codeforces 827D（kruskal+倍增+并查集）

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题解：先求出最小生成树，用倍增LCA求出不在最小生成树中的边的答案，同时再用这个答案它去更新最小生成树中的边的答案。为了提高更新这一操作的效率，枚举有序（从小到大）的边集，更新过的用并查集连在一起（由于从小到大，小的最优，下条边一定不会再次更新它们），下一次直接往上跳即可。

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>using namespace std;const int MAXN=2e5+2,INF=0x3f3f3f3f;struct kruskal {    int u,v,w,id;    friend bool operator <(const kruskal &a,const kruskal &b) {        return a.w<b.w;    }}kr[MAXN];int head[MAXN],edge;struct EDGE {    int v,nxt,w,id;}e[MAXN<<1];bool inm[MAXN];int n,m;int fa[MAXN];int ans[MAXN];int anc[MAXN][19],mx[MAXN][19],dep[MAXN],up[MAXN];inline int read() {    int x=0;char c=getchar();    while (c<'0'||c>'9') c=getchar();    while (c>='0'&&c<='9') x=x*10+c-'0',c=getchar();    return x;}inline void adde(int u,int v,int w,int id) {    e[edge].nxt=head[u],e[edge].v=v,e[edge].id=id,e[edge].w=w,head[u]=edge++;    e[edge].nxt=head[v],e[edge].v=u,e[edge].id=id,e[edge].w=w,head[v]=edge++;}int find(int x) {    return fa[x]==x?x:fa[x]=find(fa[x]);}void dfs(int p,int f,int d) {    dep[p]=dep[f]+1,anc[p][0]=f,mx[p][0]=d;    for (int i=1;i<=18;++i) anc[p][i]=anc[anc[p][i-1]][i-1],mx[p][i]=max(mx[p][i-1],mx[anc[p][i-1]][i-1]);    for (int i=head[p];~i;i=e[i].nxt) {        int v=e[i].v;        if (v==f) continue;        up[v]=e[i].id,dfs(v,p,e[i].w);    }}int lca(int x,int y,int &d) {    d=0;if (dep[x]<dep[y]) x^=y^=x^=y;    for (int i=18;i>=0;--i) {        if (dep[anc[x][i]]>=dep[y]) {            d=max(d,mx[x][i]);            x=anc[x][i];        }    }    if (x==y) return x;    for (int i=18;i>=0;--i) {        if (anc[x][i]^anc[y][i]) {            d=max(d,max(mx[x][i],mx[y][i]));            x=anc[x][i],y=anc[y][i];        }    }    d=max(d,max(mx[x][0],mx[y][0]));    return anc[x][0];}void modify(int x,int lca,int w) {    x=find(x);    while (dep[x]>dep[lca]) {        ans[up[x]]=min(ans[up[x]],w);        int y=find(anc[x][0]);        fa[x]=y;        x=find(x);    }}int main() {//  freopen("codeforces 827D.in","r",stdin);    while (~scanf("%d%d",&n,&m)) {        memset(head,-1,sizeof(head));        memset(inm,0,sizeof(inm));        edge=0;        for (register int i=1;i<=n;++i) fa[i]=i;        for (register int i=1;i<=m;++i) kr[i].id=i,kr[i].u=read(),kr[i].v=read(),kr[i].w=read();        sort(kr+1,kr+m+1);        int blo=n;        for (register int i=1;i<=m&&blo>1;++i) {            int u=kr[i].u,v=kr[i].v;            u=find(u),v=find(v);            if (u^v) {                fa[u]=v,inm[i]=true,--blo;                adde(kr[i].u,kr[i].v,kr[i].w,kr[i].id);            }        }        dfs(1,0,0);        memset(ans,INF,sizeof(ans));        for (register int i=1;i<=n;++i) fa[i]=i;        for (register int i=1;i<=m;++i) {            if (inm[i]) continue;            int u=kr[i].u,v=kr[i].v,f=lca(u,v,ans[kr[i].id]);            --ans[kr[i].id];            modify(u,f,kr[i].w-1);            modify(v,f,kr[i].w-1);        }        for (int i=1;i<=m;++i)            printf("%d\n",ans[i]==INF?-1:ans[i]);    }    return 0;}