Drivers Dissatisfaction 最小生成树+LCA

题意：给一张n个点m条边的连通图，每条边(ai,bi)有一个权值wi和费用ci，

表示这条边每降低1的权值需要ci的花费。现在一共有S费用可以用来降低某些边的权值

（可以降到负数），求图中的一棵权值和最小的生成树并输出方案

显然是找到一条边然后将这条边减到最小

先跑一边最小生成树，找到树上最小的一点，然后在枚举其他的边，

加上这条边会产生一个环，所以需要删除这个环上面权值最大的边

这个通过类似于LCA倍增的手法做到，

 #include <cstdio>
 #include <cstring>
 #include <queue>
 #include <cmath>
 #include <algorithm>
 #include <set>
 #include <iostream>
 #include <map>
 #include <stack>
 #include <string>
 #include <vector>
 #define  pi acos(-1.0)
 #define  eps 1e-6
 #define  fi first
 #define  se second
 #define  rtl   rt<<1
 #define  rtr   rt<<1|1
 #define  bug         printf("******\n")
 #define  mem(a,b)    memset(a,b,sizeof(a))
 #define  name2str(x) #x
 #define  fuck(x)     cout<<#x" = "<<x<<endl
 #define  f(a)        a*a
 #define  sf(n)       scanf("%d", &n)
 #define  sff(a,b)    scanf("%d %d", &a, &b)
 #define  sfff(a,b,c) scanf("%d %d %d", &a, &b, &c)
 #define  sffff(a,b,c,d) scanf("%d %d %d %d", &a, &b, &c, &d)
 #define  pf          printf
 #define  FRE(i,a,b)  for(i = a; i <= b; i++)
 #define  FREE(i,a,b) for(i = a; i >= b; i--)
 #define  FRL(i,a,b)  for(i = a; i < b; i++)+
 #define  FRLL(i,a,b) for(i = a; i > b; i--)
 #define  FIN         freopen("data.txt","r",stdin)
 #define  gcd(a,b)    __gcd(a,b)
 #define  lowbit(x)   x&-x
 using namespace std;
 typedef long long  LL;
 typedef unsigned long long ULL;
 const int mod = 1e9 + ;
 const int maxn = 2e5 + ;
 const int INF = 0x3f3f3f3f;
 const LL INFLL = 0x3f3f3f3f3f3f3f3fLL;
 int n, m, c[maxn], w[maxn], fa[maxn], vis[maxn];
 int dep[maxn], p[maxn][], maxx[maxn][];
 struct Edge {
     int u, v, w, id;
 } edge[maxn];
 int cmp ( Edge a, Edge b ) {
     return a.w < b.w;
 }
 struct xxx {
     int v, id;
     xxx ( int v, int id ) : v ( v ), id ( id ) {}
 };
 vector<xxx>mp[maxn];
 int Find ( int x ) {
     return fa[x] == x ? x : fa[x] = Find ( fa[x] );
 }
 void dfs ( int u, int f, int id ) {
     dep[u] = dep[f] + , p[u][] = f, maxx[u][] = id;
     for ( int i =  ; i <=  ; i++ ) {
         if ( dep[u] - (  << i ) <=  ) break;
         int v = p[u][i - ];
         p[u][i] = p[v][i - ];
         if ( w[maxx[u][i - ]] < w[maxx[v][i - ]] ) maxx[u][i] = maxx[v][i - ];
         else maxx[u][i] = maxx[u][i - ];
     }
     for ( int i =  ; i < mp[u].size() ; i++ ) {
         int v = mp[u][i].v, id = mp[u][i].id;
         if ( v != f ) dfs ( v, u, id );
     }
 }
 int get_max ( int x, int y ) {
     if ( dep[x] < dep[y] ) swap ( x, y );
     int temp = , ans = ;
     for ( int i =  ; i >=  ; i-- ) {
         if ( dep[x] - (  << i ) >= dep[y] ) {
             if ( w[maxx[x][i]] > temp ) ans = maxx[x][i], temp = w[ans];
             x = p[x][i];
         }
     }
     if ( x == y ) return ans;
     for ( int i =  ; i >=  ; i-- ) {
         if ( dep[x] - (  << i ) >  && p[x][i] != p[y][i] ) {
             if ( w[maxx[x][i]] > temp ) ans = maxx[x][i], temp = w[ans];
             if ( w[maxx[y][i]] > temp ) ans = maxx[y][i], temp = w[ans];
             x = p[x][i], y = p[y][i];
             if ( x == y ) break;
         }
     }
     if ( w[maxx[x][]] > temp ) ans = maxx[x][], temp = w[ans];
     if ( w[maxx[y][]] > temp ) ans = maxx[y][], temp = w[ans];
     return ans;
 }
 int main() {
     sff ( n, m );
     for ( int i =  ; i <= m ; i++ ) sf ( w[i] );
     for ( int i =  ; i <= m ; i++ ) sf ( c[i] );
     for ( int i =  ; i <= m ; i++ ) {
         sff ( edge[i].u, edge[i].v );
         edge[i].w = w[i], edge[i].id = i;
     }
     sort ( edge + , edge +  + m, cmp );
     LL sum = , s, minn = INF, idx = , k = ;
     scanf ( "%lld", &s );
     for ( int i =  ; i <= n ; i++ ) fa[i] = i;
     for ( int i =  ; i <= m ; i++ ) {
         int nx = Find ( edge[i].v ), ny = Find ( edge[i].u );
         if ( nx == ny ) continue;
         fa[nx] = ny;
         sum += edge[i].w;
         vis[edge[i].id] = , k++;
         if ( c[edge[i].id] < minn )  idx = edge[i].id, minn = c[edge[i].id];
         mp[edge[i].u].push_back ( xxx ( edge[i].v, edge[i].id ) );
         mp[edge[i].v].push_back ( xxx ( edge[i].u, edge[i].id ) );
         if ( k == n -  ) break;
     }
     LL ans = sum - s / minn;
     dep[] = ;
     dfs ( , ,  );
     int del = ;
     for ( int i =  ; i <= m ; i++ ) {
         if ( vis[edge[i].id]  ) continue;
         int cnt = get_max ( edge[i].u, edge[i].v );
         if ( cnt ==  ) continue;
         LL temp = sum - w[cnt] + w[edge[i].id] - s / c[edge[i].id];
         if ( temp < ans ) ans = temp,  idx = edge[i].id, del = cnt;
     }
     if ( del ) vis[del] = , vis[idx] = ;
     printf ( "%lld\n", ans );
     w[idx] -= s / c[idx];
     for ( int i =  ; i <= m ; i++ ) if ( vis[i] ) printf ( "%d %d\n", i, w[i] );
     return ;
 }