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 = 50010;
#define lson(x) 2*x+1
#define rson(x) 2*x+2

struct e
{
    int to, next;
}edge[maxn*2];
struct node
{
    int l, r, val, x;
    int Mid ()
    {
        return (l+r)/2;
    }
}tree[maxn*4];
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 =0;
    memset (head, -1, 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] = 0;
    fa[u] = f;
    deep[u] = dep;
    size[u] = 1;
    
    for (int i=head[u]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].to;
        if (v == f) continue;
        dfs1 (v, u, dep+1);
        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!=-1; 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 = 0;
}

void build (int root, int l, int r)
{
    tree[root].l = l;
    tree[root].r = r;
    tree[root].x = tree[root].val = 0;
    
    if (l == r)
    {
        tree[root].val = val[l];
        return ;
    }
    
    build (lson(root), l, tree[root].Mid());
    build (rson(root), tree[root].Mid()+1, 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()+1, 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 (0, 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 (0, id[u], id[v], x);

}

int main ()
{
    int n, m, q;
    
    while (scanf ("%d %d %d", &n, &m, &q) != EOF)
    {
        init ();
        for (int i=1; i<=n; i++)
            scanf ("%d", &x[i]);
        for (int i=0; i<m; i++)
        {
            int x, y;
            scanf ("%d %d", &x, &y);
            Add (x, y);
            Add (y, x);
        }
        
        dfs1 (1, 0, 1);
        dfs2 (1, 1);
        
        //hash原来节点
        for (int i=1; i<=n; i++)
            val[id[i]] = x[i];
        build (0, 1, n);
        
        while (q --)
        {
            char str[10];
            int l, r, x;
            scanf ("%s", str);
            
            if (str[0] == 'Q')
            {
                scanf ("%d", &x);
                printf ("%d
", query (0, id[x]));
            }
            else if (str[0] == '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 0;
}