BZOJ4890 Tjoi2017城市

　　显然删掉的边肯定是直径上的边。考虑枚举删哪一条。然后考虑怎么连。显然新边应该满足其两端点在各自树中作为根能使树深度最小。只要线性求出这个东西就可以了，这与求树的重心的过程类似。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
#define ll long long
#define N 5010
char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<'0'||c>'9')) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int n,p[N],deep[N],fa[N],f[N],len[N],t,root,ans=N*N;
bool flag[N];
struct data{int to,nxt,len;
}edge[N<<1];
void addedge(int x,int y,int z){t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].len=z,p[x]=t;}
void dfs(int k) 
{
    for (int i=p[k];i;i=edge[i].nxt)
    if (edge[i].to!=fa[k])
    {
        deep[edge[i].to]=deep[k]+edge[i].len;
        fa[edge[i].to]=k;
        len[edge[i].to]=edge[i].len;
        dfs(edge[i].to);
    }
}
int dp(int k,int ban)
{
    flag[k]=1;
    int mx=0,mx2=0,ans=0;
    for (int i=p[k];i;i=edge[i].nxt)
    if (!flag[edge[i].to]&&edge[i].to!=ban)
    {
        ans=max(ans,dp(edge[i].to,ban));
        int x=f[edge[i].to]+edge[i].len;
        if (x>mx) mx2=mx,mx=x;
        else if (x>mx2) mx2=x;
    }
    f[k]=mx;
    return max(ans,mx+mx2);
}
int findroot(int k,int ban,int last)
{
    int mx=0,mx2=0,l=0,len=0;
    for (int i=p[k];i;i=edge[i].nxt)
    if (edge[i].to!=fa[k]&&edge[i].to!=ban)
    {
        int x=f[edge[i].to]+edge[i].len;
        if (x>mx) mx2=mx,mx=x,l=edge[i].to,len=edge[i].len;
        else if (x>mx2) mx2=x;
    }
    if (max(last,mx2)+len<mx) return findroot(l,ban,max(last,mx2)+len);
    else return k;
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj4890.in","r",stdin);
    freopen("bzoj4890.out","w",stdout);
    const char LL[]="%I64d
";
#else
    const char LL[]="%lld
";
#endif
    n=read();
    for (int i=1;i<n;i++)
    {
        int x=read(),y=read(),z=read();
        addedge(x,y,z),addedge(y,x,z);
    }
    dfs(1);
    int root=1;for (int i=2;i<=n;i++) if (deep[i]>deep[root]) root=i;
    fa[root]=deep[root]=0;dfs(root);
    int x=1;for (int i=2;i<=n;i++) if (deep[i]>deep[x]) x=i;
    while (x!=root)
    {
        memset(f,0,sizeof(f));
        memset(flag,0,sizeof(flag));
        int t=max(dp(root,x),dp(x,fa[x]));
        int u=findroot(root,x,0),v=findroot(x,fa[x],0);
        memset(f,0,sizeof(f));
        memset(flag,0,sizeof(flag));
        dp(u,x),dp(v,fa[x]);
        ans=min(ans,max(f[u]+f[v]+len[x],t));
        x=fa[x];
    }
    cout<<ans;
    return 0;
}