); return std::max(liftw(getanc(node, exp), dist - (1 << exp)), getweighttoanc(node, exp)); } int lca(int u, int v) { if (depth[u] < depth[v]) std::swap(u, v); u = lift(u, depth[u] - depth[v]); if (u == v) return u; for (int iExp = 31 - __builtin_clz(depth[u]); iExp > -1; iExp--) if (getanc(u, iExp) != getanc(v, iExp)) { u = getanc(u, iExp); v = getanc(v, iExp); } return getanc(u, 0); } int main() { std::ios::sync_with_stdio(false); std::cout.tie(nullptr); std::cin.tie(nullptr); int nodes, edges, special, queries; std::cin >> nodes >> edges >> special >> queries; for (int iEdge = 0; iEdge < edges; iEdge++) { int u, v, w; std::cin >> u >> v >> w; u--; v--; graph[u].emplace_back(u, v, w); graph[v].emplace_back(v, u, w); } for (int iSpec = 0; iSpec < special; iSpec++) dijkstra.emplace(iSpec, iSpec, 0); for (int iNode = 0; iNode < nodes; iNode++) closestSpecial[iNode] = -1; computeinfluence(); for (int iNode = 0; iNode < nodes; iNode++) { component[iNode] = iNode; for (Edge &edge : graph[iNode]) if (closestSpecial[iNode] != closestSpecial[edge.end]) paths.emplace_back( closestSpecial[iNode], closestSpecial[edge.end], distToClosest[iNode] + edge.weight + distToClosest[edge.end]); } std::sort(paths.rbegin(), paths.rend()); for (Edge &path : paths) merge(path); std::fill_n((int *)ancester, special * LOGN, -1); root(0); for (int iQuery = 0; iQuery < queries; iQuery++) { int u, v; std::cin >> u >> v; u--; v--; int w = lca(u, v); std::cout << std::max(liftw(u, depth[u] - depth[w]), liftw(v, depth[v] - depth[w])) << ' '; } std::cout << '\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; } 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; template <class T> bool mmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template <class T> bool mmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } void yesno(bool c) { cout << (c ? "YES" : "NO") << '\n'; } void yes() { yesno(true); } void no() { yesno(false); } void imp() { cout << "-1" << '\n'; } const int inf = 0x3f3f3f3f; const long long infl = 0x3f3f3f3f3f3f3f3f; vector<int> va, vb; vector<int> aval, bval, wval; struct base_graph { int n, ecnt = 0; bool is_wei; vector<int> from, to; vector<long long> w; base_graph(int n, bool is_wei = false) : n(n), is_wei(is_wei) {} virtual int add(int a, int b, int ww = 0) = 0; int base_add(int a, int b, int ww = 0) { from.push_back(a); to.push_back(b); if (is_wei) w.push_back(ww); return ecnt++; } void readin(int m, bool add_rev = false, int offset = 1) { reserve(add_rev ? 2 * m : m); for (int i = 0; i < m; i++) { int a, b, ww = 0; cin >> a >> b; a -= offset; b -= offset; if (is_wei) cin >> ww; add(a, b, ww); if (add_rev) add(b, a, ww); } } void readin_tree(bool add_rev, int offset = 1) { int m = n - 1; reserve(add_rev ? 2 * m : m); for (int i = 2; i <= m; i++) { int p; cin >> p; int a = i - offset; add(a, p); if (add_rev) add(p, a); } } protected: void reserve(int m) { from.reserve(m); to.reserve(m); if (is_wei) w.reserve(m); } }; struct dir_graph : public base_graph { bool has_rev; vector<vector<pair<int, int>>> out, in; dir_graph(int n, bool has_rev = false, bool is_wei = false) : base_graph(n, is_wei), has_rev(has_rev), out(n), in(n) {} int add(int a, int b, int ww = 0) { int e = base_add(a, b, ww); out[a].push_back({e, b}); in[b].push_back({e, a}); return e; } void readin(int m, int offset = 1) { base_graph::readin(m, has_rev, offset); } void readin_tree(int offset = 1) { base_graph::readin_tree(has_rev, offset); } }; struct undir_graph : public base_graph { vector<vector<pair<int, int>>> edg; undir_graph(int n, bool is_wei = false) : base_graph(n, is_wei), edg(n) {} int add(int a, int b, int ww = 0) { if (b > a) swap(a, b); int e = base_add(a, b, ww); edg[a].push_back({e, b}); edg[b].push_back({e, a}); return e; } void readin(int m, int offset = 1) { base_graph::readin(m, false, offset); } void readin_tree(int offset = 1) { base_graph::readin_tree(false, offset); } }; struct dijkstra_vec { vector<long long> dist, par; dir_graph& g; dijkstra_vec(dir_graph& g) : dist(g.n, infl), par(g.n), g(g) {} void solve(const vector<int>& s) { using P = pair<long long, int>; priority_queue<P, vector<P>, greater<P>> q; auto upd = [&](int u, int p, long long d) { if (mmin(dist[u], d)) { par[u] = p; q.push({d, u}); } }; for (int ss : s) upd(ss, -1, 0); while (!q.empty()) { int u; long long d; tie(d, u) = q.top(); q.pop(); if (d > dist[u]) continue; for (auto [e, v] : g.out[u]) { long long newd = d + g.w[e]; upd(v, u, newd); } } } }; struct dsu { int _n; std::vector<int> parent_or_size; dsu() : _n(0) {} dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } }; int qval; bool br = false; struct query_dsu : dsu { unordered_map<int, unordered_map<int, vector<int>>> betw; undir_graph& g; query_dsu(int n, undir_graph& g) : dsu(n), g(g) { for (int e = 0; e < g.ecnt; e++) { int u = g.from[e], v = g.to[e]; betw[u][v].push_back(e); betw[v][u].push_back(e); } } vector<int>& getbetw(int a, int b) { int x = leader(a), y = leader(b); return betw[x][y]; } int merge(int a, int b) { int x = leader(a), y = leader(b); if (x == y) return -1; if (br) { cout << a << " " << b << " " << x << " " << y << '\n'; exit(0); } if (dsu::merge(a, b) != x) swap(x, y); betw[x][y].clear(); betw[y][x].clear(); for (auto [e, v] : g.edg[y]) { v = leader(v); if (v == x) continue; g.edg[x].push_back({e, v}); betw[x][v].push_back(e); betw[v][x].push_back(e); } g.edg[y].clear(); return x; } }; void solve() { int n, m, k, q; cin >> n >> m >> k >> q; qval = q; dir_graph g(n, true, true); g.readin(m); dijkstra_vec dij(g); vector<int> s; for (int i = 0; i < (k); i++) s.push_back(i); dij.solve(s); for (int e = 0; e < (g.ecnt); e++) { g.w[e] += dij.dist[g.from[e]] + dij.dist[g.to[e]]; } undir_graph qg(n); qg.readin(q); query_dsu d(n, qg); vector<pair<long long, long long>> ws; for (int e = 0; e < (g.ecnt); e++) { if (e % 2) ws.push_back(make_pair(g.w[e], e)); } sort((ws).begin(), (ws).end()); vector<long long> ans(q); int cnt = 0; for (pair<long long, long long> we : ws) { cnt++; int u = g.from[we.second], v = g.to[we.second]; for (int qq : d.getbetw(u, v)) ans[qq] = we.first; d.merge(u, v); } for (int qq = 0; qq < (q); qq++) { cout << ans[qq] << '\n'; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int tc = 1; while (tc--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const long double pi = 3.1415926535897932384626433832795l; template <typename T> inline auto sqr(T x) -> decltype(x * x) { return x * x; } template <typename T> inline T abs(T x) { return x > T() ? x : -x; } template <typename T1, typename T2> inline bool umx(T1& a, T2 b) { if (a < b) { a = b; return 1; } return 0; } template <typename T1, typename T2> inline bool umn(T1& a, T2 b) { if (b < a) { a = b; return 1; } return 0; } const int N = 300100; const long long inf = (1ll << 60); int p[N]; int sz[N]; int k; bool out[N]; vector<pair<int, int> > a[N]; int get(int a) { if (a == p[a]) { return a; } return p[a] = get(p[a]); } bool uni(int l, int r) { l = get(l), r = get(r); if (l == r) { return false; } if (l >= k && r < k) { swap(l, r); } else { if (sz[l] < sz[r]) { swap(l, r); } } p[r] = l; sz[l] += sz[r]; return true; } pair<long long, int> d[N]; set<pair<long long, int> > s; vector<pair<long long, int> > b[N]; int tw[20][N]; long long maxx[20][N]; int h[N]; void dfs(int v, pair<long long, int> pr, int h1) { ; h[v] = h1; maxx[0][v] = pr.first; tw[0][v] = pr.second; for (int i = int(0); i < int(((int)(b[v]).size())); ++i) { int to = b[v][i].second; if (to == pr.second) { continue; } dfs(to, make_pair(b[v][i].first, v), h1 + 1); } } int up(int v, int h) { for (int i = int(0); i < int(20); ++i) { if (h & (1 << i)) { v = tw[i][v]; } } return v; } int get_lca(int u, int v) { if (h[u] > h[v]) { swap(u, v); } v = up(v, h[v] - h[u]); if (u == v) { return u; } for (int i = int(20) - 1; i >= int(0); --i) { if (tw[i][v] != tw[i][u]) { v = tw[i][v]; u = tw[i][u]; } } return tw[0][v]; } long long get_max_up(int v, int h) { long long result = 0ll; for (int i = int(0); i < int(20); ++i) { if (h & (1 << i)) { umx(result, maxx[i][v]); v = tw[i][v]; } } return result; } long long get_maxx(int u, int v) { int lca = get_lca(u, v); ; ; return max(get_max_up(u, h[u] - h[lca]), get_max_up(v, h[v] - h[lca])); } void precalc() { for (int i = int(1); i < int(20); ++i) { for (int j = int(0); j < int(k); ++j) { int mid = tw[i - 1][j]; tw[i][j] = tw[i - 1][mid]; maxx[i][j] = max(maxx[i - 1][j], maxx[i - 1][mid]); } } } int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); cout.setf(ios::showpoint | ios::fixed); cout.precision(20); int n, m, q; cin >> n >> m >> k >> q; for (int i = int(0); i < int(m); ++i) { int u, v, c; cin >> u >> v >> c; --u, --v; a[u].push_back(make_pair(v, c)); a[v].push_back(make_pair(u, c)); } for (int i = int(0); i < int(n); ++i) { p[i] = i; sz[i] = 1; if (i < k) { d[i] = make_pair(0ll, i); } else { d[i] = make_pair(inf, inf); } s.insert(make_pair(d[i].first, i)); } memset(out, 0, sizeof(out)); while (!s.empty()) { pair<long long, int> k = *s.begin(); s.erase(k); int v = k.second; out[v] = true; for (int i = int(0); i < int(((int)(a[v]).size())); ++i) { int to = a[v][i].first; long long cost = a[v][i].second; if (d[to].first > d[v].first + cost) { s.erase(make_pair(d[to].first, to)); d[to].first = d[v].first + cost; d[to].second = d[v].second; s.insert(make_pair(d[to].first, to)); } } } vector<pair<long long, pair<int, int> > > e; for (int i = int(0); i < int(n); ++i) { for (int j = int(0); j < int(((int)(a[i]).size())); ++j) { int to = a[i][j].first; long long cost = a[i][j].second; e.push_back(make_pair(d[i].first + d[to].first + cost, make_pair(d[to].second, d[i].second))); } } sort((e).begin(), (e).end()); for (int i = int(0); i < int(((int)(e).size())); ++i) { int u = e[i].second.first, v = e[i].second.second; if (uni(u, v)) { ; b[u].push_back(make_pair(e[i].first, v)); b[v].push_back(make_pair(e[i].first, u)); } } dfs(0, make_pair(0ll, 0), 0); precalc(); for (int i = int(0); i < int(q); ++i) { int st, fn; cin >> st >> fn; --st, --fn; cout << get_maxx(st, fn) << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 3e5 + 10, mod = 1e9 + 7; long long inf = 0x3f3f3f3f3f3f3f3f; int n, m, k, Q, fa[N], hd[N], ne, mxd[N]; long long d[N], val[N]; struct E { int v, c, nxt; } e[N << 1]; struct E2 { int u, v; long long c; bool operator<(const E2& b) const { return c < b.c; } } e2[N]; void link(int u, int v, int c) { e[ne] = {v, c, hd[u]}, hd[u] = ne++; } struct D { int u; long long g; bool operator<(const D& b) const { return g > b.g; } }; void Dij() { priority_queue<D> q; memset(d, inf, sizeof d); for (int i = 1; i <= k; ++i) q.push({i, d[i] = 0}); while (q.size()) { int u = q.top().u; long long g = q.top().g; q.pop(); if (d[u] != g) continue; for (int i = hd[u]; ~i; i = e[i].nxt) { int v = e[i].v, c = e[i].c; if (d[v] > d[u] + c) d[v] = d[u] + c, q.push({v, d[v]}); } } } int fd(int x) { return fa[x] ? fd(fa[x]) : x; } void mg(int x, int y, long long c) { int fx = fd(x), fy = fd(y); if (fx == fy) return; if (mxd[fx] > mxd[fy]) swap(fx, fy); fa[fx] = fy, val[fx] = c, mxd[fy] = max(mxd[fy], mxd[fx] + 1); } void Kruskal() { sort(e2, e2 + m); for (int i = 1; i <= n; ++i) mxd[i] = 1, fa[i] = 0; for (int i = 0; i < m; ++i) { int u = e2[i].u, v = e2[i].v; long long c = e2[i].c; mg(u, v, c); } } long long qry(int u, int v) { long long ret = 0; for (; u != v; u = fa[u]) { if (mxd[u] > mxd[v]) swap(u, v); ret = max(ret, val[u]); } return ret; } int main() { memset(hd, -1, sizeof hd), ne = 0; scanf("%d%d%d%d", &n, &m, &k, &Q); for (int i = 0; i < m; ++i) { int u, v, c; scanf("%d%d%d", &u, &v, &c); link(u, v, c); link(v, u, c); e2[i] = {u, v, c}; } Dij(); for (int i = 0; i < m; ++i) e2[i].c += d[e2[i].u] + d[e2[i].v]; Kruskal(); while (Q--) { int u, v; scanf("%d%d", &u, &v); printf("%lld\n", qry(u, v)); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> bool umin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template <class T> bool umax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } const long long B = 1e15; long long dis[300009]; vector<pair<int, int> > adj[300009]; pair<pair<int, int>, int> arr[300009]; long long ans[300009]; int ata[300009]; set<int> s[300009]; int tap(int x) { if (ata[x] == x) return x; return ata[x] = tap(ata[x]); } void merge(int x, int y, long long w) { if ((x = tap(x)) == (y = tap(y))) return; if (s[x].size() < s[y].size()) swap(x, y); for (__typeof((s[y]).begin()) it = (s[y]).begin(); it != (s[y]).end(); it++) { if (s[x].count(*it)) ans[*it] = w; else s[x].insert(*it); } s[y].clear(); ata[y] = x; } int main() { int n, m, k, qr; scanf("%d%d%d%d", &n, &m, &k, &qr); for (int i = 1; i <= m; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); adj[u].push_back(make_pair(v, w)); adj[v].push_back(make_pair(u, w)); arr[i] = make_pair(make_pair(u, v), w); } for (int i = 1; i <= qr; i++) { int u, v; scanf("%d%d", &u, &v); s[u].insert(i); s[v].insert(i); } queue<int> q; for (int i = 1; i <= k; i++) q.push(i); for (int i = k + 1; i <= n; i++) dis[i] = B; while (!q.empty()) { int nd = q.front(); q.pop(); for (__typeof((adj[nd]).begin()) it = (adj[nd]).begin(); it != (adj[nd]).end(); it++) if (umin(dis[it->first], dis[nd] + it->second)) q.push(it->first); } vector<pair<long long, pair<int, int> > > edge; for (int i = 1; i <= m; i++) { int u = arr[i].first.first, v = arr[i].first.second, w = arr[i].second; edge.push_back(make_pair(w + dis[u] + dis[v], make_pair(u, v))); } sort(edge.begin(), edge.end()); for (int i = 1; i <= n; i++) ata[i] = i; for (__typeof((edge).begin()) it = (edge).begin(); it != (edge).end(); it++) merge(it->second.first, it->second.second, it->first); for (int i = 1; i <= qr; i++) printf("%lld\n", ans[i]); 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] += 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; } 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; const long long N = 1e5 + 10, M = 10 * N; const long long INF = 1e18; long long n, m, k, q; long long h[N], ht[N], e[M], ne[M], w[M], idx; long long fa[N]; long long fat[N][25], depth[N], d[N][25]; long long dist[N]; bool st[N]; vector<pair<long long, pair<long long, long long>>> edge; void add(long long h[], long long a, long long b, long long c) { e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx++; } long long find(long long x) { if (fa[x] == x) return x; return fa[x] = find(fa[x]); } void dijkstra() { priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> heap; for (long long i = 1; i <= n; i++) { dist[i] = INF; fa[i] = i; } for (long long i = 1; i <= k; i++) { dist[i] = 0; heap.push({0, i}); } while (heap.size()) { long long t = heap.top().second; heap.pop(); if (st[t]) continue; st[t] = true; for (long long i = h[t]; ~i; i = ne[i]) { long long p = e[i]; if (dist[p] > dist[t] + w[i]) { dist[p] = dist[t] + w[i]; fa[p] = find(t); heap.push({dist[p], p}); } } } } void build() { for (long long i = 1; i <= n; i++) { for (long long j = h[i]; ~j; j = ne[j]) { long long p = e[j]; long long a = find(i); long long b = find(p); if (a == b) continue; edge.push_back({dist[i] + dist[p] + w[j], {a, b}}); } } sort(edge.begin(), edge.end()); for (auto x : edge) { long long a = x.second.first; long long b = x.second.second; if (find(a) == find(b)) continue; add(ht, a, b, x.first); add(ht, b, a, x.first); fa[find(a)] = find(b); } } void bfs(long long h[]) { queue<long long> q; q.push(1); memset(depth, 0x3f, sizeof depth); depth[0] = 0; depth[1] = 1; while (q.size()) { auto