luoguP4234 最小差值生成树

Posted 2021-01-03 ljc00118

https://www.luogu.org/problemnew/show/P4234

按照边的权值从小到大排序，依次加入，并删除能够删除的权值最小的一条边，用 set 维护当前所有边的边权，并查集维护联通性，LCT 维护两点间最小值和 link cut 操作即可

#include <bits/stdc++.h>
#define mp make_pair
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 = 250000 + 10;

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

set < pair <int, int> > Min;
int fa[N], ch[N][2], rev[N], minn[N], val[N], wz[N], st[N], f[N], n, m, len, cnt, 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) {
    minn[u] = val[u]; wz[u] = u;
    if(minn[ch[u][0]] < minn[u] && ch[u][0]) minn[u] = minn[ch[u][0]], wz[u] = wz[ch[u][0]];
    if(minn[ch[u][1]] < minn[u] && ch[u][1]) minn[u] = minn[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;
}

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, val[i] = INT_MAX;
    for(int i = 1; i <= m; i++) {
        read(p[i].u);
        read(p[i].v);
        read(p[i].a);
    }
    sort(p + 1, p + m + 1);
    for(int i = 1; i <= m; i++) {
        int x = p[i].u, y = p[i].v;
        if(find(x) != find(y)) {
            cnt++; f[find(x)] = find(y);
            val[i + n] = p[i].a;
            link(i + n, x);
            link(i + n, y);
            Min.insert(mp(p[i].a, i)); 
        } else {
            if(x == y) continue;
            int wz = query(x, y);
            val[i + n] = p[i].a;
            cut(wz, p[wz - n].u);
            cut(wz, p[wz - n].v);
            link(i + n, x);
            link(i + n, y);
            Min.erase(mp(p[wz - n].a, wz - n));
            Min.insert(mp(p[i].a, i));
        }
        if(cnt == n - 1) {
            set < pair <int, int> > :: iterator it = Min.begin();
            ans = min(ans, p[i].a - it -> first);
        }
    }
    cout << ans << endl;
    return 0;
}