CF911F Tree Destruction 解题报告

Posted 2021-01-11 ppprseter

CF911F Tree Destruction

题意翻译

给你一棵树,每次挑选这棵树的两个叶子,加上他们之间的边数(距离),然后将其中一个点去掉,问你边数(距离)之和最大可以是多少.

输入输出格式

输入格式：

The first line contains one integer number n (n) ( (2 le n le 2 imes 10^{5}) ) — the number of vertices in the tree.

Next (n-1) lines describe the edges of the tree in form (a_{i}),(b_{i})( (1<=a_{i}), (b_{i}<=n) , (a_{i} ot= b_{i}) ). It is guaranteed that given graph is a tree.

输出格式：

In the first line print one integer number — maximal possible answer.

In the next (n-1) lines print the operations in order of their applying in format (a_{i},b_{i},c_{i}) , where (a_{i},b_{i})— pair of the leaves that are chosen in the current operation ( (1 le a_{i}) ,(b_{i} le n) ), (c_{i}) ( (1 le c_{i} le n) , (c_{i}=a_{i}) or (c_{i}=b_{i}) ) — choosen leaf that is removed from the tree in the current operation.

See the examples for better understanding.

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给了一个贪心的思路：不会产生比最好情况下还要差的结果（由最优推最优）

首先如果只有一条链，答案是很显然的。

如果链外有点，点到链的某个端点一定是所有情况的最优贡献，并且删去链外的点对链本身没有影响。

所以策略就是找到直径的那条链，一个一个删外面的点，最后删直径的。

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Code:

#include <cstdio>
#define ll long long
const int N=2e5+10;
int Next[N<<1],to[N<<1],head[N],cnt;
void add(int u,int v)
{
    to[++cnt]=v,Next[cnt]=head[u],head[u]=cnt;
}
int mx=-1,l,r;
void dfs1(int now,int fa,int d)
{
    if(mx<d) mx=d,l=now;
    for(int i=head[now];i;i=Next[i])
    {
        int v=to[i];
        if(v!=fa)
            dfs1(v,now,d+1);
    }
}
int pre[N];
void dfs2(int now,int fa,int d)
{
    if(mx<d) mx=d,r=now;
    for(int i=head[now];i;i=Next[i])
    {
        int v=to[i];
        if(v!=fa)
            pre[v]=now,dfs2(v,now,d+1);
    }
}
ll sum;
int ans[N][2],is[N],n,opt;
void dfs0(int now,int fa,int d,int s)
{
    for(int i=head[now];i;i=Next[i])
    {
        int v=to[i];
        if(is[v]||v==fa) continue;
        dfs0(v,now,d+1,s);
    }
    if(!is[now]) ans[++opt][0]=now,ans[opt][1]=s,sum+=1ll*d;
}
int main()
{
    scanf("%d",&n);
    for(int u,v,i=1;i<n;i++)
    {
        scanf("%d%d",&u,&v);
        add(u,v),add(v,u);
    }
    dfs1(1,0,0);
    mx=-1;
    dfs2(l,0,0);
    int now=r,cnt1=0,cnt0=0;
    while(now)
        ++cnt1,is[now]=1,now=pre[now];
    now=r;
    while(now)
    {
        ++cnt0;
        if(((cnt0-1)<<1)>cnt1-1)
            dfs0(now,0,cnt0-1,r);
        else
            dfs0(now,0,cnt1-cnt0,l);

        now=pre[now];
    }
    now=r,cnt0=0;
    while(now)
    {
        ++cnt0;
        ans[++opt][0]=now,ans[opt][1]=l,sum+=1ll*(cnt1-cnt0);
        now=pre[now];
    }
    printf("%lld
",sum);
    for(int i=1;i<n;i++)
        printf("%d %d %d
",ans[i][0],ans[i][1],ans[i][0]);
    return 0;
}

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2018.10.11