t = q.front(); q.pop(); for (long long i = h[t]; ~i; i = ne[i]) { long long p = e[i]; if (depth[p] > depth[t] + 1) { depth[p] = depth[t] + 1; q.push(p); fat[p][0] = t; d[p][0] = w[i]; for (long long j = 1; j <= 20; j++) { fat[p][j] = fat[fat[p][j - 1]][j - 1]; d[p][j] = max(d[p][j - 1], d[fat[p][j - 1]][j - 1]); } } } } } long long lca(long long a, long long b) { long long res = 0; if (depth[a] < depth[b]) swap(a, b); for (long long i = 20; i >= 0; i--) if (depth[fat[a][i]] >= depth[b]) { res = max(res, d[a][i]); a = fat[a][i]; } if (a == b) return res; for (long long i = 20; i >= 0; i--) if (fat[a][i] != fat[b][i]) { res = max(res, d[a][i]); res = max(res, d[b][i]); a = fat[a][i]; b = fat[b][i]; } res = max(res, d[a][0]); res = max(res, d[b][0]); return res; } signed main() { ios ::sync_with_stdio(false); cin.tie(0); memset(h, -1, sizeof h); memset(ht, -1, sizeof ht); cin >> n >> m >> k >> q; while (m--) { long long a, b, c; cin >> a >> b >> c; add(h, a, b, c); add(h, b, a, c); } dijkstra(); build(); bfs(ht); while (q--) { long long a, b; cin >> a >> b; cout << lca(a, b) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int MX = 1e5; int par[MX + 1], sz[MX + 1]; long long ans[3 * MX], dist[MX + 1]; vector<int> token[MX + 1]; vector<pair<int, long long>> adj[MX + 1]; pair<int, int> query[3 * MX]; tuple<long long, int, int> edge[3 * MX]; int find(int a) { if (par[a] == a) return a; return par[a] = find(par[a]); } void unite(int a, int b, long long c) { a = find(a); b = find(b); if (a != b) { if (sz[a] > sz[b]) { swap(a, b); } par[a] = b; sz[b] += sz[a]; for (auto i : token[a]) { if (query[i].first == query[i].second) continue; if (query[i].first != a) { swap(query[i].first, query[i].second); } query[i].first = b; if (query[i].second == b) { ans[i] = c; } else { token[b].push_back(i); } } } } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n, m, k, q; cin >> n >> m >> k >> q; for (int i = 0; i < m; ++i) { int u, v; long long w; cin >> u >> v >> w; edge[i] = make_tuple(w, u, v); adj[u].emplace_back(v, w); adj[v].emplace_back(u, w); } memset(dist, 0x3F3F3F3F, sizeof dist); priority_queue<pair<long long, int>> dijkstra; for (int i = 1; i <= k; ++i) { dist[i] = 0; dijkstra.emplace(0, i); } while (!dijkstra.empty()) { int u; long long d; tie(d, u) = dijkstra.top(); dijkstra.pop(); if (-d > dist[u]) continue; for (auto e : adj[u]) { if (-d + e.second < dist[e.first]) { dist[e.first] = -d + e.second; dijkstra.emplace(-dist[e.first], e.first); } } } for (int i = 0; i < m; ++i) { int u, v; tie(ignore, u, v) = edge[i]; get<0>(edge[i]) += dist[u] + dist[v]; } sort(edge, edge + m); for (int i = 0; i < q; ++i) { int a, b; cin >> a >> b; query[i] = {a, b}; token[a].push_back(i); token[b].push_back(i); } iota(par + 1, par + 1 + n, 1); fill(sz + 1, sz + 1 + n, 1); for (int i = 0; i < m; ++i) { int u, v; long long w; tie(w, u, v) = edge[i]; unite(u, v, w); } for (int i = 0; i < q; ++i) { cout << ans[i] << '\n'; } }
#include <bits/stdc++.h> #pragma GCC optimize(2) const double esp = 1e-6; const double pi = acos(-1.0); const int INF = 0x3f3f3f3f; const int inf = 1e9; using namespace std; long long read() { char ch = getchar(); long long x = 0, f = 1; while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); } return x * f; } const int N = 1e5 + 10; int n, m, k, q, cnt; long long dis[2 * N]; struct edges { int from, to, next; long long wi; bool operator<(const edges &node) const { return wi < node.wi; } } edge[6 * N]; int head[6 * N]; vector<int> tr[N << 1]; long long tr_wi[N << 1]; int tr_num = 0; void addedge(int u, int v, long long w) { edge[cnt].from = u; edge[cnt].wi = w; edge[cnt].next = head[u]; edge[cnt].to = v; head[u] = cnt++; } void dj() { priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > que; for (int i = 1; i <= n; i++) { if (i <= k) { que.push(make_pair(0, i)); } else dis[i] = 1e18; } while (!que.empty()) { auto s = que.top(); que.pop(); long long fi = s.first; int se = s.second; if (dis[se] < fi) continue; for (int i = head[se]; ~i; i = edge[i].next) { int v = edge[i].to; if (dis[v] > fi + edge[i].wi) { dis[v] = fi + edge[i].wi; que.push(make_pair(dis[edge[i].to], edge[i].to)); } } } } int pr[3 * N]; int height[3 * N]; set<int> s[3 * N]; long long ans[3 * N]; vector<pair<int, int> > ip[N]; void init() { for (int i = 0; i <= n; i++) pr[i] = i, height[i] = 1, s[i].insert(i); } int find_pr(int u) { return pr[u] == u ? u : pr[u] = find_pr(pr[u]); } bool same(int u, int v) { return find_pr(u) == find_pr(v); } void insert(int u, int v, long long w) { u = find_pr(u), v = find_pr(v); if (u == v) return; if (height[u] < height[v]) swap(u, v); pr[v] = u; height[u] += height[v]; for (auto k : s[v]) for (auto p : ip[k]) { if (s[u].count(p.second)) ans[p.first] = w; } for (auto k : s[v]) s[u].insert(k); } int main() { memset(head, -1, sizeof(head)); n = read(), m = read(), k = read(), q = read(); int u, v; long long w; for (int i = 1; i <= m; i++) { u = read(), v = read(), w = read(); addedge(u, v, w); addedge(v, u, w); } dj(); for (int i = 0; i < cnt; i++) { edge[i].wi += dis[edge[i].from] + dis[edge[i].to]; } sort(edge, edge + cnt); int ip_cnt = 0; init(); while (q--) { u = read(), v = read(); ip[u].push_back(make_pair(ip_cnt, v)); ip[v].push_back(make_pair(ip_cnt, u)); ip_cnt++; } for (int i = 0; i < cnt; i++) { u = edge[i].from; v = edge[i].to; insert(u, v, edge[i].wi); } for (int i = 0; i < ip_cnt; i++) { printf("%lld\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; const long double PI = 3.14159265359; const long long MOD = (long long)998244353ll; const long long MAXN = (long long)3e5 + 10; const long long INF = (long long)2242545357980376863; const long double EPS = (long double)1e-8; long long source[MAXN], d0[MAXN], dis[MAXN], done[MAXN], par[MAXN]; vector<long long> C[MAXN]; vector<pair<long long, long long> > G[MAXN]; vector<pair<long long, pair<long long, long long> > > E; set<pair<long long, long long> > dj; void change_key(long long node, long long last, long long now) { dj.erase({last, node}); dis[node] = now; dj.insert({now, node}); return; } long long A[MAXN], B[MAXN], ans[MAXN]; long long W; long long get_par(long long u) { if (par[u] == u) return u; return par[u] = get_par(par[u]); } bool merge(long long u, long long v) { long long U = u, V = v; u = get_par(u); v = get_par(v); if (u == v) return false; if (C[u].size() < C[v].size()) swap(u, v); par[v] = u; for (auto x : C[v]) { C[u].push_back(x); if (get_par(A[x]) == get_par(B[x])) ans[x] = min(ans[x], W); } C[v].clear(); return true; } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); memset(ans, 31, sizeof ans); for (int i = 0; i < MAXN; i++) par[i] = i; memset(dis, 31, sizeof dis); memset(d0, 31, sizeof d0); long long n, m, k, q; scanf("%lld%lld%lld%lld", &n, &m, &k, &q); long long u, v, w; for (int i = 0; i < m; i++) { scanf("%lld%lld%lld", &u, &v, &w); G[u].push_back({v, w}); G[v].push_back({u, w}); } long long p, f; for (int i = 1; i <= k; i++) { p = i; source[p] = p; dj.insert({0, p}); dis[p] = 0; } long long fr, d, adj; while (dj.size()) { d = (*dj.begin()).first; fr = (*dj.begin()).second; dj.erase(dj.begin()); for (auto edge : G[fr]) { adj = edge.first; w = edge.second; if (done[adj] == 1) { E.push_back({dis[adj] + dis[fr] + w, {source[fr], source[adj]}}); } if (dis[adj] > d + w) { change_key(adj, dis[adj], d + w); source[adj] = source[fr]; } } done[fr] = 1; } for (int i = 0; i < q; i++) { scanf("%lld%lld", A + i, B + i); C[A[i]].push_back(i); C[B[i]].push_back(i); } sort(E.begin(), E.end()); for (auto edge : E) { W = edge.first; if (merge(edge.second.first, edge.second.second)) { } } for (int i = 0; i < q; i++) printf("%lld\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; int N, M, K, Q; vector<pair<int, int>> E[101010]; vector<pair<int, signed long long>> E2[101010]; int from[101010]; signed long long dist[101010]; int P[21][200005], D[200005]; signed long long ma[21][200005]; template <int um> class UF { public: vector<int> par, rank; UF() { rank = vector<int>(um, 0); for (int i = 0; i < um; i++) par.push_back(i); } int operator[](int x) { return (par[x] == x) ? (x) : (par[x] = operator[](par[x])); } int operator()(int x, int y) { if ((x = operator[](x)) == (y = operator[](y))) return x; if (rank[x] > rank[y]) return par[x] = y; rank[x] += rank[x] == rank[y]; return par[y] = x; } }; UF<500000> uf; void dfs(int cur) { for (auto& e : E2[cur]) if (e.first != P[0][cur]) { D[e.first] = D[cur] + 1; P[0][e.first] = cur; ma[0][e.first] = e.second; dfs(e.first); } } int lca(int a, int b) { int ret = 0, i, aa = a, bb = b; if (D[aa] > D[bb]) swap(aa, bb); for (i = 19; i >= 0; i--) if (D[bb] - D[aa] >= 1 << i) bb = P[i][bb]; for (i = 19; i >= 0; i--) if (P[i][aa] != P[i][bb]) aa = P[i][aa], bb = P[i][bb]; return (aa == bb) ? aa : P[0][aa]; } void solve() { int i, j, k, l, r, x, y; string s; scanf("%d%d%d%d", &N, &M, &K, &Q); for (i = 0; i < (M); i++) { scanf("%d%d%d", &x, &y, &r); E[x - 1].push_back({y - 1, r}); E[y - 1].push_back({x - 1, r}); } priority_queue<pair<signed long long, int>> PQ; for (i = 0; i < (N); i++) { if (i < K) from[i] = i, PQ.push({0, i}); else dist[i] = 1LL << 60; } while (PQ.size()) { signed long long co = -PQ.top().first; int cur = PQ.top().second; PQ.pop(); if (dist[cur] != co) continue; for (auto& e : E[cur]) if (dist[e.first] > co + e.second) { dist[e.first] = co + e.second; from[e.first] = from[cur]; PQ.push({-dist[e.first], e.first}); } } vector<vector<signed long long>> Es; for (i = 0; i < (N); i++) for (auto& e : E[i]) if (from[e.first] > from[i]) { Es.push_back( {dist[i] + dist[e.first] + e.second, from[i], from[e.first]}); } sort((Es.begin()), (Es.end())); for (auto& e : Es) { if (uf[e[1]] != uf[e[2]]) { uf(e[1], e[2]); E2[e[1]].push_back({e[2], e[0]}); E2[e[2]].push_back({e[1], e[0]}); } } dfs(0); for (i = 0; i < (19); i++) for (x = 0; x < (K); x++) { P[i + 1][x] = P[i][P[i][x]]; ma[i + 1][x] = max(ma[i][x], ma[i][P[i][x]]); } while (Q--) { scanf("%d%d", &x, &y); x--; y--; int lc = lca(x, y); signed long long ret = 0; for (i = 18; i >= 0; i--) { if (D[x] - D[lc] >= 1 << i) ret = max(ret, ma[i][x]), x = P[i][x]; if (D[y] - D[lc] >= 1 << i) ret = max(ret, ma[i][y]), y = P[i][y]; } cout << ret << endl; } } int main(int argc, char** argv) { string s; int i; if (argc == 1) ios::sync_with_stdio(false), cin.tie(0); for (i = 0; i < (argc - 1); i++) s += argv[i + 1], s += '\n'; for (i = 0; i < (s.size()); i++) ungetc(s[s.size() - 1 - i], stdin); cout.tie(0); solve(); 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 compute = [&](int u, int v) { if (dep[u] > dep[v]) swap(u, v); int diff = dep[v] - dep[u]; LL res = 0; for (int i = 0; i < LOG; i++) { if (diff & (1 << i)) { res = max(res, best[v][i]); v = anc[v][i]; } } if (u == v) return res; for (int i = LOG - 1; i >= 0; i--) { int pu = anc[u][i], pv = anc[v][i]; if (pu != pv) { res = max(res, best[u][i]); res = max(res, best[v][i]); u = pu, v = pv; } } res = max(res, best[u][0]); res = max(res, best[v][0]); return res; }; while (q--) { int a, b; cin >> a >> b; cout << compute(a - 1, b - 1) << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> bool mmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template <class T> bool mmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } void yesno(bool c) { cout << (c ? "YES" : "NO") << '\n'; } void yes() { yesno(true); } void no() { yesno(false); } void imp() { cout << "-1" << '\n'; } const int inf = 0x3f3f3f3f; const long long infl = 0x3f3f3f3f3f3f3f3f; vector<int> va, vb; vector<int> aval, bval, wval; struct base_graph { int n, ecnt = 0; bool is_wei; vector<int> from, to; vector<long long> w; base_graph(int n, bool is_wei = false) : n(n), is_wei(is_wei) {} virtual int add(int a, int b, int ww = 0) = 0; int base_add(int a, int b, int ww = 0) { from.push_back(a); to.push_back(b); if (is_wei) w.push_back(ww); return ecnt++; } void readin(int m, bool add_rev = false, int offset = 1) { reserve(add_rev ? 2 * m : m); for (int i = 0; i < m; i++) { int a, b, ww = 0; cin >> a >> b; a -= offset; b -= offset; if (is_wei) cin >> ww; add(a, b, ww); if (add_rev) add(b, a, ww); } } void readin_tree(bool add_rev, int offset = 1) { int m = n - 1; reserve(add_rev ? 2 * m : m); for (int i = 2; i <= m; i++) { int p; cin >> p; int a = i - offset; add(a, p); if (add_rev) add(p, a); } } protected: void reserve(int m) { from.reserve(m); to.reserve(m); if (is_wei) w.reserve(m); } }; struct dir_graph : public base_graph { bool has_rev; vector<vector<pair<int, int>>> out, in; dir_graph(int n, bool has_rev = false, bool is_wei = false) : base_graph(n, is_wei), has_rev(has_rev), out(n), in(n) {} int add(int a, int b, int ww = 0) { int e = base_add(a, b, ww); out[a].push_back({e, b}); in[b].push_back({e, a}); return e; } void readin(int m, int offset = 1) { base_graph::readin(m, has_rev, offset); } void readin_tree(int offset = 1) { base_graph::readin_tree(has_rev, offset); } }; struct undir_graph : public base_graph { vector<vector<pair<int, int>>> edg; undir_graph(int n, bool is_wei = false) : base_graph(n, is_wei), edg(n) {} int add(int a, int b, int ww = 0) { if (b > a) swap(a, b); int e = base_add(a, b, ww); edg[a].push_back({e, b}); edg[b].push_back({e, a}); return e; } void readin(int m, int offset = 1) { base_graph::readin(m, false, offset); } void readin_tree(int offset = 1) { base_graph::readin_tree(false, offset); } }; struct dijkstra_vec { vector<long long> dist, par; dir_graph& g; dijkstra_vec(dir_graph& g) : dist(g.n, infl), par(g.n), g(g) {} void solve(const vector<int>& s) { using P = pair<long long, int>; priority_queue<P, vector<P>, greater<P>> q; auto upd = [&](int u, int p, long long d) { if (mmin(dist[u], d)) { par[u] = p; q.push({d, u}); } }; for (int ss : s) upd(ss, -1, 0); while (!q.empty()) { int u; long long d; tie(d, u) = q.top(); q.pop(); if (d > dist[u]) continue; for (auto [e, v] : g.out[u]) { long long newd = d + g.w[e]; upd(v, u, newd); } } } }; struct dsu { int _n; std::vector<int> parent_or_size; dsu() : _n(0) {} dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } }; struct query_dsu : dsu { unordered_map<int, unordered_map<int, vector<int>>> betw; undir_graph& g; query_dsu(int n, undir_graph& g) : dsu(n), g(g) { for (int e = 0; e < g.ecnt; e++) { int u = g.from[e], v = g.to[e]; betw[u][v].push_back(e); betw[v][u].push_back(e); } } vector<int>& getbetw(int a, int b) { int x = leader(a), y = leader(b); return betw[x][y]; } int merge(int a, int b) { int x = leader(a), y = leader(b); if (x == y) return x; if (dsu::merge(a, b) != x) swap(x, y); betw[x][y].clear(); betw[y][x].clear(); for (auto [e, v] : g.edg[y]) { v = leader(v); if (v == x) continue; g.edg[x].push_back({e, v}); betw[x][v].push_back(e); betw[v][x].push_back(e); } g.edg[y].clear(); return x; } }; void solve() { int n, m, k, q; cin >> n >> m >> k >> q; dir_graph g(n, true, true); g.readin(m); dijkstra_vec dij(g); vector<int> s; for (int i = 0; i < (k); i++) s.push_back(i); dij.solve(s); for (int e = 0; e < (g.ecnt); e++) { g.w[e] += dij.dist[g.from[e]] + dij.dist[g.to[e]]; } undir_graph qg(n); qg.readin(q); query_dsu d(n, qg); vector<pair<long long, long long>> ws; for (int e = 0; e < (g.ecnt); e++) { if (e % 2) ws.push_back(make_pair(g.w[e], e)); } sort((ws).begin(), (ws).end()); vector<long long> ans(q); for (pair<long long, long long> we : ws) { int u = g.from[we.second], v = g.to[we.second]; for (int qq : d.getbetw(u, v)) ans[qq] = we.first; d.merge(u, v); } for (int qq = 0; qq < (q); qq++) { cout << ans[qq] << '\n'; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int tc = 1; while (tc--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; mt19937 gen(time(0)); const int maxn = 100010; const int maxm = 300010; const long long INF = 1e18; struct E1 { int to, next, w; } edge[maxm << 1]; int head[maxn], tol; inline void Addedge(int u, int v, int w) { edge[tol].to = v; edge[tol].w = w; edge[tol].next = head[u]; head[u] = tol++; } long long dis[maxn]; bool vis[maxn]; priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > Q; void dijkstra(int k, int n) { fill(dis + k + 1, dis + n + 1, INF); for (int i = 1; i <= k; ++i) Q.push(make_pair(dis[i] = 0, i)); while (!Q.empty()) { int u = Q.top().second; Q.pop(); if (vis[u]) continue; vis[u] = 1; for (int i = head[u]; i != -1; i = edge[i].next) { int v = edge[i].to; if (!vis[v] && dis[v] > dis[u] + edge[i].w) { Q.push(make_pair(dis[v] = dis[u] + edge[i].w, v)); } } } return; } struct E2 { int u, v; long long w; bool operator<(const E2& P) const { return w < P.w; } } E[maxm]; long long ans[maxm]; vector<pair<int, int> > vec[maxn]; int fa[maxn]; inline int find(int x) { return fa[x] == x ? x : fa[x] = find(fa[x]); } inline void unite(int x, int y, long long w) { int fx = find(x), fy = find(y); if (fx == fy) return; if (vec[fx].size() > vec[fy].size()) swap(fx, fy); for (pair<int, int>& elem : vec[fx]) { if (ans[elem.second]) continue; if (find(elem.first) == fy) ans[elem.second] = w; else vec[fy].push_back(elem); } fa[fx] = fy; return; } int main() { memset(head, -1, sizeof(head)); int n, m, k, q, u, v, w; scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 0; i < m; ++i) { scanf("%d%d%d", &u, &v, &w); Addedge(u, v, w); Addedge(v, u, w); E[i] = E2{u, v, w}; } dijkstra(k, n); for (int i = 0; i < m; ++i) E[i].w += dis[E[i].u] + dis[E[i].v]; sort(E, E + m); for (int i = 1; i <= n; ++i) fa[i] = i; for (int i = 0; i < q; ++i) { scanf("%d%d", &u, &v); vec[u].emplace_back(make_pair(v, i)); vec[v].emplace_back(make_pair(u, i)); } for (int i = 0; i < m; ++i) unite(E[i].u, E[i].v, E[i].w); for (int i = 0; i < q; ++i) printf("%lld\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; int A[600006], B[600006], D[600006], F[100001], G[100001], a[100001], b[600006], c[600006], d[600006], e[100001], i, j, k, m, n, o[600006], q, s, t; long long C[600006], E[100001], f[100001], p[600006]; bool g[100001]; inline bool cmp(int u, int v) { return C[u] < C[v]; } inline int find(int u) { while (F[u]) u = F[u]; return u; } inline void merge(int u, int v, long long w) { if ((u = find(u)) == (v = find(v))) return; if (G[u] < G[v]) swap(u, v); G[F[v] = u] += G[v], E[v] = w; } inline long long query(int u, int v) { long long w = 0; while (u != v) G[u] < G[v] ? w = max(w, E[u]), u = F[u] : (w = max(w, E[v]), v = F[v]); return w; } inline void put(int v, long long w) { int u = ++s; while (1 < u && w < p[u >> 1]) o[u] = o[u >> 1], p[u] = p[u >> 1], u >>= 1; o[u] = v, p[u] = w; } inline int get() { int u = 1, v = 2, w = o[1]; for (o[1] = o[s], p[1] = p[s--]; v <= s; swap(o[u], o[v]), swap(p[u], p[v]), u = v, v = u << 1) { if (v < s && p[v | 1] < p[v]) v++; if (p[u] <= p[v]) return w; } return w; } inline void del() { while (s && g[o[1]]) get(); } int u, v, w; int main() { scanf("%d%d%d%d", &n, &m, &k, &q); for (i = 1; i <= k; G[i++] = 1) put(e[i] = i, f[i] = 0ll); for (; i <= n; G[i++] = 1) f[i] = 0x7fffffffffffffff; for (i = 1; i <= m; i++) scanf("%d%d%d", &u, &v, &w), b[i << 1] = a[u], c[a[u] = i << 1] = v, b[i << 1 | 1] = a[v], c[a[v] = i << 1 | 1] = u, d[i << 1] = d[i << 1 | 1] = w; while (del(), s) { for (i = a[u = get()], g[u] = 1; i; i = b[i]) if (f[u] + d[i] < f[c[i]]) e[c[i]] = e[u], put(c[i], f[c[i]] = f[u] + d[i]); else if (g[c[i]] && e[u] != e[c[i]]) A[++t] = e[u], B[t] = e[c[i]], C[D[t] = t] = f[u] + f[c[i]] + d[i]; } for (sort(D + 1, D + t + 1, cmp), i = 1; i <= t; i++) merge(A[D[i]], B[D[i]], C[D[i]]); for (i = 1; i <= q; i++) scanf("%d%d", &u, &v), printf("%lld\n", query(u, v)); return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-9; const long long oo = 0x3f3f3f3f3f3f3f3f; const int mod = 1000000007; struct disjoint_set { vector<int> ds; disjoint_set(int n) { ds = vector<int>(n, -1); } int root(int a) { return ds[a] < 0 ? a : ds[a] = root(ds[a]); } bool join(int a, int b) { a = root(a), b = root(b); if (a == b) return false; if (a > b) swap(a, b); ds[a] = b; return true; } }; void myassert(bool target) { while (!target) ; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n, m, k, q; cin >> n >> m >> k >> q; vector<vector<pair<int, long long>>> adj(n); for (int i = 0; i < m; ++i) { int u, v; long long c; cin >> u >> v >> c; --u; --v; adj[u].push_back({v, c}); adj[v].push_back({u, c}); } vector<pair<long long, int>> dist(n, {oo, -1}); priority_queue<pair<long long, int>> pq; for (int i = 0; i < k; ++i) { dist[i] = {0, i}; pq.push({0, i}); } while (!pq.empty()) { auto cur = pq.top(); pq.pop(); long long d = -cur.first; int u = cur.second; if (dist[u].first < d) continue; for (auto e : adj[u]) { long long c = e.second; int v = e.first; if (dist[v].first > d + c) { dist[v] = {d + c, dist[u].second}; pq.push({-dist[v].first, v}); } } } vector<pair<long long, pair<int, int>>> edges; for (int i = 0; i < n; ++i) { for (auto e : adj[i]) { int u = dist[i].second; int v = dist[e.first].second; if (u <= v) continue; edges.push_back({dist[i].first + dist[e.first].first + e.second, {u, v}}); auto x = edges.back(); } } sort(edges.begin(), edges.end()); disjoint_set ds(k); vector<vector<pair<int, long long>>> tree(k); for (auto e : edges) { if (ds.join(e.second.first, e.second.second)) { tree[e.second.first].push_back({e.second.second, e.first}); tree[e.second.second].push_back({e.second.first, e.first}); } } vector<int> h(k); vector<vector<pair<int, long long>>> parent(k); function<void(int, int, long long)> dfs = [&](int s, int p, long long cost) { if (p != -1) { parent[s].push_back({p, cost}); int i = 0; while (true) { int p = parent[s][i].first; if (parent[p].size() > i) { auto x = parent[p][i]; auto c = parent[s][i].second; parent[s].push_back({x.first, max(x.second, c)}); } else { break; } ++i; } } for (auto e : tree[s]) { if (e.first == p) continue; h[e.first] = h[s] + 1; dfs(e.first, s, e.second); } }; dfs(0, -1, 0); auto lca = [&](int a, int b) { if (h[a] > h[b]) swap(a, b); long long answer = 0; for (int i = 0; h[b] > h[a]; ++i) { if ((h[b] - h[a]) >> i & 1) { answer = max(answer, parent[b][i].second); b = parent[b][i].first; } } if (a == b) return answer; int it = parent[a].size() - 1; for (int i = it; i >= 0; --i) { if (parent[a].size() <= i) continue; if (parent[b].size() <= i) continue; int pa = parent[a][i].first; int pb = parent[b][i].first; if (pa != pb) { answer = max(answer, parent[a][i].second); answer = max(answer, parent[b][i].second); a = pa; b = pb; } } answer = max(answer, parent[a][0].second); answer = max(answer, parent[b][0].second); return answer; }; while (q-- > 0) { int u, v; cin >> u >> v; u--; v--; cout << lca(u, v) << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; long long d[100010]; vector<int> e[100010], ec[100010]; int u[300010], v[300010], w[300010], qu[300010], qv[300010], qk[300010], be[100010]; long long ans[300010]; int par[100010]; int find(int x) { return par[x] == x ? x : (par[x] = find(par[x])); } const int C = 340; vector<int> qd[C]; int main() { int n, m, k, q; scanf("%d%d%d%d", &n, &m, &k, &q); for (int i = 0; i < m; i++) { scanf("%d%d%d", &u[i], &v[i], &w[i]); --u[i]; --v[i]; e[u[i]].push_back(v[i]); ec[u[i]].push_back(w[i]); e[v[i]].push_back(u[i]); ec[v[i]].push_back(w[i]); } for (int i = 0; i < q; i++) { scanf("%d%d", &qu[i], &qv[i]); --qu[i], --qv[i]; } for (int i = 0; i < n; i++) { d[i] = 1ll << 60; } priority_queue<pair<long long, int> > qq; for (int i = 0; i < k; i++) { d[i] = 0; be[i] = i; par[i] = i; qq.push(make_pair(0, i)); } vector<pair<long long, pair<int, int> > > fvv; while (qq.size()) { long long co = -qq.top().first; int tv = qq.top().second; qq.pop(); if (d[tv] != co) continue; for (int i = 0; i < e[tv].size(); i++) { int to = e[tv][i]; if (d[to] > co + ec[tv][i]) { d[to] = co + ec[tv][i]; be[to] = be[tv]; qq.push(make_pair(-co - ec[tv][i], to)); } } } for (int i = 0; i < m; i++) { if (be[u[i]] != be[v[i]]) { fvv.push_back(pair<long long, pair<int, int> >( d[u[i]] + d[v[i]] + w[i], make_pair(be[u[i]], be[v[i]]))); } } sort(fvv.begin(), fvv.end()); vector<long long> f; vector<vector<pair<int, int> > > fv; for (int i = 0; i < fvv.size(); i++) { if (!f.size() || f.back() != fvv[i].first) { if (fv.size() && !fv.back().size()) { f.pop_back(); fv.pop_back(); } f.push_back(fvv[i].first); fv.push_back(vector<pair<int, int> >()); } int su = find(fvv[i].second.first), sv = find(fvv[i].second.second); if (su == sv) continue; fv.back().push_back(fvv[i].second); par[su] = sv; } for (int i = 0; i < k; i++) { par[i] = i; } int la = 0; for (int i = 0; i <= f.size(); i++) { if (i && i % C == 0) { for (int j = 0; j < q; j++) { if (qk[j]) continue; if (find(qu[j]) == find(qv[j])) { qd[i / C - 1].push_back(j); qk[j] = 1; } } la = i / C; } if (i == f.size()) continue; for (int j = 0; j < fv[i].size(); j++) { int tu = fv[i][j].first, tv = fv[i][j].second; tu = find(tu); tv = find(tv); par[tu] = tv; } } for (int i = 0; i < q; i++) { if (!qk[i]) qd[la].push_back(i); } for (int i = 0; i < k; i++) { par[i] = i; } for (int i = 0; i < f.size(); i++) { for (int j = 0; j < fv[i].size(); j++) { int tu = fv[i][j].first, tv = fv[i][j].second; tu = find(tu); tv = find(tv); par[tu] = tv; } for (int j = 0; j < qd[i / C].size(); j++) { int z = qd[i / C][j]; if (ans[z]) continue; if (find(qu[z]) == find(qv[z])) { ans[z] = f[i]; } } } for (int i = 0; i < q; i++) { printf("%I64d\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; inline long long read() { long long x = 0, f = 1; char ch = getchar(); while (!isdigit(ch)) { if (ch == '-') f = -1; char ch = getchar(); } while (isdigit(ch)) { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return x * f; } struct edge { int to, nxt, from; long long dis; } g[1010101]; int head[1010101], tot, n, m, K, Q; inline void made(int from, int to, long long dis) { g[++tot].to = to; g[tot].nxt = head[from]; head[from] = tot; g[tot].dis = dis; g[tot].from = from; } int F[1010101], sz[1010101]; long long dis[1010101]; int find(int u) { if (F[u] != u) F[u] = find(F[u]); return F[u]; } struct que { int x, y; int id; } q[1010101]; long long ans[1010101]; vector<que> G[1010101]; inline bool cmp(edge a, edge b) { return a.dis < b.dis; } long long NOW; bool vis[1010101]; int main() { n = read(), m = read(), K = read(), Q = read(); for (int i = 1; i <= m; i++) { int x = read(), y = read(); long long z = read(); made(x, y, z); made(y, x, z); } for (int i = 1; i <= n; i++) { F[i] = i; sz[i] = 1; } priority_queue<pair<long long, int> > dl; memset(dis, 0x3f, sizeof dis); while (!dl.empty()) dl.pop(); for (int i = 1; i <= K; i++) dis[i] = 0, dl.push(make_pair(0, i)); while (!dl.empty()) { int u = dl.top().second; dl.pop(); if (vis[u]) continue; vis[u] = 1; for (int i = head[u]; i; i = g[i].nxt) { int v = g[i].to; if (dis[v] > dis[u] + g[i].dis) { dis[v] = dis[u] + g[i].dis; if (!vis[v]) { dl.push(make_pair(-dis[v], v)); } } } } for (int i = 1; i <= tot; i++) { g[i].dis = g[i].dis + dis[g[i].from] + dis[g[i].to]; } sort(g + 1, g + 1 + tot, cmp); for (int i = 1; i <= Q; i++) { q[i].id = i; q[i].x = read(), q[i].y = read(); G[q[i].x].push_back(q[i]); G[q[i].y].push_back(q[i]); } for (int i = 1; i <= tot; i++) { int u = g[i].from, v = g[i].to; NOW = g[i].dis; int fu = find(u), fv = find(v); if (fu != fv) { if (sz[fu] < sz[fv]) { swap(fu, fv); swap(u, v); } sz[fu] += sz[fv]; F[fv] = fu; for (auto now : G[fv]) { if (find(now.x) == find(now.y)) { if (!ans[now.id]) { ans[now.id] = NOW; } } else { G[fu].push_back(now); } } } } for (int i = 1; i <= Q; i++) { cout << ans[i] << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MAXN = 6e5 + 5; long long n, m, k, T, w, x, y, t, tot, head[MAXN], ver[MAXN], edge[MAXN], Next[MAXN]; long long f[MAXN][21], maxx[MAXN][21]; pair<long long, long long> dis[MAXN]; long long d[MAXN]; bool v[MAXN]; void addedge(long long x, long long y, long long z) { ver[++tot] = y, edge[tot] = z, Next[tot] = head[x], head[x] = tot; } struct node { long long x, y, z; } a[MAXN], b[MAXN]; priority_queue<pair<long long, long long> > q; vector<pair<long long, long long> > g[MAXN]; void dij() { memset(v, 0, sizeof(v)); for (long long i = 1; i <= n; i++) { if (i <= k) dis[i].first = 0, dis[i].second = i, q.push(make_pair(0, i)); else dis[i].first = 1ll << 62, dis[i].second = 0; } while (q.size()) { long long x = q.top().second; q.pop(); if (v[x]) continue; v[x] = 1; for (long long i = head[x]; i; i = Next[i]) { long long y = ver[i], z = edge[i]; if (dis[y].first > dis[x].first + z) { dis[y].first = dis[x].first + z; dis[y].second = dis[x].second; q.push(make_pair(-dis[y].first, y)); } } } } bool cmp(node a, node b) { return a.z < b.z; } long long pre[MAXN]; long long Find(long long x) { return x == pre[x] ? x : pre[x] = Find(pre[x]); } long long lca(long long x, long long y) { if (d[x] > d[y]) swap(x, y); long long ans = 0; for (long long i = t; i >= 0; i--) { if (d[f[y][i]] >= d[x]) ans = max(ans, maxx[y][i]), y = f[y][i]; } if (x == y) return ans; for (long long i = t; i >= 0; i--) { if (f[x][i] != f[y][i]) ans = max(ans, max(maxx[x][i], maxx[y][i])), x = f[x][i], y = f[y][i]; } ans = max(ans, maxx[x][0]); ans = max(ans, maxx[y][0]); return ans; } int main() { ios::sync_with_stdio(false); cin.tie(0); while (cin >> n >> m >> k >> T) { t = (long long)(log(n) / log(2)) + 1; for (long long i = 1; i <= k; i++) g[i].clear(), pre[i] = i; memset(head, 0, sizeof(head)); tot = 0; long long pos = 0; for (long long i = 1; i <= m; i++) { cin >> x >> y >> w; addedge(x, y, w); addedge(y, x, w); a[++pos].x = x, a[pos].y = y, a[pos].z = w; a[++pos].x = y, a[pos].y = x, a[pos].z = w; } dij(); pos = 0; for (long long i = 1; i <= 2 * m; i++) { if (dis[a[i].x].second != dis[a[i].y].second) { b[++pos].x = dis[a[i].x].second; b[pos].y = dis[a[i].y].second; b[pos].z = a[i].z + dis[a[i].x].first + dis[a[i].y].first; } } sort(b + 1, b + pos + 1, cmp); for (long long i = 1; i <= pos; i++) { long long xx = Find(b[i].x); long long yy = Find(b[i].y); if (xx == yy) continue; pre[xx] = yy; g[b[i].x].push_back(make_pair(b[i].y, b[i].z)); g[b[i].y].push_back(make_pair(b[i].x, b[i].z)); } queue<long long> Q; memset(d, 0, sizeof(d)); Q.push(1); d[1] = 1; while (Q.size()) { long long x = Q.front(); Q.pop(); long long len = g[x].size(); for (long long i = 0; i <= len - 1; i++) { long long y = g[x][i].first; if (d[y]) continue; d[y] = d[x] + 1; f[y][0] = x; maxx[y][0] = g[x][i].second; for (long long j = 1; j <= t; j++) { f[y][j] = f[f[y][j - 1]][j - 1]; maxx[y][j] = max(maxx[y][j - 1], maxx[f[y][j - 1]][j - 1]); } Q.push(y); } } while (T--) { cin >> x >> y; cout << lca(x, y) << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; void dijk(); void build(); void dfs(int u); long long getv(int u, int v); bool add(int u, int v, long long w); int n, m, k, dpth[100002], r[100002]; pair<int, long long> pr[17][100002]; long long d[100002]; vector<pair<int, long long> > ad[100002]; pair<long long, pair<int, int> > edge[100002 * 6]; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int i, q; cin >> n >> m >> k >> q; for (i = 1; i <= m; ++i) { int u, v, w; cin >> u >> v >> w; ad[u].push_back({v, w}); ad[v].push_back({u, w}); } dijk(); build(); dfs(1); for (i = 1; i <= q; ++i) { int u, v; cin >> u >> v; cout << getv(u, v) << '\n'; } return 0; } long long getv(int u, int v) { if (dpth[u] < dpth[v]) swap(u, v); int cv = dpth[u] - dpth[v], i; long long rev = 0; for (i = 0; i < 17; ++i) if ((cv >> i) & 1) { rev = max(rev, pr[i][u].second); u = pr[i][u].first; } for (i = 16; i >= 0; --i) if (pr[i][u].first != pr[i][v].first) { rev = max(rev, max(pr[i][u].second, pr[i][v].second)); u = pr[i][u].first; v = pr[i][v].first; } if (u == v) return rev; return max(rev, max(pr[0][u].second, pr[0][v].second)); } void dfs(int u) { int i; for (auto v : ad[u]) { if (v.first == pr[0][u].first) continue; pr[0][v.first] = {u, v.second}; dpth[v.first] = dpth[u] + 1; for (i = 1; i < 17; ++i) { pr[i][v.first].first = pr[i - 1][pr[i - 1][v.first].first].first; pr[i][v.first].second = max(pr[i - 1][v.first].second, pr[i - 1][pr[i - 1][v.first].first].second); } dfs(v.first); } } int getr(int x) { return r[x] ? r[x] = getr(r[x]) : x; } bool add(int u, int v, long long w) { int ru = getr(u), rv = getr(v); if (ru == rv) return 0; r[ru] = rv; ad[u].push_back({v, w}); ad[v].push_back({u, w}); return 1; } void build() { int i; m = 0; for (i = 1; i <= n; ++i) { for (auto j : ad[i]) edge[++m] = {d[i] + d[j.first] + j.second, {i, j.first}}; ad[i].clear(); } sort(edge + 1, edge + m + 1); for (i = 1; i <= m; ++i) add(edge[i].second.first, edge[i].second.second, edge[i].first); } void dijk() { int i, u; long long cv; priority_queue<pair<long long, int> > pq; for (i = 1; i <= k; ++i) { pq.push({0, i}); d[i] = 0; } for (; i <= n; ++i) d[i] = 1e18; while (pq.size()) { u = pq.top().second; cv = -pq.top().first; pq.pop(); if (cv > d[u]) continue; for (auto v : ad[u]) if (d[v.first] > cv + v.second) { d[v.first] = cv + v.second; pq.push({-d[v.first], v.first}); } } }
