609E - Minimum spanning tree for each edge

给出一个带权图，对每个边求经过这条边的MST

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先求一遍MST自然是极好的，然后对于在MST上的边，自然就是全局MST了

对于不在MST上的边，找到这个边两个端点在MST上的路径上最大权的边并去掉，然后加上询问的这条边的权就好了

#include<bits/stdc++.h>using namespace std;#define LL long long const int maxn = 212345,maxm = 212345,max_log = 18;const int ROOT = 1;vector<pair<int,LL> >edge[maxn];void Link(int st,int ed,LL v){    edge[st].push_back(make_pair(ed,v));}int deep[maxn],fa[maxn][max_log];int nofa[maxn];struct Info{    LL x;    Info(LL x = 0):x(x){};};Info operator + (const Info a,const Info b){    return Info(max(a.x,b.x));}Info info[maxn][max_log];void dfs(int st,int Fa,int Deep=1){    for(int i=1;i<max_log;i++)        fa[st][i] = -1,info[st][i] = Info();    fa[st][0] = Fa,deep[st] = Deep;    for(auto x : edge[st]){        if(x.first == Fa) continue;        dfs(x.first,st,Deep+1);        info[x.first][0] = Info(x.second);    }}void init(int n){    memset(fa,-1,sizeof(fa));    dfs(ROOT,-1);    for (int j = 1;j < max_log;j++){        for (int i = 1;i <= n;i++){            if (fa[i][j-1] != -1){                fa[i][j] = fa[fa[i][j-1]][j-1];                info[i][j] = info[i][j-1] + info[fa[i][j-1]][j-1];            }        }    }}pair<int,Info> lca(int x,int y){    Info ix,iy;    if (deep[x] < deep[y]) swap(x,y);    for (int i = max_log-1;i >= 0;i--){        if (deep[fa[x][i]] >= deep[y]){            ix = ix + info[x][i];            x = fa[x][i];        }    }    if (x == y) return make_pair(x,ix);    for (int i = max_log-1;i >= 0;i--){        if (fa[x][i] != fa[y][i]){            ix = ix + info[x][i]; x = fa[x][i];             iy = iy + info[y][i]; y = fa[y][i];         }    }    return make_pair(fa[x][0], ix/*.rev()*/+info[x][0] + info[y][0] + iy);}struct Edge{    int x,y;    LL v,i;    void init(int id){        scanf("%d %d %I64d",&x,&y,&v);        i = id;    }}edg[maxm];struct Dsu{    int arr[maxn];    void init(int n){for(int i=0;i<=n;i++) arr[i] = i;}    int fnd(int x){return x == arr[x] ? x : arr[x] = fnd(arr[x]);}    bool join(int x,int y){        x = fnd(x),y = fnd(y);        if(x == y) return false;        arr[x] = y;        return true;    }}dsu;int main(){    int n,m;    scanf("%d %d",&n,&m);    for(int i=0;i<m;i++){        edg[i].init(i);    }    sort(edg,edg+m,[](Edge a,Edge b){return a.v < b.v;});    dsu.init(n);    LL all = 0;    for(int i=0;i<m;i++){        if(dsu.join(edg[i].x,edg[i].y)){            all += edg[i].v;            Link(edg[i].x,edg[i].y,edg[i].v);            Link(edg[i].y,edg[i].x,edg[i].v);        }    }    init(n);    sort(edg,edg+m,[](Edge a,Edge b){return a.i < b.i;});    for(int i=0;i<m;i++){        printf("%I64d\n",all + edg[i].v - lca(edg[i].x,edg[i].y).second.x);    }    return 0;}