2019杭电多校 hdu6662 Acesrc and Travel （树形dp

http://acm.hdu.edu.cn/showproblem.php?pid=6662

题意：有两个人在树上博弈，每个点节点有两个分数a[i]和b[i]，先手先选择一个点，后手在先手选的点的相邻点中选择一个点，然后先手在后手选的点的相邻点中选择一个两个人都没有走过的点，直到不能走，游戏就结束。一个人走到节点x，那么先手会获得分数a[x]，后手就会会获得分数b[x]。最后询问先手能获得与后手的差值最大值。

思路：先手固定好位置后，后手走。有两种走法，向下和向上。

向下好办，用down[i][0]表示我从i走到i的儿子后所能得到的最大值，down[i][1]为对手走的最小值,那么down[i][0] = v[i]+max(down[son][1]), down[i][1]=v[i]+min(down[son][0])

向上的话，走完后对面也分为向上或向下。

向下走时，不能走当前上去的路，所以存每个点向下走的最值和次值，当最值和上去那条路得出的值相同，就换成次值。

向上走时，从上到下一路维护即可。

 #include<bits/stdc++.h>
 #define ll long long
 #define rep(i,a,b) for(int i=a;i<=b;i++)
 using namespace std;
 const int maxn = 1e5+;
 const ll inf = 0x3f3f3f3f3f3f3f3f;
 ll a[maxn],b[maxn];
 int head[maxn],fa[maxn],to[maxn<<],nex[maxn<<],now;

 void add(int a,int b){
     nex[++now] = head[a];
     head[a] = now;
     to[now] = b;
 }

 ll down[maxn][][],up[maxn][];
 bool lef[maxn];

 void dfs(int p){
     down[p][][] = down[p][][] = -inf;
     down[p][][] = down[p][][] = inf;
     lef[p] = ;
     for(int i=head[p];i;i=nex[i]){
         if(to[i]==fa[p]) continue;
         lef[p] = ;
         fa[to[i]] = p;
         dfs(to[i]);
         if(down[to[i]][][]+a[p]>=down[p][][]){
             down[p][][] = down[p][][];
             down[p][][] = down[to[i]][][]+a[p];
         }
         else if(down[to[i]][][]+a[p]>=down[p][][]){
             down[p][][] = down[to[i]][][]+a[p];
         }
         if(down[to[i]][][]+a[p]<=down[p][][]){
             down[p][][] = down[p][][];
             down[p][][] = down[to[i]][][]+a[p];
         }
         else if(down[to[i]][][]+a[p]<=down[p][][]){
             down[p][][] = down[to[i]][][]+a[p];
         }
     }
     if(lef[p]) down[p][][] = down[p][][] = a[p];
 }

 ll Abs(ll a){
     return a>?a:-a;
 }

 void Dfs(int p){
     if(fa[p]==-) up[p][] = up[p][] = inf;
     else {
         up[p][] = inf;
         ll _down = down[fa[p]][][];
         if(_down==a[fa[p]]+down[p][][])
             _down = down[fa[p]][][];
         if(Abs(_down)!=inf)
             up[p][] = min(up[p][],a[p]+_down);
         if(fa[p]!=)
             up[p][] = min(up[p][],a[p]+up[fa[p]][]);
         if(up[p][]==inf)
             up[p][] = a[p]+a[fa[p]];

         up[p][] = -inf;
         _down = down[fa[p]][][];
         if(_down==a[fa[p]]+down[p][][])
             _down=down[fa[p]][][];
         if(Abs(_down)!=inf)
             up[p][]=max(up[p][],a[p]+_down);

         if(fa[p]!=)
             up[p][]=max(up[p][],a[p]+up[fa[p]][]);

         if(up[p][]==-inf)
             up[p][]=a[p]+a[fa[p]];
     }
     for(int i=head[p];i;i=nex[i]){
         if(to[i]==fa[p])continue;
         Dfs(to[i]);
     }
 }

 int main(){
     ios::sync_with_stdio();
     cin.tie();
     cout.tie();
     int t;
     cin>>t;
     while(t--){
         memset(head,,sizeof head);
         now = ;
         int n;
         cin>>n;
         rep(i,,n) cin>>a[i];
         rep(i,,n) cin>>b[i], a[i]-=b[i];
         rep(i,,n-){
             int u,v;
             cin>>u>>v;
             add(u,v);
             add(v,u);
         }
         if(n==){
             cout<<a[]<<endl;
             continue;
         }
         fa[] = -;
         dfs();
         Dfs();
         ll ans = -inf;
         for(int i=;i<=n;i++){
             ll res = inf;
             if(!lef[i]) res = min(res,down[i][][]);
             if(i!=) res = min(res,up[i][]);
             ans = max(ans,res);
         }
         cout<<ans<<endl;
     }
     return ;
 }