hdu 3966 Aragorn's Story（树链剖分+树状数组/线段树）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3966

题意：

给出一棵树，并给定各个点权的值，然后有3种操作：

I C1 C2 K: 把C1与C2的路径上的所有点权值加上K

D C1 C2 K：把C1与C2的路径上的所有点权值减去K

Q C：查询节点编号为C的权值

分析：

典型的树链剖分，对节点进行操作，可以用树状数组或者线段树。

树链剖分+树状数组：

 #include<iostream>
 #include<cstdio>
 #include<cmath>
 #include<cstring>

 using namespace std;
 const int maxn = ;

 struct Edge
 {
     int to,next;
 }edge[maxn*];
 int head[maxn],cnt,num;
 int a[maxn],n,m,p,c[maxn];
 int size[maxn],top[maxn],id[maxn],fa[maxn],son[maxn],dep[maxn];

 void init()
 {
     memset(head,-,sizeof(head));
     memset(son,-,sizeof(son));
     memset(c,,sizeof(c));
     cnt=;
     num=;
 }
 void addedge(int u,int v)
 {
     edge[cnt].to = v;
     edge[cnt].next = head[u];
        head[u] = cnt++;
 }

 void dfs_1(int u,int f,int d)
 {
     dep[u]=d;
     size[u]=;
     fa[u]=f;
     for(int i=head[u];i!=-;i=edge[i].next)
     {
         int v=edge[i].to;
         if(v==f)
             continue;
         dfs_1(v,u,d+);
         size[u]+=size[v];
         if(son[u]==-||size[son[u]]<size[v])
             son[u]=v;
     }
 }

 void dfs_2(int u,int tp)
 {
     top[u] = tp;
     id[u] = ++num;
     if(son[u]!=-)
         dfs_2(son[u],tp);
     for(int i=head[u];i!=-;i=edge[i].next)
     {
         int v=edge[i].to;
         if(v==fa[u]||v==son[u])
             continue;
         dfs_2(v,v);
     }
 }

 int lowbit(int x)
 {
     return x&-x;
 }

 int sum(int x)
 {
     int res=;
     while(x>)
     {
         res+=c[x];
         x-=lowbit(x);
     }
     return res;
 }

 void add(int x,int d)
 {
     while(x<=n)
     {
         c[x]+=d;
         x+=lowbit(x);
     }
 }

 void change(int u,int v,int val)
 {
     int tp1=top[u],tp2=top[v];
     while(tp1!=tp2)
     {
         if(dep[tp1]<dep[tp2])
         {
             swap(tp1,tp2);
             swap(u,v);
         }
         add(id[tp1],val);
         add(id[u]+,-val);
         u=fa[tp1];
         tp1=top[u];
     }
     if(dep[u]>dep[v])
         swap(u,v);
     add(id[u],val);
     add(id[v]+,-val);
 }

 int main()
 {
     while(~scanf("%d%d%d",&n,&m,&p))
     {
         init();
         for(int i=;i<=n;i++)
             scanf("%d",&a[i]);
         for(int i=;i<=m;i++)
         {
             int u,v;
             scanf("%d%d",&u,&v);
             addedge(u,v);
             addedge(v,u);
         }
         dfs_1(,,);
         dfs_2(,);
         for(int i=;i<=n;i++)
         {
             add(id[i],a[i]);
             add(id[i]+,-a[i]);
         }
         char s[];
         int c1,c2,k,c;
         for(int i=;i<p;i++)
         {
             scanf("%s",s);
             if(s[]=='I')
             {
                 scanf("%d%d%d",&c1,&c2,&k);
                 change(c1,c2,k);
             }
             if(s[]=='D')
             {
                 scanf("%d%d%d",&c1,&c2,&k);
                 change(c1,c2,-k);
             }
             if(s[]=='Q')
             {
                 scanf("%d",&c);
                 cout<<sum(id[c])<<endl;
             }
         }
     }
     return ;
 }

