luoguP2387 [NOI2014]魔法森林

https://www.luogu.org/problemnew/show/P2387

考虑先将所有边按 a 值排序，依次加入每一条边，如果这条边的两个端点 ( l, r ) 之间的简单路径中 b 的最大值大于这条边的 b 值，删掉最大的一条边，加入这条边，如果 l 和 r 不连通，则直接 link

需要注意的是将边权转换为点权，将第 i 条边变成编号为 i + n 的点，维护最大值的位置就可以了

这题还有自环( 坑了我半个小时 )

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long ull;
typedef long long ll;

template <typename _T>
inline void read(_T &f) {
    f = 0; _T fu = 1; char c = getchar();
    while(c < '0' || c > '9') {if(c == '-') fu = -1; c = getchar();}
    while(c >= '0' && c <= '9') {f = (f << 3) + (f << 1) + (c & 15); c = getchar();}
    f *= fu;
}

const int N = 150000 + 10;

struct ele {
    int u, v, a, b;
    bool operator < (const ele A) const {return a < A.a;}
}p[N];

int fa[N], ch[N][2], maxn[N], val[N], rev[N], wz[N], st[N], f[N], n, m, len, ans = INT_MAX;

int isroot(int u) {return ch[fa[u]][0] != u && ch[fa[u]][1] != u;}

int get(int u) {return ch[fa[u]][1] == u;}

void update(int u) {
    maxn[u] = val[u]; wz[u] = u;
    if(maxn[ch[u][0]] > maxn[u] && ch[u][0]) maxn[u] = maxn[ch[u][0]], wz[u] = wz[ch[u][0]];
    if(maxn[ch[u][1]] > maxn[u] && ch[u][1]) maxn[u] = maxn[ch[u][1]], wz[u] = wz[ch[u][1]];
}

void pushdown(int u) {
    if(rev[u]) {
        swap(ch[u][0], ch[u][1]);
        rev[ch[u][0]] ^= 1;
        rev[ch[u][1]] ^= 1;
        rev[u] ^= 1;
    }
}

void rotate(int u) {
    int old = fa[u], oldd = fa[old], k = get(u);
    if(!isroot(old)) ch[oldd][get(old)] = u; fa[u] = oldd;
    ch[old][k] = ch[u][k ^ 1]; fa[ch[u][k ^ 1]] = old;
    fa[old] = u; ch[u][k ^ 1] = old;
    update(old); update(u);
}

void splay(int u) {
    st[len = 1] = u;
    for(int i = u; !isroot(i); i = fa[i]) st[++len] = fa[i];
    for(int i = len; i >= 1; i--) pushdown(st[i]);
    for(; !isroot(u); rotate(u)) if(!isroot(fa[u])) rotate(get(u) == get(fa[u]) ? fa[u] : u);
}

void access(int u) {
    for(int i = 0; u; i = u, u = fa[u]) {
        splay(u);
        ch[u][1] = i;
        update(u);
    }
}

void makeroot(int u) {
    access(u);
    splay(u);
    rev[u] ^= 1;
}

int findroot(int u) {
    access(u); splay(u);
    while(ch[u][0]) u = ch[u][0];
    return u;
}

void link(int u, int v) {
    makeroot(u);
    fa[u] = v;
}

void cut(int u, int v) {
    makeroot(u);
    access(v);
    splay(v);
    fa[u] = ch[v][0] = 0;
    update(v);
}

int query(int u, int v) {
    makeroot(u);
    access(v);
    splay(v);
    return wz[v]; 
}

int find(int x) {return f[x] == x ? x : f[x] = find(f[x]);}

int main() {
    read(n); read(m);
    for(int i = 1; i <= n; i++) f[i] = i;
    for(int i = 1; i <= m; i++) {
        read(p[i].u); read(p[i].v);
        read(p[i].a); read(p[i].b);
    }
    sort(p + 1, p + m + 1);
    for(int i = 1; i <= m; i++) {
        int x = p[i].u, y = p[i].v;
        int A = p[i].a, B = p[i].b;
        if(find(x) != find(y)) {
            f[find(x)] = find(y);
            val[i + n] = maxn[i + n] = B;
            link(x, i + n); link(y, i + n);
        } else {
            if(x == y) continue;
            int weizhi = query(x, y);
            if(p[weizhi - n].b > B) {
                cut(p[weizhi - n].u, weizhi);
                cut(p[weizhi - n].v, weizhi);
                val[i + n] = maxn[i + n] = B;
                link(x, i + n); link(y, i + n);
            }
        }
        if(find(1) == find(n)) ans = min(ans, p[query(1, n) - n].b + A);
    }
    if(ans == INT_MAX) cout << -1 << endl; else cout << ans << endl;
    return 0;
}