#include <bits/stdc++.h> using namespace std; long long n, m, k, Q, d[100005], tr[100005], oo, f[100005][20], gt[100005][20], h[100005], u, v, w, ru, rv, lab[100005]; bool kt[100005]; pair<long long, pair<int, int> > ed[300005]; vector<pair<long long, int> > a[100005], ke[100005]; priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > q; void ditcha() { for (int i = 1; i <= n; ++i) if (i <= k) { q.push({0, i}); tr[i] = i; } else d[i] = oo; memset(kt, 0, sizeof(kt)); while (!q.empty()) { int u = q.top().second; q.pop(); if (kt[u]) continue; kt[u] = true; for (int i = 0; i < a[u].size(); ++i) { int v = a[u][i].second; long long w = a[u][i].first; if (d[v] > d[u] + w) { d[v] = d[u] + w; tr[v] = tr[u]; q.push({d[v], v}); } } } } void dfs(int u, int pa, long long w) { h[u] = h[pa] + 1; f[u][0] = pa; gt[u][0] = w; for (int i = 0; i < ke[u].size(); ++i) { int v = ke[u][i].second; long long w = ke[u][i].first; if (v == pa) continue; dfs(v, u, w); } } void khoitao() { for (int K = 1; (1 << K) <= k; ++K) for (int i = 1; i <= k; ++i) if (f[i][K - 1] != -1) { f[i][K] = f[f[i][K - 1]][K - 1]; gt[i][K] = max(gt[i][K - 1], gt[f[i][K - 1]][K - 1]); } } long long lca(int u, int v) { if (h[u] < h[v]) swap(u, v); int log = trunc(log2(h[u])) + 1; long long kq = 0; for (int i = log; i >= 0; --i) if (f[u][i] != -1 && h[f[u][i]] >= h[v]) { kq = max(kq, gt[u][i]); u = f[u][i]; } if (u == v) return kq; for (int i = log; i >= 0; --i) if (f[u][i] != f[v][i]) { kq = max(kq, max(gt[u][i], gt[v][i])); u = f[u][i]; v = f[v][i]; } return max(kq, max(gt[u][0], gt[v][0])); } int phin(int u) { return lab[u] < 0 ? u : lab[u] = phin(lab[u]); } void uni(int u, int v) { if (lab[u] > lab[v]) swap(u, v); lab[u] += lab[v]; lab[v] = u; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> Q; oo = 1e18; for (int i = 1; i <= m; ++i) { cin >> u >> v >> w; a[u].push_back({w, v}); a[v].push_back({w, u}); ed[i] = {w, {u, v}}; } ditcha(); for (int i = 1; i <= m; ++i) { u = ed[i].second.first; v = ed[i].second.second; w = ed[i].first; ed[i] = {d[u] + d[v] + w, {tr[u], tr[v]}}; } sort(ed + 1, ed + m + 1); memset(lab, -1, sizeof(lab)); for (int i = 1; i <= m; ++i) { u = ed[i].second.first; v = ed[i].second.second; w = ed[i].first; ru = phin(u); rv = phin(v); if (ru != rv) { uni(ru, rv); ke[u].push_back({w, v}); ke[v].push_back({w, u}); } } memset(f, -1, sizeof(f)); dfs(1, 1, 0); f[1][0] = -1; khoitao(); for (int i = 1; i <= Q; ++i) { cin >> u >> v; cout << lca(u, v) << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; vector<pair<long long, long long> > v[300010], w[300010]; long long tt[300010], lg[300010], lvl[300010]; priority_queue<pair<long long, long long> > h; long long dist[300010]; pair<long long, long long> fth[20][300010]; pair<long long, pair<long long, long long> > mch[300010]; long long n; long long rad(long long x) { while (tt[x] > 0) x = tt[x]; return x; } void dfs(long long nod, long long tata, long long cost) { long long i; fth[0][nod] = make_pair(tata, cost); for (i = 0; i < w[nod].size(); i++) { if (w[nod][i].first != tata) { lvl[w[nod][i].first] = 1 + lvl[nod]; dfs(w[nod][i].first, nod, w[nod][i].second); } } } long long path(long long x, long long y) { long long dif, p2; long long sol; sol = 0; if (lvl[x] < lvl[y]) swap(x, y); dif = lvl[x] - lvl[y]; while (dif && x != 0) { sol = max(sol, fth[lg[dif]][x].second); x = fth[lg[dif]][x].first; dif = dif - (1 << lg[dif]); } if (x == y) { return sol; } for (p2 = lg[n]; p2 >= 0; p2--) { if (fth[p2][x].first != fth[p2][y].first) { sol = max(sol, max(fth[p2][x].second, fth[p2][y].second)); x = fth[p2][x].first; y = fth[p2][y].first; } } p2 = 0; sol = max(sol, max(fth[p2][x].second, fth[p2][y].second)); return sol; } int main() { FILE *fin = stdin; FILE *fout = stdout; long long m, k, q, x, y, i, nod, vecin, rx, ry, elem, j; long long z, cost, c; fscanf(fin, "%lld%lld%lld%lld", &n, &m, &k, &q); for (i = 1; i <= m; i++) { fscanf(fin, "%lld%lld%lld", &x, &y, &z); v[x].push_back(make_pair(y, z)); v[y].push_back(make_pair(x, z)); } for (i = 2; i <= n; i++) { lg[i] = lg[i / 2] + 1; } for (i = 1; i <= n; i++) { dist[i] = 2000000000000000000; tt[i] = -1; } for (i = 1; i <= k; i++) { h.push(make_pair(0, i)); dist[i] = 0; } while (!h.empty()) { cost = -h.top().first; nod = h.top().second; h.pop(); if (dist[nod] != cost) { continue; } for (i = 0; i < v[nod].size(); i++) { vecin = v[nod][i].first; c = v[nod][i].second; if (dist[vecin] > dist[nod] + c) { dist[vecin] = dist[nod] + c; h.push(make_pair(-dist[vecin], vecin)); } } } elem = 0; for (i = 1; i <= n; i++) { for (j = 0; j < v[i].size(); j++) { v[i][j].second += dist[i] + dist[v[i][j].first]; if (v[i][j].first > i) { elem++; mch[elem].first = v[i][j].second; mch[elem].second.first = i; mch[elem].second.second = v[i][j].first; } } } sort(mch + 1, mch + elem + 1); for (i = 1; i <= elem; i++) { x = mch[i].second.first; y = mch[i].second.second; rx = rad(x); ry = rad(y); if (rx != ry) { w[x].push_back(make_pair(y, mch[i].first)); w[y].push_back(make_pair(x, mch[i].first)); if (tt[rx] < tt[ry]) { tt[rx] += tt[ry]; tt[ry] = rx; } else { tt[ry] += tt[rx]; tt[rx] = ry; } } } dfs(1, 0, 0); k = 1; while ((1 << k) <= n) { for (i = 1; i <= n; i++) { fth[k][i].first = fth[k - 1][fth[k - 1][i].first].first; fth[k][i].second = max(fth[k - 1][i].second, fth[k - 1][fth[k - 1][i].first].second); } k++; } for (; q; q--) { fscanf(fin, "%lld%lld", &x, &y); fprintf(fout, "%lld\n", path(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T1, typename T2> inline T1 max(T1 a, T2 b) { return a < b ? b : a; } template <typename T1, typename T2> inline T1 min(T1 a, T2 b) { return a < b ? a : b; } const char lf = '\n'; namespace ae86 { const int bufl = 1 << 15; char buf[bufl], *s = buf, *t = buf; inline int fetch() { if (s == t) { t = (s = buf) + fread(buf, 1, bufl, stdin); if (s == t) return EOF; } return *s++; } inline int ty() { int a = 0; int b = 1, c = fetch(); while (!isdigit(c)) b ^= c == '-', c = fetch(); while (isdigit(c)) a = a * 10 + c - 48, c = fetch(); return b ? a : -a; } } // namespace ae86 using ae86::ty; const int _ = 100007, __ = 300007, _n = _ << 1, lglg = 19; vector<pair<int, int>> e[_]; inline void adde(int a, int b, int c) { e[a].emplace_back(b, c); } inline void addde(int a, int b, int c) { adde(a, b, c), adde(b, a, c); } int n, m, chx, qn; long long dis[_], via[_]; int ed[_]; struct cxk { int a, b; long long v; cxk(int a_ = 0, int b_ = 0, long long v_ = 0) { a = a_, b = b_, v = v_; } friend int operator<(cxk a, cxk b) { return a.v < b.v; } } es[__]; int ecnts = 0; void dijks() { priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> q; memset(dis, 63, sizeof(dis)), memset(ed, 0, sizeof(ed)); for (int i = 1; i <= chx; i++) dis[i] = 0, via[i] = i, q.emplace(dis[i], i); while (!q.empty()) { int a = q.top().second; q.pop(); if (ed[a]) continue; ed[a] = 1; for (auto [b, c] : e[a]) { if (dis[b] <= dis[a] + c) continue; dis[b] = dis[a] + c, via[b] = via[a]; if (!ed[b]) q.emplace(dis[b], b); } } for (int i = 1; i <= n; i++) for (auto [b, c] : e[i]) if (b > i && via[i] != via[b]) es[++ecnts] = cxk(via[i], via[b], dis[i] + dis[b] + c); } int bfa[_n] = {0}; int findbfa(int x) { return bfa[x] == x ? x : bfa[x] = findbfa(bfa[x]); } int pfa[_n][lglg + 1] = {0}, pdep[_n] = {0}, pcnt = 0; long long pva[_n] = {0}; int lca(int a, int b) { if (pdep[a] < pdep[b]) swap(a, b); for (int i = lglg; i >= 0; i--) if (pdep[pfa[a][i]] >= pdep[b]) a = pfa[a][i]; if (a == b) return a; for (int i = lglg; i >= 0; i--) if (pfa[a][i] != pfa[b][i]) a = pfa[a][i], b = pfa[b][i]; if (a != b) a = pfa[a][0], b = pfa[b][0]; return a; } void kuro() { sort(es + 1, es + ecnts + 1); pcnt = n; for (int i = 1; i <= pcnt; i++) bfa[i] = i; for (int i = 1; i <= ecnts; i++) { auto [a, b, c] = es[i]; int aa = findbfa(a), bb = findbfa(b); if (aa == bb) continue; pcnt++, bfa[pcnt] = bfa[aa] = bfa[bb] = pcnt, pva[pcnt] = c, pfa[aa][0] = pfa[bb][0] = pcnt; } for (int i = pcnt; i >= 1; i--) pdep[i] = pdep[pfa[i][0]] + 1; for (int i = 1; i <= lglg; i++) for (int j = 1; j <= pcnt; j++) pfa[j][i] = pfa[pfa[j][i - 1]][i - 1]; } int main() { ios::sync_with_stdio(0), cout.tie(nullptr); n = ty(), m = ty(), chx = ty(), qn = ty(); for (int i = 1, a, b, c; i <= m; i++) a = ty(), b = ty(), c = ty(), addde(a, b, c); dijks(), kuro(); for (int qq = 1; qq <= qn; qq++) { int a = ty(), b = ty(); cout << pva[lca(a, b)] << lf; } return 0; }
#include <bits/stdc++.h> using namespace std; const double pai = acos(-1); const double eps = 1e-8; const long long mod = 1e9 + 7; const int MXN = 2e5; const int MXLOG = 20; vector<pair<long long, int> > g[MXN], G[MXN]; long long d[MXN]; int dfg[MXN], sour[MXN]; int fa[MXN]; int found(int x) { if (x == fa[x]) return x; return fa[x] = found(fa[x]); } int bei[MXN][MXLOG], de[MXN]; long long val[MXN][MXLOG]; void dfs(int u, int p) { for (auto i : G[u]) { if (i.second != p) { de[i.second] = de[u] + 1; bei[i.second][0] = u; val[i.second][0] = i.first; dfs(i.second, u); } } } void initLCA(int nn) { bei[1][0] = -1; de[1] = 0; dfs(1, -1); for (int k = 0; k < MXLOG - 1; k++) { for (int v = 1; v <= nn; v++) { if (bei[v][k] < 0) bei[v][k + 1] = -1; else bei[v][k + 1] = bei[bei[v][k]][k], val[v][k + 1] = max(val[v][k], val[bei[v][k]][k]); } } } long long query(int u, int v) { if (de[u] > de[v]) swap(u, v); long long re = -1; for (int k = 0; k < MXLOG; k++) { if ((de[v] - de[u]) >> k & 1) re = max(re, val[v][k]), v = bei[v][k]; } if (u == v) return re; for (int k = MXLOG - 1; k >= 0; k--) { if (bei[u][k] != bei[v][k]) { re = max(re, val[v][k]), re = max(re, val[u][k]); u = bei[u][k], v = bei[v][k]; } } re = max(re, val[u][0]); re = max(re, val[v][0]); return re; } int main() { int n, m, k, q; cin >> n >> m >> k >> q; for (int i = 1; i <= m; i++) { int su, sv, sw; scanf("%d%d%d", &su, &sv, &sw); g[su].push_back(make_pair(sw, sv)); g[sv].push_back(make_pair(sw, su)); } priority_queue<pair<long long, int> > pq; for (int i = 1; i <= n; i++) d[i] = LLONG_MAX / 2; for (int i = 1; i <= k; i++) pq.push(make_pair(0, i)), d[i] = 0, sour[i] = i; while (!pq.empty()) { auto now = pq.top(); pq.pop(); int u = now.second; if (dfg[u]) continue; dfg[u] = 1; for (auto ed : g[u]) { long long dis = ed.first + d[u]; if (dis > d[ed.second]) continue; d[ed.second] = dis; sour[ed.second] = sour[u]; pq.push(make_pair(-dis, ed.second)); } } vector<tuple<long long, int, int> > krs; for (int i = 1; i <= n; i++) fa[i] = i; for (int i = 1; i <= n; i++) { for (auto ed : g[i]) { if (sour[i] != sour[ed.second]) krs.push_back(make_tuple(ed.first + d[i] + d[ed.second], sour[i], sour[ed.second])); } } sort(krs.begin(), krs.end()); for (auto i : krs) { int xx = found(get<1>(i)); int yy = found(get<2>(i)); if (xx == yy) continue; fa[xx] = fa[yy]; G[get<1>(i)].push_back(make_pair(get<0>(i), get<2>(i))); G[get<2>(i)].push_back(make_pair(get<0>(i), get<1>(i))); } initLCA(n); while (q--) { int sa, sb; scanf("%d%d", &sa, &sb); cout << query(sa, sb) << '\n'; } return 0; }
#include <bits/stdc++.h> const int MAX_SIZE = 112345; const int MAX_SIZE_LOG = 20; int N, M, K, Q; std::vector<std::pair<int, int>> g[MAX_SIZE]; std::pair<long long int, int> dist[MAX_SIZE]; int parent[MAX_SIZE]; std::vector<std::pair<long long int, std::pair<int, int>>> edges; std::vector<std::pair<int, long long int>> tree[MAX_SIZE]; int parent_lca[MAX_SIZE][MAX_SIZE_LOG]; long long int mx_lca[MAX_SIZE][MAX_SIZE_LOG]; int depth[MAX_SIZE]; void UNION(const int &x, const int &y) { parent[x] = parent[y]; } int FIND(const int &x) { if (x != parent[x]) { parent[x] = FIND(parent[x]); } return parent[x]; } void build_dijkstra() { for (int i = 0; i < N; i += 1) { dist[i] = {LLONG_MAX, -1}; } std::priority_queue<std::pair<long long int, int>> pq; for (int i = 0; i < K; i += 1) { dist[i] = {0, i}; pq.push({-dist[i].first, i}); } while (!pq.empty()) { const long long int cost = -pq.top().first; const int i = pq.top().second; pq.pop(); if (cost > dist[i].first) { continue; } for (const auto &j : g[i]) { const long long int nxt = cost + j.second; if (nxt < dist[j.first].first) { dist[j.first] = {nxt, dist[i].second}; pq.push({-nxt, j.first}); } } } } void build_tree() { for (int i = 0; i < N; i += 1) { for (const auto &j : g[i]) { edges.push_back({dist[i].first + dist[j.first].first + j.second, {dist[i].second, dist[j.first].second}}); } } std::sort(edges.begin(), edges.end()); for (int i = 0; i < N; i += 1) { parent[i] = i; } for (const auto &edge : edges) { const int &x = FIND(edge.second.first); const int &y = FIND(edge.second.second); if (x != y) { UNION(x, y); if (edge.second.first >= K or edge.second.second >= K) { continue; } tree[edge.second.first].push_back({edge.second.second, edge.first}); tree[edge.second.second].push_back({edge.second.first, edge.first}); } } } void dfs(const int &i, const int &p) { depth[i] = depth[p] + 1; parent_lca[i][0] = p; for (int j = 1; j < MAX_SIZE_LOG; j += 1) { parent_lca[i][j] = parent_lca[parent_lca[i][j - 1]][j - 1]; mx_lca[i][j] = std::max(mx_lca[i][j - 1], mx_lca[parent_lca[i][j - 1]][j - 1]); } for (const auto &j : tree[i]) { if (j.first == p) { continue; } mx_lca[j.first][0] = j.second; dfs(j.first, i); } } int query_lca(const int &x, const int &y) { int a = x; int b = y; if (depth[a] < depth[b]) { std::swap(a, b); } const int dist = depth[a] - depth[b]; for (int j = 0; j < MAX_SIZE_LOG; j += 1) { if (dist & (1 << j)) { a = parent_lca[a][j]; } } if (a == b) { return a; } for (int j = MAX_SIZE_LOG - 1; j >= 0; j -= 1) { if (parent_lca[a][j] != parent_lca[b][j]) { a = parent_lca[a][j]; b = parent_lca[b][j]; } } return parent_lca[a][0]; } long long int query(const int &vertex, const int &lca) { long long int ans = LLONG_MIN; const int dist = depth[vertex] - depth[lca]; for (int i = 0, x = vertex; i < MAX_SIZE_LOG; i += 1) { if (dist & (1 << i)) { ans = std::max(ans, mx_lca[x][i]); x = parent_lca[x][i]; } } return ans; } int main() { std::ios_base::sync_with_stdio(0); std::cin.tie(0); std::cout.tie(0); std::cin >> N >> M >> K >> Q; for (int i = 0; i < M; i += 1) { int x, y, w; std::cin >> x >> y >> w; x -= 1; y -= 1; g[x].push_back({y, w}); g[y].push_back({x, w}); } build_dijkstra(); build_tree(); dfs(0, 0); for (int i = 0; i < Q; i += 1) { int x, y; std::cin >> x >> y; x -= 1; y -= 1; const int lca = query_lca(x, y); std::cout << std::max(query(x, lca), query(y, lca)) << std::endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MAXN = 3e5 + 7; const long long INF = 1e18 + 7; vector<pair<long long, long long>> adj[MAXN]; vector<long long> v[MAXN]; long long p[MAXN], sz[MAXN], mp[2 * MAXN]; long long ans[MAXN]; long long n, m, k, q; struct Edge { long long u, v, w; }; vector<long long> djk() { vector<long long> dist(n); priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> pq; for (long long i = 0; i < n; i++) { if (i < k) { pq.push(pair<long long, long long>(0, i)); dist[i] = 0; } else { dist[i] = INF; } } while (!pq.empty()) { long long d = pq.top().first, u = pq.top().second; pq.pop(); if (dist[u] < d) continue; for (pair<long long, long long> x : adj[u]) { long long v = x.first, w = x.second; if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; pq.push(pair<long long, long long>(dist[v], v)); } } } return dist; } long long find(long long a) { if (p[a] == a) return a; return p[a] = find(p[a]); } void merge(long long a, long long b, long long w) { a = find(a); b = find(b); if (a == b) return; if (sz[a] > sz[b]) swap(a, b); for (long long tk1 : v[a]) { long long tk2 = tk1 ^ 1; if (find(mp[tk2]) == b) { long long idx = tk1 / 2; ans[idx] = w; } v[b].push_back(tk1); } v[a].resize(0); sz[b] += sz[a]; p[a] = b; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); cin >> n >> m >> k >> q; for (long long i = 0; i < MAXN; i++) { p[i] = i; sz[i] = 1; } vector<Edge> edges; for (long long i = 0; i < m; i++) { long long u, v, w; cin >> u >> v >> w; u--; v--; adj[u].push_back(pair<long long, long long>(v, w)); adj[v].push_back(pair<long long, long long>(u, w)); edges.push_back({u, v, w}); } vector<long long> dist = djk(); for (long long i = 0; i < q; i++) { long long a, b; cin >> a >> b; a--; b--; long long tk1 = 2 * i, tk2 = tk1 + 1; mp[tk1] = a; mp[tk2] = b; v[a].push_back(tk1); v[b].push_back(tk2); } for (Edge &e : edges) { e.w += dist[e.u] + dist[e.v]; } sort(edges.begin(), edges.end(), [](Edge a, Edge b) { return a.w < b.w; }); for (long long i = 0; i < m; i++) { merge(edges[i].u, edges[i].v, edges[i].w); } for (long long i = 0; i < q; i++) { cout << ans[i] << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 123456; const int LN = 19; const long long INF = 1LL << 60LL; int n, m, k, q; int parent[N]; int depth[N]; int anc[LN][N]; long long dp[LN][N]; long long dist[N]; vector<pair<int, int>> adj[N]; vector<tuple<long long, int, int>> edges; vector<pair<int, long long>> tree[N]; void dijkstra() { priority_queue<pair<long long, int>> states; for (int i = 1; i <= n; i++) { dist[i] = INF; } for (int i = 1; i <= k; i++) { dist[i] = 0; states.push({-dist[i], i}); } while (!states.empty()) { auto [cur_dist, u] = states.top(); cur_dist = -cur_dist; states.pop(); if (cur_dist > dist[u]) continue; for (auto [v, w] : adj[u]) { if (cur_dist + w < dist[v]) { dist[v] = cur_dist + w; states.push({-dist[v], v}); } } } } inline int root(int x) { if (parent[x] == x) { return x; } else { return parent[x] = root(parent[x]); } } inline bool join(int u, int v) { u = root(u); v = root(v); if (u == v) return false; parent[v] = u; return true; } void dfs(int u, int p, long long pe = -1) { anc[0][u] = p; dp[0][u] = pe; for (int i = 1; i < LN; i++) { anc[i][u] = anc[i - 1][anc[i - 1][u]]; dp[i][u] = max(dp[i - 1][u], dp[i - 1][anc[i - 1][u]]); } for (auto [v, w] : tree[u]) { if (v != p) { depth[v] = depth[u] + 1; dfs(v, u, w); } } } inline long long solve(int u, int v) { if (depth[u] < depth[v]) swap(u, v); long long ans = 0; for (int i = LN - 1; i >= 0; i--) { if (depth[u] - (1 << i) >= depth[v]) { ans = max(ans, dp[i][u]); u = anc[i][u]; } } if (u == v) return ans; for (int i = LN - 1; i >= 0; i--) { if (anc[i][u] != anc[i][v]) { ans = max(ans, max(dp[i][u], dp[i][v])); u = anc[i][u]; v = anc[i][v]; } } return max(ans, max(dp[0][u], dp[0][v])); } int main() { ios ::sync_with_stdio(false); cin >> n >> m >> k >> q; for (int i = 1; i <= m; i++) { int u, v, w; cin >> u >> v >> w; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } dijkstra(); for (int i = 1; i <= n; i++) { parent[i] = i; for (auto [j, w] : adj[i]) { if (i > j) continue; edges.push_back(make_tuple(dist[i] + dist[j] + w, i, j)); } } sort(edges.begin(), edges.end()); for (auto [w, u, v] : edges) { if (join(u, v)) { tree[u].push_back({v, w}); tree[v].push_back({u, w}); } } dfs(1, 1); while (q--) { int u, v; cin >> u >> v; cout << solve(u, v) << endl; } }
#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 = 0x3f3f3f3f; 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; 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 (int i = head[u]; ~i; i = es[i].next) { int v = es[i].to; LL w = es[i].cost; if (dis[v] > dis[u] + w) { dis[v] = dis[u] + w; que.push(P(dis[v], v)); } } } for (int i = 0; i < cnt; ++i) { es[i].cost += dis[es[i].from] + dis[es[i].to]; } } 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() { init(); scanf("%d%d%d%d", &n, &m, &k, &q); int u, v; LL w; for (int i = 0; i < m; ++i) { scanf("%d%d%lld", &u, &v, &w); addedge(u, v, w); addedge(v, u, w); } dijkstra(); Kruskal(); preLCA(); int x, y; int lca; while (q--) { cin >> x >> y; lca = LCA(x, y); printf("%lld\n", max(getMax(x, dep[x] - dep[lca]), getMax(y, dep[y] - dep[lca]))); } return 0; }
#include <bits/stdc++.h> using namespace std; struct E { long long w; int to, from; }; const long long INF = 1e18; const int N = 2e5 + 5; vector<E> g[N]; int anime[N], from[N]; long long dist[N], ans[N]; set<int> st[N]; int findSet(int x) { return anime[x] < 0 ? x : anime[x] = findSet(anime[x]); } void un(int a, int b, long long w) { a = findSet(a); b = findSet(b); if (a == b) return; if (anime[a] > anime[b]) swap(a, b); anime[a] += anime[b]; anime[b] = a; for (int x : st[b]) { if (st[a].count(x)) { st[a].erase(x); ans[x] = w; } else { st[a].insert(x); } } } signed main() { ios_base::sync_with_stdio(0); cin.tie(NULL); int n, m, k, q; cin >> n >> m >> k >> q; for (int i = 0; i < m; i++) { int a, b, w; cin >> a >> b >> w; a--, b--; g[a].push_back({w, b, a}); g[b].push_back({w, a, b}); } fill(from, from + n, -1); fill(dist, dist + n, INF); priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq; for (int i = 0; i < k; i++) { anime[i] = -1; dist[i] = 0; from[i] = i; pq.push({0, i}); } for (int i = 0; i < q; i++) { int x, y; cin >> x >> y; x--, y--; st[x].insert(i); st[y].insert(i); } while (!pq.empty()) { int node = pq.top().second; long long cd = pq.top().first; pq.pop(); if (cd != dist[node]) { continue; } for (E e : g[node]) { if (dist[e.to] > dist[node] + e.w) { dist[e.to] = dist[node] + e.w; from[e.to] = from[node]; pq.push({dist[e.to], e.to}); } } } vector<E> edges; for (int i = 0; i < n; i++) { for (E e : g[i]) { if (e.to > i && from[e.to] != from[i]) edges.push_back({dist[e.to] + dist[i] + e.w, from[i], from[e.to]}); } } sort(edges.begin(), edges.end(), [](const E &a, const E &b) { return a.w < b.w; }); for (E e : edges) { un(e.to, e.from, e.w); } for (int i = 0; i < q; i++) { cout << ans[i] << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10, Q = 3e5 + 10, M = 3e5 + 10; const long long inf = 1e15 + 42; struct edge_t { int u, v; long long w; bool operator<(const edge_t &o) const { return w < o.w; } }; vector<pair<long long, long long>> g[N]; vector<pair<int, int>> queries[N]; edge_t e[M]; long long dist[N], ans[Q]; int back[N], par[N]; int get_root(int u); void merge(int u, int v, long long w); int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n, m, k, q; cin >> n >> m >> k >> q; for (int i = 1; i <= m; ++i) { cin >> e[i].u >> e[i].v >> e[i].w; g[e[i].u].push_back({e[i].v, e[i].w}); g[e[i].v].push_back({e[i].u, e[i].w}); } priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> pq; for (int i = 1; i <= k; ++i) { pq.push({0, i}); back[i] = i; par[i] = i; } for (int i = k + 1; i <= n; ++i) { dist[i] = inf; } while (!pq.empty()) { auto cur = pq.top(); pq.pop(); int u = cur.second; if (dist[u] < cur.first) { continue; } for (auto &edge : g[u]) { int v = edge.first, w = edge.second; if (dist[u] + w < dist[v]) { dist[v] = dist[u] + w; back[v] = back[u]; pq.push({dist[v], v}); } } } vector<edge_t> edges; for (int i = 1; i <= m; ++i) { int u = back[e[i].u], v = back[e[i].v]; long long w = dist[e[i].u] + dist[e[i].v] + e[i].w; if (u != v) { edges.push_back({u, v, w}); } } sort(edges.begin(), edges.end()); for (int i = 1; i <= q; ++i) { int a, b; cin >> a >> b; queries[a].push_back({b, i}); queries[b].push_back({a, i}); ans[i] = inf; } for (auto &edge : edges) { merge(edge.u, edge.v, edge.w); } for (int i = 1; i <= q; ++i) { cout << ans[i] << '\n'; } } int get_root(int u) { if (u != par[u]) { par[u] = get_root(par[u]); } return par[u]; } void merge(int u, int v, long long w) { u = get_root(u); v = get_root(v); if (u == v) { return; } else if (queries[u].size() < queries[v].size()) { swap(u, v); } for (auto &q : queries[v]) { if (get_root(q.first) == u) { ans[q.second] = min(ans[q.second], w); } else { queries[u].push_back(q); } } par[v] = u; }
#include <bits/stdc++.h> using namespace std; const long long MAXN = 4e5 + 5; const long long MAXM = 6e5 + 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][22], dep[MAXN], maxm[MAXN][22]; 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 maxn = 3e5 + 100; const long long mod = 1e9 + 7; const long long inf = 1e18; long long n, m, k, p, dis[maxn], par[maxn], dsu[maxn], ans[maxn]; bool vis[maxn]; vector<pair<long long, pair<long long, long long> > > e; vector<pair<long long, long long> > g[maxn], vec[maxn]; vector<long long> a[maxn]; priority_queue<pair<long long, long long> > q; void init() { for (long long i = 1; i <= k; i++) { dsu[i] = i; a[i].push_back(i); } return; } void Union(long long v, long long u, long long c) { long long x, y; v = dsu[v]; u = dsu[u]; if (v == u) return; if (a[v].size() < a[u].size()) swap(v, u); for (long long i = 0; i < a[u].size(); i++) { x = a[u][i]; a[v].push_back(x); dsu[x] = v; for (long long j = 0; j < vec[x].size(); j++) { y = vec[x][j].first; if (dsu[y] == dsu[x]) { ans[vec[x][j].second] = min(ans[vec[x][j].second], c); } } } return; } int main() { long long v, u, c; ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); ; cin >> n >> m >> k >> p; for (long long i = 0; i < m; i++) { cin >> v >> u >> c; g[v].push_back({u, c}); g[u].push_back({v, c}); } for (long long i = 0; i < p; i++) { cin >> v >> u; vec[v].push_back({u, i}); vec[u].push_back({v, i}); ans[i] = inf; } fill(dis, dis + maxn, inf); for (long long i = 1; i <= k; i++) { dis[i] = 0; par[i] = i; q.push({-dis[i], i}); } while (!q.empty()) { v = q.top().second; q.pop(); if (vis[v]) continue; for (long long i = 0; i < g[v].size(); i++) { u = g[v][i].first; c = g[v][i].second; if (dis[u] > dis[v] + c) { dis[u] = dis[v] + c; par[u] = par[v]; q.push({-dis[u], u}); } } } for (long long i = 1; i <= n; i++) { for (long long j = 0; j < g[i].size(); j++) { u = g[i][j].first; c = g[i][j].second; if (u > i && par[i] != par[u]) { e.push_back({dis[i] + c + dis[u], {par[i], par[u]}}); } } } init(); sort(e.begin(), e.end()); for (long long i = 0; i < e.size(); i++) { c = e[i].first; v = e[i].second.first; u = e[i].second.second; Union(v, u, c); } for (long long i = 0; i < p; i++) { cout << ans[i] << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; class edge { public: int u, v; long long w; edge() {} edge(int u, int v, long long w) : u(u), v(v), w(w) {} bool operator<(const edge& other) const { return w < other.w; } }; class node { public: int n; long long w; node() {} node(int n, long long w) : n(n), w(w) {} bool operator<(const node& other) const { return other.w < w; } }; const int MAXN = 3e5; const int LOG = 19; vector<edge> g[MAXN + 10]; long long D[MAXN + 10]; int n, m, k, q; edge E[MAXN + 10]; int P[MAXN + 10]; int find(int x) { if (x == P[x]) return x; return P[x] = find(P[x]); } void join(int x, int y) { P[find(x)] = find(y); } void dijkstra() { priority_queue<node> pq; for (int i = 1; i <= k; i++) { pq.push(node(i, 0LL)); D[i] = 0; } for (int i = k + 1; i <= n; i++) D[i] = LLONG_MAX; while (!pq.empty()) { node aux = pq.top(); pq.pop(); int cur = aux.n; long long w = aux.w; for (int i = 0; i < (int)g[cur].size(); i++) { int next = g[cur][i].v; long long nw = w + g[cur][i].w; if (D[next] <= nw) continue; D[next] = nw; pq.push(node(next, nw)); } } } int p[LOG][MAXN + 10]; int d[MAXN + 10]; long long M[LOG][MAXN + 10]; void dfs(int cur, int prev, int depth = 0, long long w = 0) { p[0][cur] = prev; M[0][cur] = w; d[cur] = depth; for (int i = 0; i < (int)g[cur].size(); i++) { int next = g[cur][i].v; if (next == prev) continue; dfs(next, cur, depth + 1, g[cur][i].w); } } void pre() { for (int i = 1; i < LOG; i++) { for (int j = 1; j <= n; j++) { p[i][j] = p[i - 1][p[i - 1][j]]; M[i][j] = max(M[i - 1][j], M[i - 1][p[i - 1][j]]); } } } long long query(int u, int v) { long long worst = 0; if (d[u] > d[v]) swap(u, v); int logi; for (logi = 0; (1 << logi) <= d[v]; logi++) ; logi--; for (int i = logi; i >= 0; i--) { if (d[v] - (1 << i) >= d[u]) { worst = max(worst, M[i][v]); v = p[i][v]; } } if (u == v) return worst; for (int i = logi; i >= 0; i--) { if (p[i][u] != p[i][v]) { worst = max(worst, max(M[i][u], M[i][v])); u = p[i][u]; v = p[i][v]; } } worst = max(worst, max(M[0][u], M[0][v])); return worst; } int main() { 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); E[i] = edge(u, v, w); g[u].push_back(edge(u, v, w)); g[v].push_back(edge(v, u, w)); } dijkstra(); for (int i = 0; i < m; i++) { int u = E[i].u, v = E[i].v; E[i].w += D[u] + D[v]; } sort(E, E + m); for (int i = 1; i <= m; i++) g[i].clear(); for (int i = 1; i <= n; i++) P[i] = i; for (int i = 0; i < m; i++) { int u = E[i].u, v = E[i].v; if (find(u) == find(v)) continue; join(u, v); g[u].push_back(edge(u, v, E[i].w)); g[v].push_back(edge(v, u, E[i].w)); } dfs(1, 1); pre(); for (int i = 0; i < q; i++) { int u, v; scanf("%d %d", &u, &v); printf("%lld\n", query(u, v)); } return 0; }
