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HDU 3966 Aragorn's Story --树链剖分

题意: 树上路径之间的点统一加减k,查询某点的值

解法:不会LCA的解法,于是用树链剖分了,比较简单的剖分,然后用线段树维护就行了,相当于区间更新,单点查询,查询点 i 的值时,只需在线段树中查询pos[u]位置的值即可。

加IO优化900+ms

代码:

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <cmath>#include <algorithm>using namespace std;#define N 50007int siz[N];  //子树大小int son[N];  //重儿子int dep[N];  //深度int pos[N];  //在线段树中的位置int Top[N];  //所在重链的祖先int fa[N];   //父节点int head[2*N],tot,POS,n,m,q;struct Edge{    int v,next;}G[2*N];int tree[4*N],mark[4*N],a[N];void init(){    POS = tot = 0;    memset(head,-1,sizeof(head));    memset(son,-1,sizeof(son));    memset(tree,0,sizeof(tree));    memset(mark,0,sizeof(mark));}void addedge(int u,int v){    G[tot].v = v, G[tot].next = head[u], head[u] = tot++;    G[tot].v = u, G[tot].next = head[v], head[v] = tot++;}void pushdown(int l,int r,int rt){    int mid = (l+r)/2;    if(mark[rt])    {        mark[2*rt] += mark[rt];        mark[2*rt+1] += mark[rt];        tree[2*rt] += mark[rt]*(mid-l+1);        tree[2*rt+1] += mark[rt]*(r-mid);        mark[rt] = 0;    }}void update(int l,int r,int aa,int bb,int k,int rt){    if(aa <= l && bb >= r)    {        tree[rt] += k*(r-l+1);        mark[rt] += k;        return;    }    int mid = (l+r)/2;    if(aa <= mid)        update(l,mid,aa,bb,k,2*rt);    if(bb > mid)        update(mid+1,r,aa,bb,k,2*rt+1);}int query(int l,int r,int pos,int rt){    if(l == r)        return tree[rt];    pushdown(l,r,rt);    int mid = (l+r)/2;    if(pos <= mid) return query(l,mid,pos,2*rt);    else return query(mid+1,r,pos,2*rt+1);}void dfs(int u,int f){    dep[u] = dep[f]+1;    siz[u] = 1;    for(int i=head[u];i!=-1;i=G[i].next)    {        int v = G[i].v;        if(v == f) continue;        fa[v] = u;        dfs(v,u);        if(son[u] == -1 || siz[v] > siz[son[u]]) son[u] = v;        siz[u] += siz[v];    }}void dfs2(int u,int father){    pos[u] = ++POS;    Top[u] = father;    if(son[u] != -1) dfs2(son[u],father);    for(int i=head[u];i!=-1;i=G[i].next)    {        int v = G[i].v;        if(v != fa[u] && v != son[u])            dfs2(v,v);    }}void Change(int u,int v,int k){    int fx = Top[u], fy = Top[v];    while(fx != fy)    {        if(dep[fx] < dep[fy])        {            swap(u,v);            swap(fx,fy);        }        update(1,POS,pos[fx],pos[u],k,1);        u = fa[fx];        fx = Top[u];    }    if(dep[u] > dep[v]) swap(u,v);    update(1,POS,pos[u],pos[v],k,1);}inline int in(){    char ch;    int a = 0;    while((ch = getchar()) ==   || ch == \n);    a += ch - 0;    while((ch = getchar()) !=   && ch != \n)    {        a *= 10;        a += ch - 0;    }    return a;}int main(){    int u,v,k,i;    char ss[5];    while(scanf("%d%d%d",&n,&m,&q)!=EOF)    {        init();        for(i=1;i<=n;i++)            a[i] = in();        for(i=1;i<n;i++)        {            u = in(), v = in();            addedge(u,v);        }        dep[0] = 0;        dfs(1,0);        dfs2(1,1);        for(i=1;i<=n;i++)            update(1,POS,pos[i],pos[i],a[i],1);        while(q--)        {            scanf("%s",ss);            if(ss[0] == Q)            {                u = in();                printf("%d\n",query(1,POS,pos[u],1));            }            else            {                u = in(), v = in(), k = in();                if(ss[0] == I)                    Change(u,v,k);                else                    Change(u,v,-k);            }        }    }    return 0;}
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HDU 3966 Aragorn's Story --树链剖分