hdu 4912 贪心+最近公共祖先

先对所有的路径求取lca,然后按照lca从大到小的顺序选取路径

若一条路径p1的lca(p1) 的深度大于p2的lca(p2),那么若p1和p2出现冲突,那么p1一定包含p2的lca(p2),那么p2只可能与以lca(p2)为子树中的路径冲突,而p1要冲突的范围更大,两个的贡献同样是1,如果存在一棵比lca(p1)和lca(p2)深度都大的子树中的子树中路径,如果它和p1不冲突,却和p2冲突,那么它已经将p2淘汰,但不会影响p1的选取,所以当前贪心策略是正确的.

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#define MAX 200007

using namespace std;

int ce , cq;

struct edge
{
    int v,next;
}e[MAX<<1];

struct query
{
    int u,v,next,lca,dep;
    bool operator < ( const query& a ) const
    {
        return dep > a.dep;
    }
}q[MAX<<1];

int head1[MAX];
int head2[MAX];
int depth[MAX];

void adde ( int u , int v )
{
    e[ce].v = v;
    e[ce].next = head1[u];
    head1[u] = ce++;
}

void addq ( int u , int v )
{
    q[cq].u = u;
    q[cq].v = v;
    q[cq].next = head2[u];
    head2[u] = cq++;
}

int fa[MAX];

int find ( int x )
{
    return fa[x] == x ? x : fa[x] = find ( fa[x] );
}

void lca ( int u = 1 , int p = -1 )
{
    for ( int i = head1[u] ; i != -1 ; i = e[i].next )
    {
        int v = e[i].v;
        if ( v == p ) continue;
        lca ( v , u );
        fa[v] = u;
    }
    for ( int i = head2[u] ; i != -1 ; i = q[i].next )
    {
        int v = q[i].v;
        q[i].lca = q[i^1].lca = find ( v );
        q[i].dep = q[i^1].dep = depth[q[i].lca];
    }
} 

bool vis[MAX];
int pa[MAX];

void dfs ( int u = 1 , int p = -1 , int deep = 1 )
{
    depth[u] = deep;
    if (  p == -1  ) pa[u] = u;
    else pa[u] = p;
    for ( int i = head1[u] ; i != -1 ; i = e[i].next )
    {
        int v = e[i].v;
        if ( v == p ) continue;
        dfs ( v , u , deep + 1 );
    }
}

void paint ( int i  , int u )
{
    int lca = q[i].lca;
    while ( u != lca )   
        vis[u] = 1 , u = pa[u];
    u = q[i].v;
    while ( u != lca )
        vis[u] = 1 , u = pa[u];
    vis[lca] = 1;
}

bool judge ( int i , int u )
{
    int lca = q[i].lca;
    if ( vis[u] || vis[lca] || vis[q[i].v] ) return false;
    while ( u != lca )
    {
       // cout<< u <<  "vis :" << vis[u] << endl;
        if ( vis[u] ) return false;
        else u = pa[u];
    }
    u = q[i].v;
    while ( u != lca )
    {
     // cout << u << " vis : " << vis[u] << endl;
      if ( vis[u] ) return false;
      else u = pa[u];
    }
    if ( vis[lca] ) return false;
    return true;  
}

int main ( )
{
    int n,m,u,v;
    while ( ~scanf ( "%d%d" , &n , &m ) )
    {
        ce = cq = 0;
        memset ( head1 , -1 , sizeof ( head1 ));
        memset ( head2 , -1 , sizeof ( head2 ));
        memset ( vis , 0 , sizeof ( vis ) );
        for ( int i = 1 ; i <= n ; i++ ) fa[i] = i;
        for ( int i = 1 ; i < n ; i++ )
        {
            scanf ( "%d%d" , &u , &v );
            adde ( u , v );
            adde ( v , u );
        }
        for ( int i = 0 ; i < m ; i++ )
        {
            scanf ( "%d%d" , &u , &v );
            addq ( u , v );
            addq ( v , u );
        }
        dfs ();
        lca ();
        sort ( q , q+2*m );
        int ans = 0;
      //  for ( int i = 1 ; i <= n ; i++ )
      //      cout << i <<" :  " << pa[i] << endl; 
        for ( int i = 0 ; i < cq ; i++ )
        {
            //if ( !vis[q[id].u] && !vis[q[id].v] && !vis[q[id].lca] )
           if ( judge ( i , q[i].u ) )
            {
               // cout << q[id].u << " " << q[id].v << endl;
             //   cout << "YES" << endl;
                ans++;
                paint ( i , q[i].u );
            }
           // for ( int i = 1 ; i <= n ; i ++ )
             //      cout << vis[u] << " ";
           // cout << endl;
        }
        printf ( "%d\n" , ans );
    }
}