#include <bits/stdc++.h> using namespace std; class DebugStream { } LOG; template <typename T> DebugStream &operator<<(DebugStream &s, const T &) { return s; } mt19937 rnd(time(NULL)); const int maxN = 1e5 + 9, maxV = 1e6 + 9, MOD = 1e9 + 7, SQ = 335, lg = 20, bs = 29; vector<pair<long long, long long>> adj[maxN]; vector<pair<long long, long long>> qrs[maxN]; int comp[maxN], n, k, m, q; long long dst[maxN], ans[maxN * 3]; namespace DSU { int comp[maxN]; void prepare() { for (int i = 0; i < n; i++) comp[i] = i; } int get(int u) { if (comp[u] != u) comp[u] = get(comp[u]); return comp[u]; } void considerEdge(long long weight, int u, int v) { u = get(u), v = get(v); if (u == v) return; if (qrs[u].size() > qrs[v].size()) swap(u, v); for (auto el : qrs[u]) if (get(el.second) == v) ans[el.first] = weight; else qrs[v].push_back(el); comp[u] = v; } } // namespace DSU int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); 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; cin >> n >> m >> k >> q; for (int i = 0; i < n; i++) { if (i < k) pq.push(pair<long long, pair<long long, long long>>( 0, pair<long long, long long>(i, i))); comp[i] = -1; } for (long long i = 0, u, v, c; i < m; i++) { cin >> u >> v >> c, u--, v--; adj[u].push_back(pair<long long, long long>(c, v)); adj[v].push_back(pair<long long, long long>(c, u)); } for (int i = 0, u, v; i < q; i++) { cin >> u >> v; u--, v--; qrs[u].emplace_back(i, v); qrs[v].emplace_back(i, u); } while (pq.size()) { auto cr = pq.top(); pq.pop(); if (comp[cr.second.first] != -1) continue; comp[cr.second.first] = cr.second.second; dst[cr.second.first] = cr.first; for (auto sn : adj[cr.second.first]) if (comp[sn.second] == -1) pq.push(pair<long long, pair<long long, long long>>( cr.first + sn.first, pair<long long, long long>(sn.second, cr.second.second))); } vector<pair<long long, pair<long long, long long>>> edg; DSU::prepare(); for (int i = 0; i < n; i++) for (auto el : adj[i]) if (comp[i] != comp[el.second]) edg.emplace_back(dst[i] + dst[el.second] + el.first, pair<long long, long long>(comp[i], comp[el.second])); sort(edg.begin(), edg.end()); for (auto el : edg) DSU::considerEdge(el.first, el.second.first, el.second.second); for (int i = 0; i < q; i++) cout << ans[i] << '\n'; }
#include <bits/stdc++.h> using namespace std; const int MX = 4e5, MOD = 1e9 + 7; long long n, m, k, q; long long P[MX]; vector<tuple<long long, long long, long long>> edges; vector<pair<long long, long long>> adjList[MX]; set<int> qr[MX]; long long r[MX], p[MX]; long long ans[MX]; long long curAns = 0; void dijkstra() { priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> pq; for (int i = int(0); i < int(n); i++) P[i] = 1e18; for (int i = int(0); i < int(k); i++) pq.push({0, i}), P[i] = 0; while (!pq.empty()) { pair<long long, long long> p = pq.top(); pq.pop(); long long u = p.second, w = p.first; if (P[u] != w) continue; for (pair<long long, long long> v : adjList[u]) if (w + v.second < P[v.first]) pq.push({w + v.second, v.first}), P[v.first] = w + v.second; } } void buildDSU() { for (int i = int(0); i < int(n); i++) r[i] = 0, p[i] = i; } int getSet(int i) { return i == p[i] ? i : p[i] = getSet(p[i]); } bool isSameSet(int i, int j) { return getSet(i) == getSet(j); } void unionSet(int i, int j) { if (!isSameSet(i, j)) { i = getSet(i), j = getSet(j); if (r[i] > r[j]) { p[j] = i; for (long long u : qr[j]) { if (qr[i].count(u)) { qr[i].erase(u); ans[u] = curAns; } else { qr[i].insert(u); } } } else { p[i] = j; for (long long u : qr[i]) { if (qr[j].count(u)) { qr[j].erase(u); ans[u] = curAns; } else { qr[j].insert(u); } } if (r[i] == r[j]) r[j]++; } } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> n >> m >> k >> q; for (int i = int(0); i < int(m); i++) { int u, v, w; cin >> u >> v >> w; u--; v--; adjList[u].push_back({v, w}); adjList[v].push_back({u, w}); edges.push_back({u, v, w}); } dijkstra(); buildDSU(); for (int Q = int(0); Q < int(q); Q++) { int a, b; cin >> a >> b; a--; b--; qr[a].insert(Q); qr[b].insert(Q); } priority_queue<tuple<long long, long long, long long>, vector<tuple<long long, long long, long long>>, greater<tuple<long long, long long, long long>>> pq; for (int i = int(0); i < int(m); i++) { long long u, v, w; tie(u, v, w) = edges[i]; pq.push({w + P[u] + P[v], u, v}); } while (!pq.empty()) { long long u, v, w; tie(w, u, v) = pq.top(); pq.pop(); if (!isSameSet(u, v)) { curAns = w; unionSet(u, v); } } for (int i = int(0); i < int(q); i++) cout << ans[i] << endl; }
#include <bits/stdc++.h> using namespace std; struct UnionFindPersistent { vector<int> par; vector<int64_t> time; vector<vector<pair<int64_t, int>>> sz; const int64_t INF = 1e18; UnionFindPersistent(int n = 0) { if (n > 0) initialize(n); } void initialize(int n) { par.resize(n); time.resize(n); sz.resize(n); for (int i = 0; i < n; i++) { par[i] = i; time[i] = INF; sz[i].push_back({-1, 1}); } } int find(int x, int64_t t) { if (time[x] > t) { return x; } else { return find(par[x], t); } } int size(int x, int64_t t) { x = find(x, t); return (*(lower_bound(sz[x].begin(), sz[x].end(), make_pair(t + 1, 0)) - 1)) .second; } void unite(int x, int y, int64_t t) { x = find(x, t); y = find(y, t); if (x == y) return; int new_sz = sz[x].back().second + sz[y].back().second; if (sz[x].back().second > sz[y].back().second) swap(x, y); par[x] = y; time[x] = t; sz[y].push_back({t, new_sz}); } bool same(int x, int y, int64_t t) { return find(x, t) == find(y, t); } }; int main() { int N, M, K, Q; cin >> N >> M >> K >> Q; vector<pair<int64_t, int64_t>> edges[100000]; for (int i = 0; i < M; i++) { int a, b, c; scanf("%d %d %d", &a, &b, &c); a--; b--; edges[a].emplace_back(b, c); edges[b].emplace_back(a, c); } vector<pair<int64_t, int64_t>> dist(N); pair<int64_t, int64_t> INFP = {1e18, 1e18}; priority_queue<vector<int64_t>, vector<vector<int64_t>>, greater<vector<int64_t>>> que; for (int i = 0; i < K; i++) { dist[i] = {0, i}; que.push({0, i, i}); } for (int i = K; i < N; i++) dist[i] = INFP; while (que.size()) { auto p = que.top(); que.pop(); int64_t d = p[0], i = p[1], s = p[2]; if (dist[i].first < d) continue; for (auto& e : edges[i]) { int64_t j = e.first, d2 = d + e.second; if (dist[j].first > d2) { dist[j] = {d2, s}; que.push({d2, j, s}); } } } vector<vector<int64_t>> es; for (int i = 0; i < N; i++) for (auto& e : edges[i]) { int j = e.first, c = e.second; es.push_back( {dist[i].first + dist[j].first + c, dist[i].second, dist[j].second}); } sort(es.begin(), es.end()); UnionFindPersistent uf(N); for (auto& e : es) uf.unite(e[1], e[2], e[0]); for (int i = 0; i < Q; i++) { int a, b; scanf("%d %d", &a, &b); a--; b--; int64_t ok = 1e18, ng = -1; while (ok - ng > 1) { int64_t mid = (ok + ng) / 2; (uf.same(a, b, mid) ? ok : ng) = mid; } printf("%lld\n", ok); } return 0; }
#include <bits/stdc++.h> using namespace std; long long n, m, k, q; vector<vector<pair<long long, long long>>> graph; vector<vector<pair<long long, long long>>> tree; vector<vector<long long>> edges; void dijkstra() { vector<long long> dist(n, 1e18); vector<int> used(n, 0); vector<int> prev(n, -1); priority_queue<vector<long long>> q; for (long long i = 0; i < k; i++) { dist[i] = 0; q.push({-dist[i], i}); prev[i] = i; } while (q.size()) { long long v = q.top()[1]; q.pop(); if (used[v]) continue; used[v] = 1; for (auto e : graph[v]) { if (dist[e.first] > dist[v] + e.second) { prev[e.first] = prev[v]; dist[e.first] = dist[v] + e.second; q.push({-dist[e.first], e.first}); } if (prev[v] - prev[e.first]) edges.push_back( {prev[v], prev[e.first], dist[e.first] + dist[v] + e.second}); } } } vector<int> p; vector<int> sz; int get(int a) { if (a == p[a]) return a; return p[a] = get(p[a]); } void unite(int a, int b) { a = get(a); b = get(b); if (a == b) return; if (sz[a] < sz[b]) swap(a, b); sz[a] += sz[b]; p[b] = a; } bool comp(vector<long long> &a, vector<long long> &b) { return (a[2] < b[2]); } int t = 0, len = 20; vector<int> tin; vector<int> tout; vector<vector<int>> up; vector<vector<long long>> mx; void dfs(long long v, long long p) { tin[v] = t++; up[0][v] = p; for (long long i = 1; i < len; i++) { up[i][v] = up[i - 1][up[i - 1][v]]; mx[i][v] = max(mx[i - 1][v], mx[i - 1][up[i - 1][v]]); } for (auto h : tree[v]) { if (h.first == p) continue; mx[0][h.first] = h.second; dfs(h.first, v); } tout[v] = t++; } int isancestor(long long a, long long b) { return (tin[a] <= tin[b] and tout[b] <= tout[a]); } int getlca(long long a, long long b) { if (isancestor(a, b)) return a; if (isancestor(b, a)) return b; for (long long i = len - 1; i >= 0; i--) { if (!isancestor(up[i][a], b)) a = up[i][a]; } return up[0][a]; } long long getmx(long long a, long long b) { if (a == b) return 0; long long ans = 0; for (long long i = len - 1; i >= 0; i--) { if (!isancestor(up[i][a], b)) { ans = max(ans, mx[i][a]); a = up[i][a]; } } return max(ans, mx[0][a]); } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> q; graph.assign(n, vector<pair<long long, long long>>()); for (long long i = 0; i < m; i++) { long long a, b, w; cin >> a >> b >> w; a--; b--; graph[a].push_back({b, w}); graph[b].push_back({a, w}); } dijkstra(); p.assign(k, 0); sz.assign(k, 1); tree.assign(k, vector<pair<long long, long long>>()); for (long long i = 0; i < k; i++) p[i] = i; sort(edges.begin(), edges.end(), comp); for (auto e : edges) { if (get(e[0]) == get(e[1])) continue; tree[e[0]].push_back({e[1], e[2]}); tree[e[1]].push_back({e[0], e[2]}); unite(e[0], e[1]); } up.assign(len, vector<int>(k, 0)); mx.assign(len, vector<long long>(k, 0)); tin.assign(k, 0); tout.assign(k, 0); dfs(0, 0); for (q; q; q--) { int a, b; cin >> a >> b; a--; b--; int lca = getlca(a, b); long long ans = max(getmx(a, lca), getmx(b, lca)); cout << ans << '\n'; } }
#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; } 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 int maxn = 600005; long long n, m, k, q; struct Edge { int u, v; long long c; bool operator<(const Edge x) const { return c < x.c; } } e[maxn]; struct Node { int v; long long c; Node *next; } * h[maxn], pool[maxn]; int tot; void addEdge(int u, int v, long long c) { Node *p = &pool[++tot]; p->v = v; p->c = c; p->next = h[u]; h[u] = p; } struct Que { int v; long long dis; bool operator<(const Que a) const { return a.dis < dis; } }; priority_queue<Que> pq; void push(int v, long long dis) { Que temp; temp.v = v; temp.dis = dis; pq.push(temp); } long long vis[maxn], dis[maxn]; void dij() { memset(dis, 0x3f, sizeof(dis)); for (int i = 1; i <= k; i++) { dis[i] = 0; push(i, 0); } while (!pq.empty()) { int u = pq.top().v; pq.pop(); if (vis[u] == 1) continue; vis[u] = 1; for (Node *p = h[u]; p; p = p->next) { if (dis[p->v] > dis[u] + p->c) { dis[p->v] = dis[u] + p->c; if (vis[p->v] == 0) push(p->v, dis[p->v]); } } } } int fa[maxn]; int getfather(int x) { if (fa[x] == x) return x; else return fa[x] = getfather(fa[x]); } void Merge(int x, int y) { int fx = getfather(x); int fy = getfather(y); if (fx == fy) return; fa[fx] = fy; } long long f[maxn][25], b[maxn][25]; int dep[maxn]; void dfs(int u, int fa) { for (Node *p = h[u]; p; p = p->next) { if (p->v == fa) continue; f[p->v][0] = u; b[p->v][0] = p->c; dep[p->v] = dep[u] + 1; dfs(p->v, u); } } long long query(int u, int v) { long long ans = 0; if (dep[u] < dep[v]) swap(u, v); int t = dep[u] - dep[v]; for (int i = 0; i < 24; i++) { if ((1 << i) & t) { ans = max(ans, b[u][i]); u = f[u][i]; } } if (u == v) return ans; for (int i = 23; i >= 0; i--) { if (f[u][i] != f[v][i]) { ans = max(ans, max(b[u][i], b[v][i])); u = f[u][i]; v = f[v][i]; } } return max(ans, max(b[v][0], b[u][0])); } int main() { memset(f, -1, sizeof(f)); cin >> n >> m >> k >> q; int x, y, z; for (int i = 1; i <= m; i++) { scanf("%d %d %d", &e[i].u, &e[i].v, &e[i].c); addEdge(e[i].u, e[i].v, e[i].c); addEdge(e[i].v, e[i].u, e[i].c); } dij(); for (int i = 1; i <= m; i++) { e[i].c = e[i].c + dis[e[i].u] + dis[e[i].v]; } sort(e + 1, e + m + 1); int tc = 0; memset(h, NULL, sizeof(h)); tot = 0; for (int i = 1; i <= n; i++) fa[i] = i; for (int i = 1; i <= m; i++) { if (getfather(e[i].u) != getfather(e[i].v)) { Merge(e[i].u, e[i].v); addEdge(e[i].u, e[i].v, e[i].c); addEdge(e[i].v, e[i].u, e[i].c); tc++; if (tc == n - 1) break; } } dfs(1, -1); for (int i = 1; i <= 23; i++) { for (int j = 1; j <= n; j++) { if (f[j][i - 1] != -1) { f[j][i] = f[f[j][i - 1]][i - 1]; b[j][i] = max(b[j][i - 1], b[f[j][i - 1]][i - 1]); } } } for (int i = 1; i <= q; i++) { scanf("%d %d", &x, &y); printf("%lld\n", query(x, y)); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 100007; const int maxq = 300007; vector<int> head[maxn]; int n, m, q, k; struct rev { int from; int to; long long we; rev(int uu = 0, int vv = 0, long long ww = -1) { from = uu, to = vv, we = ww; } bool operator<(const rev& b) const { if (we != b.we) return we < b.we; if (to != b.to) return to < b.to; return from < b.from; } }; vector<rev> edge; int id[maxq << 1]; long long ans[maxq << 1]; inline void add_edge(int u, int v, int w) { head[u].push_back(edge.size()), edge.push_back(rev(u, v, w)); } vector<int> has[maxn]; int fa[maxn]; int sz[maxn]; int fd(int x) { while (fa[x] != x) x = fa[x]; return x; } void merge(int x, int y, long long slack) { int fx, fy; fx = fd(x), fy = fd(y); if (fx == fy) return; if (sz[fx] > sz[fy]) swap(fx, fy); fa[fx] = fy, sz[fy] += sz[fx]; for (auto o : has[fx]) { has[fy].push_back(o); if (fd(id[o ^ 1]) == fy) { if (ans[min(o, o ^ 1)] == -1) ans[min(o, o ^ 1)] = slack; } } } long long dis[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({0LL, i}); else dis[i] = -1; } while (!q.empty()) { auto tp = q.top(); q.pop(); int u = tp.second; long long slack = tp.first; if (slack != dis[u]) continue; for (auto i : head[u]) { auto e = edge[i]; int v = e.to; long long we = e.we; if (dis[v] == -1 || we + slack < dis[v]) dis[v] = we + slack, q.push({dis[v], v}); } } } int main(void) { ios::sync_with_stdio(false); cin.tie(0); cin >> n >> m >> k >> q; for (int i = (0); i < (m); ++i) { int u, v, w; cin >> u >> v >> w; add_edge(u, v, w), add_edge(v, u, w); } int now = 0; for (int i = (0); i < (q); ++i) { int a, b; cin >> a >> b; has[a].push_back(now), has[b].push_back(now + 1); id[now++] = a, id[now++] = b; } for (int i = (0); i < (2 * q); ++i) ans[i] = -1; dij(); vector<rev> es; for (int i = 0; i < 2 * m; i += 2) { auto e = edge[i]; int u, v; u = e.from, v = e.to; long long we = dis[u] + dis[v] + e.we; es.push_back(rev(u, v, we)); } sort((es).begin(), (es).end()); for (int i = (1); i <= (n); ++i) { fa[i] = i, sz[i] = 1; } for (auto e : es) merge(e.from, e.to, e.we); for (int i = 0; i < 2 * q; i += 2) cout << ans[i] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; long long int dist[100005]; long long int n, m, k, q, ind[100005], parent[100005], depth[100005], maxi[100005][25], parent2[100005][25], sol[300005]; vector<pair<int, int> > v[100005]; vector<pair<int, long long int> > v2[100005]; set<pair<long long int, int> > s; map<pair<int, int>, long long int> m1; vector<pair<int, pair<int, int> > > e; vector<pair<long long int, pair<int, int> > > e2; set<int> s1[100005]; void dijkstra() { for (int i = 0; i < n; i++) { dist[i] = 1e18; if (i < k) { dist[i] = 0; ind[i] = i; } s.insert(make_pair(dist[i], i)); } while (!s.empty()) { long long int d = (*s.begin()).first, x = (*s.begin()).second; s.erase(s.begin()); for (int i = 0; i < v[x].size(); i++) { if (d + v[x][i].second < dist[v[x][i].first]) { ind[v[x][i].first] = ind[x]; s.erase(make_pair(dist[v[x][i].first], v[x][i].first)); dist[v[x][i].first] = d + v[x][i].second; s.insert(make_pair(dist[v[x][i].first], v[x][i].first)); } } } } int find_par(int x) { if (x == parent[x]) return x; int par = find_par(parent[x]); parent[x] = par; return par; } void spoji(int x, int y, long long int a) { x = find_par(x); y = find_par(y); if (x == y) return; if (depth[x] == depth[y]) depth[x] += 1; if (depth[x] > depth[y]) parent[y] = x; else parent[x] = y; if (s1[x].size() > s1[y].size()) { for (set<int>::iterator it = s1[y].begin(); it != s1[y].end(); it++) { if (s1[x].find(*it) != s1[x].end()) sol[*it] = a; s1[x].insert(*it); } s1[y].clear(); if (x != parent[y]) swap(s1[x], s1[y]); } else { for (set<int>::iterator it = s1[x].begin(); it != s1[x].end(); it++) { if (s1[y].find(*it) != s1[y].end()) sol[*it] = a; s1[y].insert(*it); } s1[x].clear(); if (y != parent[x]) swap(s1[x], s1[y]); } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (int i = 0; i < m; i++) { int a, b, w; cin >> a >> b >> w; v[a - 1].push_back(make_pair(b - 1, w)); v[b - 1].push_back(make_pair(a - 1, w)); e.push_back(make_pair(w, make_pair(a - 1, b - 1))); } dijkstra(); for (int i = 0; i < m; i++) { int x = e[i].second.first, y = e[i].second.second; if (ind[x] == ind[y]) continue; if (m1[make_pair(ind[x], ind[y])] == 0 or dist[x] + e[i].first + dist[y] < m1[make_pair(ind[x], ind[y])]) { m1[make_pair(ind[x], ind[y])] = dist[x] + e[i].first + dist[y]; m1[make_pair(ind[y], ind[x])] = dist[x] + e[i].first + dist[y]; } } for (int i = 0; i < m; i++) { int x = e[i].second.first, y = e[i].second.second; if (ind[x] == ind[y] or m1[make_pair(ind[x], ind[y])] == 0) continue; e2.push_back( make_pair(m1[make_pair(ind[x], ind[y])], make_pair(ind[x], ind[y]))); m1[make_pair(ind[x], ind[y])] = 0; m1[make_pair(ind[y], ind[x])] = 0; } sort(e2.begin(), e2.end()); for (int i = 0; i < k; i++) parent[i] = i; for (int i = 0; i < q; i++) { int a, b; cin >> a >> b; s1[ind[a - 1]].insert(i); s1[ind[b - 1]].insert(i); } for (int i = 0; i < e2.size(); i++) { int x = e2[i].second.first, y = e2[i].second.second; if (find_par(x) == find_par(y)) continue; spoji(x, y, e2[i].first); } for (int i = 0; i < q; i++) { cout << sol[i] << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, k, q; vector<pair<long long, long long>> adj[100001]; int owner[100001]; long long dst[100001]; struct edge { long long a, b, c; bool operator<(const edge& masik) const { return c < masik.c; } }; vector<edge> lst; int par[100001]; set<int> qs[100001]; long long ans[300001]; void init() { for (int i = 1; i <= n; ++i) { par[i] = -1; } } int get(int x) { if (par[x] == -1) return x; return par[x] = get(par[x]); } void merge(int x, int y, long long w) { int px = get(x), py = get(y); if (px == py) return; if (qs[px].size() > qs[py].size()) { swap(px, py); } for (auto i : qs[px]) { auto it = qs[py].find(i); if (it != qs[py].end()) { qs[py].erase(i); ans[i] = w; } else { qs[py].insert(i); } } par[px] = py; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m >> k >> q; for (int i = 0; i < m; ++i) { int a, b, c; cin >> a >> b >> c; adj[a].push_back({b, c}); adj[b].push_back({a, c}); } priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> pq; for (int i = 1; i <= k; ++i) { owner[i] = i; pq.push({0, i}); } while (!pq.empty()) { auto tp = pq.top(); pq.pop(); if (dst[tp.second] < tp.first) continue; for (auto i : adj[tp.second]) { if (owner[i.first] != owner[tp.second]) { if (owner[i.first] == 0) { dst[i.first] = i.second + tp.first; owner[i.first] = owner[tp.second]; pq.push({dst[i.first], i.first}); } else { if (dst[i.first] > i.second + tp.first) { dst[i.first] = i.second + tp.first; owner[i.first] = owner[tp.second]; pq.push({dst[i.first], i.first}); } else { lst.push_back({owner[i.first], owner[tp.second], dst[i.first] + dst[tp.second] + i.second}); } } } else { if (dst[i.first] > i.second + tp.first) { dst[i.first] = i.second + tp.first; pq.push({dst[i.first], i.first}); } } } } sort(lst.begin(), lst.end()); for (int i = 0; i < q; ++i) { int a, b; cin >> a >> b; qs[a].insert(i); qs[b].insert(i); } init(); for (auto i : lst) { merge(i.a, i.b, i.c); } for (int i = 0; i < q; ++i) { cout << ans[i] << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1000 * 100 + 10; const int M = 3 * N; long long dis[N]; int col[N]; vector<pair<int, int>> c[N]; vector<pair<long long, pair<int, int>>> edges; vector<int> ch[M]; int par[N]; set<pair<long long, int>> curr; long long qx[M], qy[M], ql[M], qr[M]; int dfind(int u) { return par[u] < 0 ? u : par[u] = dfind(par[u]); } void dmerge(int u, int v) { u = dfind(u); v = dfind(v); if (u == v) return; if (par[u] > par[v]) swap(u, v); par[u] += par[v]; par[v] = u; } int main() { ios::sync_with_stdio(false); cin.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--; c[u].push_back({v, w}); c[v].push_back({u, w}); } memset(dis, 63, sizeof dis); for (int i = 0; i < k; i++) { dis[i] = 0; col[i] = i; curr.insert({dis[i], i}); } while (curr.size()) { int s = curr.begin()->second; curr.erase(curr.begin()); for (auto x : c[s]) if (dis[x.first] > dis[s] + x.second) { curr.erase({dis[x.first], x.first}); dis[x.first] = dis[s] + x.second; col[x.first] = col[s]; curr.insert({dis[x.first], x.first}); } } for (int x = 0; x < n; x++) for (auto y : c[x]) { if (x < y.first && col[x] != col[y.first]) edges.push_back( {dis[x] + dis[y.first] + y.second, {col[x], col[y.first]}}); } sort(edges.begin(), edges.end()); for (int i = 0; i < q; i++) { cin >> qx[i] >> qy[i]; qx[i]--; qy[i]--; ql[i] = -1, qr[i] = ((int)(edges).size()) - 1; } for (int t = 0; t < 20; t++) { for (int i = 0; i < q; i++) if (qr[i] - ql[i] > 1) { int mid = (ql[i] + qr[i]) / 2; ch[mid].push_back(i); } memset(par, -1, sizeof par); for (int i = 0; i < ((int)(edges).size()); i++) { dmerge(edges[i].second.first, edges[i].second.second); for (auto x : ch[i]) if (dfind(qx[x]) == dfind(qy[x])) qr[x] = i; else ql[x] = i; ch[i].clear(); } } for (int i = 0; i < q; i++) cout << edges[qr[i]].first << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; long long const ms = 1e5 + 10, mlg = 30; vector<pair<long long, long long>> g[ms]; vector<pair<long long, long long>> mst[ms]; long long d1[ms]; long long n, m, k, q; struct edge { long long u, v, w; edge() {} edge(long long u, long long v, long long w) : u(u), v(v), w(w) {} }; vector<edge> me; void dij() { priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> hp; for (int i = 0; i < n; i++) { if (i < k) { d1[i] = 0; hp.push({0, i}); } else d1[i] = 1e18; } while (hp.size()) { long long nv = hp.top().second, dv = hp.top().first; hp.pop(); if (d1[nv] < dv) continue; for (auto e : g[nv]) { long long av = e.first, wv = e.second; if (d1[nv] + wv < d1[av]) { d1[av] = d1[nv] + wv; hp.push({d1[av], av}); } } } } void cong(long long a, long long b, long long w) { g[a].push_back({b, w}); g[b].push_back({a, w}); } void conm(long long a, long long b, long long w) { mst[a].push_back({b, w}); mst[b].push_back({a, w}); } long long ds[ms], sz[ms]; void mks() { for (int i = 0; i < n; i++) ds[i] = i, sz[i] = 1; } long long find(long long i) { if (ds[i] == i) return i; else return ds[i] = find(ds[i]); } void onion(long long a, long long b) { a = find(a), b = find(b); if (sz[a] < sz[b]) swap(a, b); if (a != b) sz[a] += sz[b]; ds[b] = a; } long long par[ms][mlg + 1], maxw[ms][mlg + 1], lvl[ms]; void dfs(long long v, long long p, long long l = 0, long long take = 0) { lvl[v] = l; par[v][0] = p; maxw[v][0] = take; for (long long kk = 1; kk <= mlg; kk++) { par[v][kk] = par[par[v][kk - 1]][kk - 1]; maxw[v][kk] = max(maxw[v][kk - 1], maxw[par[v][kk - 1]][kk - 1]); } for (auto &u : mst[v]) { if (u.first != p) dfs(u.first, v, l + 1, u.second); } } long long lca(long long a, long long b) { if (lvl[b] > lvl[a]) swap(a, b); for (long long i = mlg; i >= 0; i--) { if (lvl[a] - (1 << i) >= lvl[b]) a = par[a][i]; } if (a == b) return a; for (long long i = mlg; i >= 0; i--) { if (par[a][i] != par[b][i]) a = par[a][i], b = par[b][i]; } return par[a][0]; } long long lift(long long v, long long d) { long long ret = 0; for (long long i = mlg; i >= 0; i--) { if ((1 << i) <= d) ret = max(ret, maxw[v][i]), v = par[v][i], d -= (1 << i); } return ret; } int main() { cin.tie(0); ios::sync_with_stdio(0); cin >> n >> m >> k >> q; long long a, b, w; for (int i = 0; i < m; i++) { cin >> a >> b >> w; a--, b--; cong(a, b, w); } dij(); for (int i = 0; i < n; i++) { for (auto e : g[i]) { me.push_back(edge(i, e.first, d1[i] + d1[e.first] + e.second)); } } sort(me.begin(), me.end(), [](edge &a, edge &b) -> bool { return a.w < b.w; }); mks(); for (int i = 0; i < me.size(); i++) { if (find(me[i].u) != find(me[i].v)) { conm(me[i].u, me[i].v, me[i].w); onion(me[i].u, me[i].v); } } memset(maxw, 0, sizeof maxw); dfs(0, 0); long long q1, q2, lc; while (q--) { cin >> q1 >> q2; q1--, q2--; lc = lca(q1, q2); cout << max(lift(q1, lvl[q1] - lvl[lc]), lift(q2, lvl[q2] - lvl[lc])) << '\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>, 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 int maxn = 3e5; int n, m, k, q; struct node { int v; int nxt; long long w; node() {} node(int v, long long w) : v(v), w(w) {} } edge[maxn * 2 + 10]; struct Node { int u; int v; long long w; Node() {} Node(int u, int v, long long w) : u(u), v(v), w(w) {} bool operator<(const Node &C) const { return w > C.w; } }; int head[maxn + 10]; bool vis[maxn + 10]; vector<Node> ve[maxn + 10]; priority_queue<Node> Q, P; int fa[maxn + 10]; int tot; int f[maxn + 10][25]; long long dis[maxn + 10][25]; int dep[maxn + 10]; long long d[maxn + 10]; void init() { tot = 0; memset(vis, false, sizeof(vis)); memset(head, -1, sizeof(head)); for (int i = 0; i <= n; i++) ve[i].clear(); while (!Q.empty()) { Q.pop(); } while (!P.empty()) { P.pop(); } for (int i = 0; i <= n; i++) fa[i] = i; memset(dis, 0, sizeof(dis)); memset(d, 0, sizeof(d)); } int cha(int u) { if (fa[u] != u) { fa[u] = cha(fa[u]); } return fa[u]; } void addedge(int u, int v, long long w) { edge[tot].v = v; edge[tot].w = w; edge[tot].nxt = head[u]; head[u] = tot++; edge[tot].v = u; edge[tot].w = w; edge[tot].nxt = head[v]; head[v] = tot++; } void dfs(int u, int pre) { dep[u] = dep[pre] + 1; f[u][0] = pre; for (int i = 1; i <= 20; i++) { f[u][i] = f[f[u][i - 1]][i - 1]; dis[u][i] = max(dis[f[u][i - 1]][i - 1], dis[u][i - 1]); } for (int i = head[u]; i != -1; i = edge[i].nxt) { int v = edge[i].v; if (v == pre) continue; dep[v] = dep[u] + 1; f[v][0] = u; dis[v][0] = edge[i].w; dfs(v, u); } } long long lca(int x, int y) { if (dep[x] < dep[y]) swap(x, y); long long ans = 0; for (int i = 20; i >= 0; i--) { if (dep[f[x][i]] >= dep[y]) { ans = max(ans, dis[x][i]); x = f[x][i]; } if (x == y) return ans; } for (int i = 20; i >= 0; i--) { if (f[x][i] != f[y][i]) { ans = max(ans, dis[x][i]); ans = max(ans, dis[y][i]); x = f[x][i]; y = f[y][i]; } } if (x != y) { ans = max(ans, dis[x][0]); ans = max(ans, dis[y][0]); } return ans; } int main() { while (~scanf("%d%d%d%d", &n, &m, &k, &q)) { init(); for (int i = 0; i < m; i++) { int u, v; long long w; scanf("%d%d%lld", &u, &v, &w); u--, v--; ve[u].push_back(Node(u, v, w)); ve[v].push_back(Node(v, u, w)); } for (int i = 0; i < k; i++) { vis[i] = true; d[i] = 0; for (int j = 0; j < ve[i].size(); j++) { Q.push(Node(ve[i][j].u, ve[i][j].v, ve[i][j].w)); } } while (!Q.empty()) { Node tmp = Q.top(); Q.pop(); int uu = cha(tmp.u); int vv = cha(tmp.v); if (uu == vv) continue; if (vis[tmp.v]) { P.push(Node(tmp.u, tmp.v, tmp.w + d[tmp.v])); continue; } fa[uu] = vv; addedge(tmp.u, tmp.v, tmp.w); vis[tmp.v] = true; d[tmp.v] = tmp.w; int v = tmp.v; for (int i = 0; i < ve[v].size(); i++) { Q.push(Node(v, ve[v][i].v, ve[v][i].w + tmp.w)); } } while (!P.empty()) { Node tmp = P.top(); P.pop(); int uu = cha(tmp.u); int vv = cha(tmp.v); if (uu == vv) continue; int v = tmp.v; addedge(tmp.u, tmp.v, tmp.w); fa[uu] = vv; } dfs(0, 0); for (int i = 0; i < q; i++) { int u, v; scanf("%d%d", &u, &v); u--, v--; printf("%lld\n", lca(u, v)); } } return 0; }
#include <bits/stdc++.h> using namespace std; const long long LL_INF = (long long)2e18 + 5; template <typename T, bool maximum_mode = false> struct RMQ { int n = 0, levels = 0; vector<T> values; vector<vector<int>> range_low; RMQ(const vector<T> &_values = {}) { if (!_values.empty()) build(_values); } static int largest_bit(int x) { return 31 - __builtin_clz(x); } int better_index(int a, int b) const { return (values[a] < values[b]) ^ maximum_mode ? a : b; } void build(const vector<T> &_values) { values = _values; n = values.size(); levels = largest_bit(n) + 1; range_low.resize(levels); for (int k = 0; k < levels; k++) range_low[k].resize(n - (1 << k) + 1); for (int i = 0; i < n; i++) range_low[0][i] = i; for (int k = 1; k < levels; k++) for (int i = 0; i <= n - (1 << k); i++) range_low[k][i] = better_index(range_low[k - 1][i], range_low[k - 1][i + (1 << (k - 1))]); } int query_index(int a, int b) const { assert(0 <= a && a < b && b <= n); int level = largest_bit(b - a); return better_index(range_low[level][a], range_low[level][b - (1 << level)]); } T query_value(int a, int b) const { return values[query_index(a, b)]; } }; struct edge { int node = -1; long long weight = 0; edge() {} edge(int _node, long long _weight) : node(_node), weight(_weight) {} }; template <typename T_weight> struct weighted_LCA { int n = 0; vector<vector<edge>> adj; vector<int> parent, depth, subtree_size; vector<T_weight> weighted_depth, up_weight; vector<int> euler, first_occurrence; vector<int> tour_start, tour_end, tour_list, postorder; vector<int> heavy_root; RMQ<int> rmq; weighted_LCA(int _n = 0) { init(_n); } weighted_LCA(const vector<vector<edge>> &_adj) { init(_adj); } void init(int _n) { n = _n; adj.assign(n, {}); parent.resize(n); depth.resize(n); subtree_size.resize(n); weighted_depth.resize(n); up_weight.assign(n, numeric_limits<T_weight>::min()); first_occurrence.resize(n); tour_start.resize(n); tour_end.resize(n); tour_list.resize(n); postorder.resize(n); heavy_root.resize(n); } void init(const vector<vector<edge>> &_adj) { init(_adj.size()); adj = _adj; } void add_edge(int a, int b, T_weight weight) { adj[a].emplace_back(b, weight); adj[b].emplace_back(a, weight); } void erase_edge(int from, int to) { for (edge &e : adj[from]) if (e.node == to) { swap(e, adj[from].back()); adj[from].pop_back(); return; } assert(false); } void dfs(int node, int par, T_weight weight) { parent[node] = par; depth[node] = par < 0 ? 