[题目链接]
https://www.lydsy.com/JudgeOnline/problem.php?id=3669
[算法]
首先离线 ， 将边按A值从小到大排序
然后用LCT动态维护以B值为关键字的最小生成树即可
时间复杂度 : O(NlogN ^ 2)
[代码]
#include<bits/stdc++.h> using namespace std; const int MAXN = 2e5 + 10; typedef long long ll; typedef long double ld; typedef unsigned long long ull; const ll inf = 2e9; struct edge { int x , y , a , b; } e[MAXN]; int n , m; struct Link_Cut_Tree { struct Node { int father , son[2] , id , mx , value; bool tag; } a[MAXN]; inline void update(int x) { a[x].mx = a[x].value; a[x].id = x; if (a[x].son[0]) { if (a[a[x].son[0]].mx > a[x].mx) { a[x].mx = a[a[x].son[0]].mx; a[x].id = a[a[x].son[0]].id; } } if (a[x].son[1]) { if (a[a[x].son[1]].mx > a[x].mx) { a[x].mx = a[a[x].son[1]].mx; a[x].id = a[a[x].son[1]].id; } } } inline void init() { for (int i = n + 1; i <= n + m + 1; i++) { a[i].mx = a[i].value = e[i - n].b; a[i].id = i; } } inline void pushdown(int x) { if (a[x].tag) { swap(a[x].son[0] , a[x].son[1]); a[a[x].son[0]].tag ^= 1; a[a[x].son[1]].tag ^= 1; a[x].tag = false; } } inline bool get(int x) { pushdown(a[x].father); return a[a[x].father].son[1] == x; } inline bool nroot(int x) { return a[a[x].father].son[0] == x | a[a[x].father].son[1] == x; } inline void rotate(int x) { int f = a[x].father , g = a[f].father; int tmpx = get(x) , tmpf = get(f); int w = a[x].son[tmpx ^ 1]; if (nroot(f)) a[g].son[tmpf] = x; a[x].son[tmpx ^ 1] = f; a[f].son[tmpx] = w; if (w) a[w].father = f; a[f].father = x; a[x].father = g; update(f); } inline int find_root(int x) { access(x); splay(x); while (a[x].son[0]) { pushdown(x); x = a[x].son[0]; } return x; } inline void access(int x) { for (int y = 0; x; x = a[y = x].father) { splay(x); a[x].son[1] = y; update(x); } } inline void splay(int x) { int y = x , z = 0; static int st[MAXN]; st[++z] = y; while (nroot(y)) st[++z] = y = a[y].father; while (z) pushdown(st[z--]); while (nroot(x)) { int y = a[x].father , z = a[y].father; if (nroot(y)) rotate((a[y].son[0] == x) ^ (a[z].son[0] == y) ? x : y); rotate(x); } update(x); } inline void split(int x , int y) { make_root(x); access(y); splay(y); } inline void make_root(int x) { access(x); splay(x); a[x].tag ^= true; pushdown(x); } inline void link(int x , int y) { make_root(x); if (find_root(y) != x) a[x].father = y; } inline void cut(int x , int y) { make_root(x); if (find_root(y) == x && a[x].father == y && !a[x].son[1]) { a[x].father = a[y].son[0] = 0; update(y); } } inline bool connected(int x , int y) { return (find_root(x) == find_root(y)); } inline int query(int x , int y) { split(x , y); return a[y].id; } } LCT; template <typename T> inline void chkmax(T &x,T y) { x = max(x,y); } template <typename T> inline void chkmin(T &x,T y) { x = min(x,y); } template <typename T> inline void read(T &x) { T f = 1; x = 0; char c = getchar(); for (; !isdigit(c); c = getchar()) if (c == '-') f = -f; for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0'; x *= f; } inline bool cmp(edge a , edge b) { return a.a < b.a; } int main() { read(n); read(m); for (int i = 1; i <= m; i++) { read(e[i].x); read(e[i].y); read(e[i].a); read(e[i].b); } sort(e + 1 , e + m + 1 , cmp); LCT.init(); int ans = inf; for (int i = 1; i <= m; i++) { if (LCT.connected(e[i].x , e[i].y)) { int id = LCT.query(e[i].x , e[i].y); if (id - n > 0 && e[i].b < e[id - n].b) { LCT.cut(e[id - n].x , id); LCT.cut(e[id - n].y , id); LCT.link(e[i].x , i + n); LCT.link(e[i].y , i + n); } } else { LCT.link(e[i].x , i + n); LCT.link(e[i].y , i + n); } if (LCT.connected(1 , n)) chkmin(ans , e[i].a + e[LCT.query(1 , n) - n].b); } if (LCT.connected(1 , n)) printf("%d " , ans); else printf("-1 "); return 0; }