Hdu 3966 Aragorn's Story (树链剖分 + 线段树区间更新)

题目链接：

　　Hdu 3966 Aragorn's Story

题目描述：

　　给出一个树，每个节点都有一个权值，有三种操作：

　　1：( I, i, j, x ) 从i到j的路径上经过的节点全部都加上x；

　　2：( D, i, j, x ) 从i到j的路径上经过的节点全部都减去x；

　　3：(Q, x) 查询节点x的权值为多少？

解题思路：

　　可以用树链剖分对节点进行hash，然后用线段树维护(修改，查询)，数据范围比较大，要对线段树进行区间更新

 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <algorithm>
 using namespace std;

 const int maxn = ;
 #define lson(x) 2*x+1
 #define rson(x) 2*x+2

 struct e
 {
     int to, next;
 }edge[maxn*];
 struct node
 {
     int l, r, val, x;
     int Mid ()
     {
         return (l+r)/;
     }
 }tree[maxn*];
 int val[maxn], x[maxn], deep[maxn], size[maxn], tot, num;
 int son[maxn], top[maxn], id[maxn], head[maxn], fa[maxn];

 void init ()
 {
     num = tot =;
     memset (head, -, sizeof(head));
 }

 void Add (int from, int to)
 {
     edge[tot].to = to;
     edge[tot].next = head[from];
     head[from] = tot ++;
 }

 //找重边
 void dfs1 (int u, int f, int dep)
 {
     son[u] = ;
     fa[u] = f;
     deep[u] = dep;
     size[u] = ;

     for (int i=head[u]; i!=-; i=edge[i].next)
     {
         int v = edge[i].to;
         if (v == f) continue;
         dfs1 (v, u, dep+);
         size[u] += size[v];
         if (size[son[u]] < size[v])
             son[u] = v;
     }
 }

 //重边连接成重链
 void dfs2 (int u, int tp)
 {
     top[u] = tp;
     id[u] = ++num;
     if (son[u]) dfs2 (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;
         dfs2 (v, v);
     }
 }

 //区间更新线段树，向下一层更新
 void pushup (int x)
 {
     tree[lson(x)].x += tree[x].x;
     tree[rson(x)].x += tree[x].x;
     tree[lson(x)].val +=  tree[x].x;
     tree[rson(x)].val +=  tree[x].x;
     tree[x].x = ;
 }

 void build (int root, int l, int r)
 {
     tree[root].l = l;
     tree[root].r = r;
     tree[root].x = tree[root].val = ;

     if (l == r)
     {
         tree[root].val = val[l];
         return ;
     }

     build (lson(root), l, tree[root].Mid());
     build (rson(root), tree[root].Mid()+, r);
 }

 void updata (int root, int l, int r, int x)
 {
     if (tree[root].l == l && r == tree[root].r)
     {
         tree[root].val +=  x;
         tree[root].x += x;
         return ;
     }

     if (tree[root].x)
         pushup (root);

     if (r <= tree[root].Mid())
         updata (lson(root), l, r, x);
     else if (tree[root].Mid() < l)
         updata (rson(root), l, r, x);
     else
     {
         updata (lson(root), l, tree[root].Mid(), x);
         updata (rson(root), tree[root].Mid()+, r, x);
     }
 }

 int query (int root, int x)
 {
     if (tree[root].l == tree[root].r && tree[root].l == x)
         return tree[root].val;

     if (tree[root].x)
         pushup (root);

     if (x <= tree[root].Mid())
         query (lson(root), x);
     else
         query (rson(root), x);
 }

 //处理节点u，v
 void alter (int u, int v,int x)
 {
     int tp1 = top [u];
     int tp2 = top [v];

     while (tp1 != tp2)
     {//两个节点不在同一个重链上
         if (deep[tp1] < deep[tp2])
         {
             swap (tp1, tp2);
             swap (u, v);
         }//deep深的重链上升

         updata (, id[tp1], id[u], x);
         u = fa[tp1];
         tp1 = top[u];
     }

     //在同一条重链上
     if (deep[u] > deep[v])
         swap (u, v);
     updata (, id[u], id[v], x);

 }

 int main ()
 {
     int n, m, q;

     while (scanf ("%d %d %d", &n, &m, &q) != EOF)
     {
         init ();
         for (int i=; i<=n; i++)
             scanf ("%d", &x[i]);
         for (int i=; i<m; i++)
         {
             int x, y;
             scanf ("%d %d", &x, &y);
             Add (x, y);
             Add (y, x);
         }

         dfs1 (, , );
         dfs2 (, );

         //hash原来节点
         for (int i=; i<=n; i++)
             val[id[i]] = x[i];
         build (, , n);

         while (q --)
         {
             char str[];
             int l, r, x;
             scanf ("%s", str);

             if (str[] == 'Q')
             {
                 scanf ("%d", &x);
                 printf ("%d\n", query (, id[x]));
             }
             else if (str[] == 'I')
             {
                 scanf ("%d %d %d", &l, &r, &x);
                 alter (l, r, x);
             }
             else
             {
                 scanf ("%d %d %d", &l, &r, &x);
                 alter (l, r, -x);
             }

         }
     }
     return ;
 }