树链剖分+线段树：

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<cmath>
 using namespace std;
 const int maxn = ;
 int n,m,p;
 int val[maxn],a[maxn];
 struct Edge
 {
     int to,next;
 }edge[maxn*];
 int head[maxn],add[maxn*];
 int dep[maxn],fa[maxn],size[maxn],son[maxn],top[maxn],id[maxn];
 int cnt,num;
 void init()
 {
         memset(head,-,sizeof(head));
     memset(son,-,sizeof(son));
     memset(add,,sizeof(add));
     cnt=;
         num=;
 }

 void addedge(int u,int v)
 {
     edge[cnt].to=v;
     edge[cnt].next=head[u];
     head[u]=cnt++;
 }

 void dfs_1(int u,int f,int d)
 {
     dep[u]=d;
     size[u]=;
     fa[u]=f;
     for(int i=head[u];i!=-;i=edge[i].next)
     {
         int v=edge[i].to;
         if(v==f)
             continue;
         dfs_1(v,u,d+);
         size[u]+=size[v];
         if(son[u]==-||size[son[u]]<size[v])
             son[u]=v;
     }
 }

 void dfs_2(int u,int tp)
 {
     top[u] = tp;
     id[u] = ++num;
     if(son[u]!=-)
         dfs_2(son[u],tp);
     for(int i=head[u];i!=-;i=edge[i].next)
     {
         int v = edge[i].to;
         if(v == fa[u] ||v == son[u])
             continue;
         dfs_2(v,v);
     }
 }

 struct Tree
 {
     int left,right;
     int sum;
 }tree[maxn*];

 void pushup(int i)
 {
     tree[i].sum = tree[i*].sum + tree[i*+].sum;
 }

 void build(int i,int begin,int end)
 {
     tree[i].left=begin;
     tree[i].right=end;
     if(begin==end)
     {
         tree[i].sum=val[begin];
         return;
     }
     int mid=(begin+end)/;
     build(i*,begin,mid);
     build(i*+,mid+,end);
     pushup(i);
 }

 void pushdown(int i)
 {
     if(add[i])
     {
         add[i*] += add[i];
         add[i*+] += add[i];
         int mid=(tree[i].left+tree[i].right)/;
         tree[i*].sum += add[i]*(mid-tree[i].left+);
         tree[i*+].sum += add[i]*(tree[i].right-mid);
         add[i]=;
     }
 }

 void update(int i,int begin,int end,int value)
 {
     if(tree[i].left>=begin&&tree[i].right<=end)
     {
         add[i]+=value;
         tree[i].sum+=value*(tree[i].right-tree[i].left+);
         return;
     }
     pushdown(i);
     int mid=(tree[i].left+tree[i].right)/;
     if(mid>=begin)
         update(i*,begin,end,value);
     if(mid<end)
         update(i*+,begin,end,value);
     pushup(i);
 }

 void change(int u,int v,int value)
 {
     int tp1=top[u],tp2=top[v];
     while(tp1!=tp2)
     {
         if(dep[tp1]<dep[tp2])
         {
             swap(tp1,tp2);
             swap(u,v);
         }
         update(,id[tp1],id[u],value);
         u = fa[tp1];
         tp1 = top[u];
     }
     if(dep[u]>dep[v])
         swap(u,v);
     update(,id[u],id[v],value);
 }

 long long query(int i,int begin,int end)
 {
     if(tree[i].left>=begin&&tree[i].right<=end)
         return tree[i].sum;
     pushdown(i);
     int mid=(tree[i].left+tree[i].right)/;
     long long ans=;
     if(mid>=begin)
         ans+=query(i*,begin,end);
     if(mid<end)
         ans+=query(i*+,begin,end);
     return ans;
 }

 int main()
 {
     while(~scanf("%d%d%d",&n,&m,&p))
     {
         init();
         for(int i=;i<=n;i++)
             scanf("%d",&a[i]);
         for(int i=;i<=m;i++)
         {
             int u,v;
             scanf("%d%d",&u,&v);
             addedge(u,v);
             addedge(v,u);
         }
         dfs_1(,,);
         dfs_2(,);

         for(int i=;i<=n;i++)
             val[id[i]]=a[i];
         build(,,n);
         char s[];
         int c1,c2,k,c;
         for(int i=;i<p;i++)
         {
             scanf("%s",s);
             if(s[]=='I')
             {
                 scanf("%d%d%d",&c1,&c2,&k);
                 change(c1,c2,k);
             }
             if(s[]=='D')
             {
                 scanf("%d%d%d",&c1,&c2,&k);
                 change(c1,c2,-k);
             }
             if(s[]=='Q')
             {
                 scanf("%d",&c);
                 cout<<query(,id[c],id[c])<<endl;
             }
         }
     }
     return ;
 }