0 : depth[par] + 1; subtree_size[node] = 1; weighted_depth[node] = weight; if (par >= 0) erase_edge(node, par); for (edge &e : adj[node]) { up_weight[e.node] = e.weight; dfs(e.node, node, weight + e.weight); subtree_size[node] += subtree_size[e.node]; } sort(adj[node].begin(), adj[node].end(), [&](const edge &a, const edge &b) { return subtree_size[a.node] > subtree_size[b.node]; }); } int tour, post_tour; void tour_dfs(int node, bool heavy) { heavy_root[node] = heavy ? heavy_root[parent[node]] : node; first_occurrence[node] = euler.size(); euler.push_back(node); tour_list[tour] = node; tour_start[node] = tour++; bool heavy_child = true; for (edge &e : adj[node]) { tour_dfs(e.node, heavy_child); euler.push_back(node); heavy_child = false; } tour_end[node] = tour; postorder[node] = post_tour++; } void build() { parent.assign(n, -1); for (int i = 0; i < n; i++) if (parent[i] < 0) dfs(i, -1, 0); tour = post_tour = 0; for (int i = 0; i < n; i++) if (parent[i] < 0) { tour_dfs(i, false); euler.push_back(-1); } assert((int)euler.size() == 2 * n); vector<int> euler_depths; for (int node : euler) euler_depths.push_back(node < 0 ? node : depth[node]); rmq.build(euler_depths); build_path_maxes(); } int get_lca(int a, int b) const { a = first_occurrence[a]; b = first_occurrence[b]; if (a > b) swap(a, b); return euler[rmq.query_index(a, b + 1)]; } bool is_ancestor(int a, int b) const { return tour_start[a] <= tour_start[b] && tour_start[b] < tour_end[a]; } bool on_path(int x, int a, int b) const { int anc = get_lca(a, b); return is_ancestor(anc, x) && (is_ancestor(x, a) || is_ancestor(x, b)); } int get_dist(int a, int b) const { return depth[a] + depth[b] - 2 * depth[get_lca(a, b)]; } T_weight get_weighted_dist(int a, int b) const { return weighted_depth[a] + weighted_depth[b] - 2 * weighted_depth[get_lca(a, b)]; } int child_ancestor(int a, int b) const { assert(a != b); assert(is_ancestor(a, b)); int child = euler[rmq.query_index(first_occurrence[a], first_occurrence[b] + 1) + 1]; assert(is_ancestor(child, b)); return child; } static int largest_bit(int x) { return 31 - __builtin_clz(x); } vector<vector<pair<int, T_weight>>> ancestor_max; void build_path_maxes() { ancestor_max.assign(largest_bit(n) + 1, vector<pair<int, T_weight>>(n)); for (int i = 0; i < n; i++) ancestor_max[0][i] = {parent[i], up_weight[i]}; for (int k = 0; k < largest_bit(n); k++) for (int i = 0; i < n; i++) { int k_anc = ancestor_max[k][i].first; T_weight k_max = ancestor_max[k][i].second; if (k_anc < 0) ancestor_max[k + 1][i] = {-1, k_max}; else ancestor_max[k + 1][i] = {ancestor_max[k][k_anc].first, max(k_max, ancestor_max[k][k_anc].second)}; } } T_weight query_path_max(int a, int b) const { int anc = get_lca(a, b); int a_dist = depth[a] - depth[anc]; int b_dist = depth[b] - depth[anc]; T_weight path_max = numeric_limits<T_weight>::min(); for (int k = 0; 1 << k <= a_dist; k++) if (a_dist >> k & 1) { path_max = max(path_max, ancestor_max[k][a].second); a = ancestor_max[k][a].first; } for (int k = 0; 1 << k <= b_dist; k++) if (b_dist >> k & 1) { path_max = max(path_max, ancestor_max[k][b].second); b = ancestor_max[k][b].first; } return path_max; } }; 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 union_find { vector<int> parent; vector<int> size; int components = 0; union_find(int n = -1) { if (n >= 0) init(n); } void init(int n) { parent.resize(n + 1); size.assign(n + 1, 1); components = n; for (int i = 0; i <= n; i++) parent[i] = i; } int find(int x) { return x == parent[x] ? x : parent[x] = find(parent[x]); } bool unite(int x, int y) { x = find(x); y = find(y); if (x == y) return false; if (size[x] < size[y]) swap(x, y); parent[y] = x; size[x] += size[y]; components--; return true; } }; template <typename T> struct kruskal { struct edge { int a, b; T weight; bool in_tree = false; edge() {} edge(int _a, int _b, T _weight) : a(_a), b(_b), weight(_weight) {} bool operator<(const edge &other) const { return weight < other.weight; } }; union_find UF; vector<edge> edges; kruskal(int n = -1) { if (n >= 0) init(n); } void init(int n) { UF.init(n); edges = {}; } void add_edge(int a, int b, T weight) { edges.emplace_back(a, b, weight); } T solve() { sort(edges.begin(), edges.end()); T total = 0; for (edge &e : edges) if (UF.unite(e.a, e.b)) { total += e.weight; e.in_tree = true; } return total; } }; 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(); kruskal<long long> mst(N); for (int i = 0; i < N; i++) for (edge &e : adj[i]) { e.weight += dist[i] + dist[e.node]; mst.add_edge(i, e.node, e.weight); } mst.solve(); weighted_LCA<long long> lca(N); for (kruskal<long long>::edge &e : mst.edges) if (e.in_tree) lca.add_edge(e.a, e.b, e.weight); lca.build(); for (int q = 0; q < Q; q++) { int a, b; cin >> a >> b; a--; b--; cout << max(lca.query_path_max(a, b), 0LL) << '\n'; } }
#include <bits/stdc++.h> using namespace std; struct state { long long len; int node; const bool operator<(const state oth) const { return len > oth.len; } }; struct edge { int a, b; long long c; } e[400005]; int n, m, k, q; int dad[400005], up[20][400005], dep[400005]; long long mx[20][400005], d[400005]; vector<int> v[400005]; int find(int x) { if (x == dad[x]) return x; return dad[x] = find(dad[x]); } void merge(int x, int y) { dad[dad[x]] = dad[y]; } void dfs(int node, int u) { dep[node] = dep[u] + 1; for (int i = 1; i < 20; i++) { mx[i][node] = max(mx[i - 1][node], mx[i - 1][up[i - 1][node]]); up[i][node] = up[i - 1][up[i - 1][node]]; } for (int ed : v[node]) { int go = e[ed].a ^ e[ed].b ^ node; if (go == u) continue; mx[0][go] = e[ed].c; up[0][go] = node; dfs(go, node); } } long long query(int a, int b) { long long ans = -1; if (dep[a] > dep[b]) swap(a, b); for (int i = 20 - 1; i >= 0; i--) { if (dep[b] - (1 << i) >= dep[a]) { ans = max(ans, mx[i][b]); b = up[i][b]; } } if (a == b) return ans; for (int i = 20 - 1; i >= 0; i--) { if (up[i][a] != up[i][b]) { ans = max(ans, max(mx[i][a], mx[i][b])); a = up[i][a]; b = up[i][b]; } } ans = max(ans, max(mx[0][a], mx[0][b])); return ans; } void build_tree() { for (int i = 1; i <= n; i++) { dad[i] = i; v[i].clear(); } for (int i = 1; i <= m; i++) { e[i].c = d[e[i].a] + d[e[i].b] + e[i].c; } sort(e + 1, e + 1 + m, [](edge a, edge b) { return a.c < b.c; }); for (int i = 1; i <= m; i++) { if (find(e[i].a) != find(e[i].b)) { merge(e[i].a, e[i].b); v[e[i].a].push_back(i); v[e[i].b].push_back(i); } } dfs(1, up[0][1]); } void msp() { memset(d, -1, sizeof(d)); priority_queue<state> Q; for (int i = 1; i <= k; i++) Q.push({0, i}); while (!Q.empty()) { state cur = Q.top(); Q.pop(); if (~d[cur.node]) continue; d[cur.node] = cur.len; for (int ed : v[cur.node]) { int go = e[ed].a ^ e[ed].b ^ cur.node; Q.push({cur.len + e[ed].c, go}); } } } int main() { scanf("%d %d %d %d", &n, &m, &k, &q); for (int i = 1; i <= m; i++) { scanf("%d %d %lld", &e[i].a, &e[i].b, &e[i].c); v[e[i].a].push_back(i); v[e[i].b].push_back(i); } msp(); build_tree(); while (q--) { int x, y; scanf("%d %d", &x, &y); printf("%lld\n", query(x, y)); } }
#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 = 0x3f3f3f3f; 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; int last[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; last[i] = i; 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 (int i = head[u]; ~i; i = es[i].next) { int v = es[i].to; LL w = es[i].cost; if (dis[v] > dis[u] + w) { dis[v] = dis[u] + w; last[v] = last[u]; que.push(P(dis[v], v)); } } } for (int i = 0; i < cnt; ++i) { es[i].cost += dis[es[i].from] + dis[es[i].to]; es[i].from = last[es[i].from]; es[i].to = last[es[i].to]; } } 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() { init(); scanf("%d%d%d%d", &n, &m, &k, &q); int u, v; LL w; for (int i = 0; i < m; ++i) { scanf("%d%d%lld", &u, &v, &w); addedge(u, v, w); addedge(v, u, w); } dijkstra(); Kruskal(); preLCA(); int x, y; int lca; while (q--) { scanf("%d%d", &x, &y); lca = LCA(x, y); printf("%lld\n", max(getMax(x, dep[x] - dep[lca]), getMax(y, dep[y] - dep[lca]))); } return 0; }
#include <bits/stdc++.h> long long dx[8] = {0, 1, 0, -1, 1, 1, -1, -1}; long long dy[8] = {1, 0, -1, 0, -1, 1, 1, -1}; using namespace std; class pa3 { public: long long x; long long y, z; pa3(long long x = 0, long long y = 0, long long z = 0) : x(x), y(y), z(z) {} bool operator<(const pa3 &p) const { if (x != p.x) return x < p.x; if (y != p.y) return y < p.y; return z < p.z; } bool operator>(const pa3 &p) const { if (x != p.x) return x > p.x; if (y != p.y) return y > p.y; return z > p.z; } bool operator==(const pa3 &p) const { return x == p.x && y == p.y && z == p.z; } bool operator!=(const pa3 &p) const { return !(x == p.x && y == p.y && z == p.z); } }; class pa4 { public: long long x; long long y, z, w; pa4(long long x = 0, long long y = 0, long long z = 0, long long w = 0) : x(x), y(y), z(z), w(w) {} bool operator<(const pa4 &p) const { if (x != p.x) return x < p.x; if (y != p.y) return y < p.y; if (z != p.z) return z < p.z; return w < p.w; } bool operator>(const pa4 &p) const { if (x != p.x) return x > p.x; if (y != p.y) return y > p.y; if (z != p.z) return z > p.z; return w > p.w; } bool operator==(const pa4 &p) const { return x == p.x && y == p.y && z == p.z && w == p.w; } }; class pa2 { public: long long x, y; pa2(long long x = 0, long long y = 0) : x(x), y(y) {} pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); } pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); } bool operator<(const pa2 &p) const { return y != p.y ? y < p.y : x < p.x; } bool operator>(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; } bool operator==(const pa2 &p) const { return abs(x - p.x) == 0 && abs(y - p.y) == 0; } bool operator!=(const pa2 &p) const { return !(abs(x - p.x) == 0 && abs(y - p.y) == 0); } }; string itos(long long i) { ostringstream s; s << i; return s.str(); } long long gcd(long long v, long long b) { if (v == 0) return b; if (b == 0) return v; if (v > b) return gcd(b, v); if (v == b) return b; if (b % v == 0) return v; return gcd(v, b % v); } long long mod; long long extgcd(long long a, long long b, long long &x, long long &y) { if (b == 0) { x = 1; y = 0; return a; } long long d = extgcd(b, a % b, y, x); y -= a / b * x; return d; } pair<long long, long long> operator+(const pair<long long, long long> &l, const pair<long long, long long> &r) { return {l.first + r.first, l.second + r.second}; } pair<long long, long long> operator-(const pair<long long, long long> &l, const pair<long long, long long> &r) { return {l.first - r.first, l.second - r.second}; } long long pr[10000100]; long long inv[10000010]; long long beki(long long wa, long long rr, long long warukazu) { if (rr == 0) return 1 % warukazu; if (rr == 1) return wa % warukazu; wa %= warukazu; if (rr % 2 == 1) return ((long long)beki(wa, rr - 1, warukazu) * (long long)wa) % warukazu; long long zx = beki(wa, rr / 2, warukazu); return (zx * zx) % warukazu; } long long comb(long long nn, long long rr) { if (rr < 0 || rr > nn || nn < 0) return 0; long long r = pr[nn] * inv[rr]; r %= mod; r *= inv[nn - rr]; r %= mod; return r; } void gya(long long ert) { pr[0] = 1; for (long long i = 1; i <= ert; i++) { pr[i] = ((long long)pr[i - 1] * i) % mod; } inv[ert] = beki(pr[ert], mod - 2, mod); for (long long i = ert - 1; i >= 0; i--) { inv[i] = (long long)inv[i + 1] * (i + 1) % mod; } } struct unionfind { private: public: vector<long long> par, ranks, kosuu; void shoki(long long N) { par.resize(N + 1, 0); ranks.resize(N + 1, 0); kosuu.resize(N + 1, 1); for (long long i = 0; i <= N; i++) { par[i] = i; } } long long root(long long x) { return par[x] == x ? x : par[x] = root(par[x]); } bool same(long long x, long long y) { return root(x) == root(y); } bool is_root(long long x) { return x == root(x); } void unite(long long x, long long y) { x = root(x); y = root(y); long long xx = kosuu[x], yy = kosuu[y]; if (x == y) return; if (ranks[x] < ranks[y]) { par[x] = y; kosuu[y] = yy + xx; } else { par[y] = x; if (ranks[x] == ranks[y]) ranks[x] = ranks[x] + 1; kosuu[x] = yy + xx; } return; } }; vector<pair<long long, long long>> G[100020]; long long d[100020]; vector<pair<long long, long long>> T[100020]; vector<pair<long long, long long>> T2[100020]; long long depth[100020]; long long dp[100020][20] = {}; long long oya[100020][20]; void dfs(long long r, long long p, long long dep) { depth[r] = dep; for (auto v : T[r]) if (v.first != p) { oya[v.first][0] = r; dp[v.first][0] = v.second; dfs(v.first, r, dep + 1); } } long long lca(long long a, long long b) { if (depth[a] < depth[b]) swap(a, b); long long sa = depth[a] - depth[b]; for (long long i = 0; i < 20; i++) if (sa & (1 << i)) a = oya[a][i]; if (a == b) return a; for (long long i = 19; i >= 0; i--) { if (oya[a][i] != oya[b][i]) { a = oya[a][i]; b = oya[b][i]; } } return oya[a][0]; } long long kyo(long long a, long long d) { long long ans = -1000000007; for (long long i = 19; i >= 0; i--) if (d & (1 << i)) { ans = max(ans, dp[a][i]); a = oya[a][i]; } return ans; } signed main() { cin.tie(0); ios::sync_with_stdio(false); unionfind uf; uf.shoki(100020); long long n, m, k, q; cin >> n >> m >> k >> q; for (long long i = 0; i < m; i++) { long long y, yy, yyy; cin >> y >> yy >> yyy; G[y].push_back(make_pair(yy, yyy)); G[yy].push_back(make_pair(y, yyy)); } for (long long i = 1; i <= n; i++) d[i] = 1000000007 * 10000000ll; priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> pq; for (long long i = 1; i <= k; i++) pq.push(make_pair(0, i)); while (pq.size()) { pair<long long, long long> z = pq.top(); pq.pop(); if (d[z.second] != 1000000007 * 10000000ll) continue; d[z.second] = z.first; for (auto v : G[z.second]) pq.push(make_pair(z.first + v.second, v.first)); } for (long long i = 1; i <= n; i++) { for (auto &v : G[i]) v.second += d[i] + d[v.first]; } vector<pa3> eda; for (long long i = 1; i <= n; i++) for (auto v : G[i]) if (i < v.first) { eda.push_back({v.second, i, v.first}); } sort(eda.begin(), eda.end()); for (auto v : eda) { if (uf.same(v.y, v.z)) continue; uf.unite(v.y, v.z); T[v.y].push_back(make_pair(v.z, v.x)); T[v.z].push_back(make_pair(v.y, v.x)); } oya[1][0] = 1; dfs(1, 1, 1); for (long long i = 1; i < 20; i++) for (long long j = 1; j <= n; j++) { oya[j][i] = oya[oya[j][i - 1]][i - 1]; dp[j][i] = max(dp[j][i - 1], dp[oya[j][i - 1]][i - 1]); } for (long long eR = 0; eR < q; eR++) { long long a, b; cin >> a >> b; long long l = lca(a, b); long long e = -1000000007; if (a != l) e = max(e, kyo(a, depth[a] - depth[l])); if (b != l) e = max(e, kyo(b, depth[b] - depth[l])); cout << e << "\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; } else { markers[a].insert(x); } } } int main() { cin.tie(NULL); ios_base::sync_with_stdio(false); cout.tie(NULL); scanf("%d %d %d %d", &n, &m, &k, &q); vector<Edg> edges; for (int i = 0; i < m; i++) { int u, v, w; scanf("%d %d %d", &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; scanf("%d %d", &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++) { printf("%I64d\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; } constexpr int maxn = 1e5 + 10; constexpr int maxd = 20; vector<pair<int, long long>> G[maxn], G2[maxn]; long long dist[maxn]; int from[maxn]; bool vis[maxn]; int anc[maxn][maxd], dep[maxn], par[maxn]; long long fx[maxn][maxd]; int n, m, k, q; struct edge { int u, v; long long w; bool operator<(const edge &rhs) const { return w < rhs.w; } }; vector<edge> es; void dijkstra() { memset(dist, 0x3f, sizeof(dist)); priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq; for (int s = 1; s <= k; s++) { pq.push(make_pair(0, s)); from[s] = s; dist[s] = 0; } while (!pq.empty()) { long long dis = pq.top().first; int u = pq.top().second; vis[u] = 1; pq.pop(); if (dis != dist[u]) continue; for (auto p : G[u]) { int v = p.first, w = p.second; if (vis[v] && from[v] != from[u]) { es.push_back({from[u], from[v], dist[u] + dist[v] + w}); } if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; from[v] = from[u]; pq.push(make_pair(dist[v], v)); } } } } void dfs(int u, int f) { dep[u] = dep[f] + 1; anc[u][0] = f; for (auto p : G2[u]) { if (p.first == f) continue; fx[p.first][0] = p.second; dfs(p.first, u); } } void init_lca() { for (int j = 1; j < maxd; j++) { for (int i = 1; i <= k; i++) { anc[i][j] = anc[anc[i][j - 1]][j - 1]; fx[i][j] = max(fx[i][j - 1], fx[anc[i][j - 1]][j - 1]); } } } long long query(int u, int v) { if (dep[u] < dep[v]) swap(u, v); long long ans = 0; for (int i = maxd - 1; i >= 0; i--) { if (dep[anc[u][i]] >= dep[v]) { ans = max(ans, fx[u][i]); u = anc[u][i]; } } if (u == v) return ans; for (int i = maxd - 1; i >= 0; i--) { if (anc[u][i] != anc[v][i]) { ans = max(ans, max(fx[u][i], fx[v][i])); u = anc[u][i], v = anc[v][i]; } } ans = max(ans, max(fx[u][0], fx[v][0])); return ans; } int find(int x) { return par[x] == x ? par[x] : par[x] = find(par[x]); } bool unite(int u, int v) { u = find(u), v = find(v); if (u != v) { par[u] = v; return 1; } else return 0; } int main() { 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); G[u].push_back(make_pair(v, w)); G[v].push_back(make_pair(u, w)); } dijkstra(); sort(es.begin(), es.end()); for (int i = 1; i <= k; i++) { par[i] = i; } for (auto e : es) { if (unite(e.u, e.v)) { G2[e.u].push_back(make_pair(e.v, e.w)); G2[e.v].push_back(make_pair(e.u, e.w)); } } dfs(1, 0); init_lca(); for (int i = 0; i < q; i++) { int u, v; scanf("%d%d", &u, &v); long long ans = query(u, v); printf("%lld\n", ans); } return 0; }