邝斌的ACM模板（树链剖分）

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本博客整理自邝斌的ACM模板
3.3、树链剖分
3.3.1 点权
基于点权，查询单点值，修改路径的上的点权（HDU 3966 树链剖分+树状数组）

const int MAXN = 50010;struct Edge{    int to,next;} edge[MAXN*2];int head[MAXN],tot;int top[MAXN];//top[v] 表示v所在的重链的顶端节点int fa[MAXN];//父亲节点int deep[MAXN];//深度int num[MAXN];//num[v] 表示以v为根的子树的节点数int p[MAXN];//p[v]表示v对应的位置int fp[MAXN];//fp和p数组相反int son[MAXN];//重儿子int pos;void init(){    tot = 0;    memset(head,-1,sizeof(head));    pos = 1;//使用树状数组，编号从头1开始    memset(son,-1,sizeof(son));}void addedge(int u,int v){    edge[tot].to = v;    edge[tot].next = head[u];    head[u] = tot++;}void dfs1(int u,int pre,int d){    deep[u] = d;    fa[u] = pre;    num[u] = 1;    for(int i = head[u]; i != -1; i = edge[i].next)    {        int v = edge[i].to;        if(v != pre)        {            dfs1(v,u,d+1);            num[u] += num[v];            if(son[u] == -1 || num[v] > num[son[u]])                son[u] = v;        }    }}void getpos(int u,int sp){    top[u] = sp;    p[u] = pos++;    fp[p[u]] = u;    if(son[u] == -1) return;    getpos(son[u],sp);    for(int i = head[u]; i != -1; i = edge[i].next)    {        int v = edge[i].to;        if( v != son[u] && v != fa[u])            getpos(v,v);    }}//树状数组int lowbit(int x){    return x&(-x);}int c[MAXN];int n;int sum(int i){    int s = 0;    while(i > 0)    {        s += c[i];        i -= lowbit(i);    }    return s;}void add(int i,int val){    while(i <= n)    {        c[i] += val;        i += lowbit(i);    }}void Change(int u,int v,int val)//u->v的路径上点的值改变val{    int f1 = top[u], f2 = top[v];    int tmp = 0;    while(f1 != f2)    {        if(deep[f1] < deep[f2])        {            swap(f1,f2);            swap(u,v);        }        add(p[f1],val);        add(p[u]+1,-val);        u = fa[f1];        f1 = top[u];    }    if(deep[u] > deep[v]) swap(u,v);    add(p[u],val);    add(p[v]+1,-val);}int a[MAXN];int main(){    int M,P;    while(scanf("%d%d%d",&n,&M,&P) == 3)    {        int u,v;        int C1,C2,K;        char op[10];        init();        for(int i = 1; i <= n; i++)        {            scanf("%d",&a[i]);        }        while(M--)        {            scanf("%d%d",&u,&v);            addedge(u,v);            addedge(v,u);        }        dfs1(1,0,0);        getpos(1,1);        memset(c,0,sizeof(c));        for(int i = 1; i <= n; i++)        {            add(p[i],a[i]);            add(p[i]+1,-a[i]);        }        while(P--)        {            scanf("%s",op);            if(op[0] == 'Q')            {                scanf("%d",&u);                printf("%d\n",sum(p[u]));            }            else            {                scanf("%d%d%d",&C1,&C2,&K);                if(op[0] == 'D')                          K = -K;                Change(C1,C2,K);            }        }    }    return 0;}

3.3.2 边权
基于边权，修改单条边权，查询路径边权最大值（SPOJ QTREE 树链剖分+线段树）

const int MAXN = 10010;struct Edge{    int to,next;} edge[MAXN*2];int head[MAXN],tot;int top[MAXN];//top[v]表示v所在的重链的顶端节点int fa[MAXN]; //父亲节点int deep[MAXN];//深度int num[MAXN];//num[v]表示以v为根的子树的节点数int p[MAXN];//p[v]表示v与其父亲节点的连边在线段树中的位置int fp[MAXN];//和p数组相反int son[MAXN];//重儿子int pos;void init(){    tot = 0;    memset(head,-1,sizeof(head));    pos = 0;    memset(son,-1,sizeof(son));}void addedge(int u,int v){    edge[tot].to = v;    edge[tot].next = head[u];    head[u] = tot++;}void dfs1(int u,int pre,int d) //第一遍dfs求出fa,deep,num,son{    deep[u] = d;    fa[u] = pre;    num[u] = 1;    for(int i = head[u]; i != -1; i = edge[i].next)    {        int v = edge[i].to;        if(v != pre)        {            dfs1(v,u,d+1);            num[u] += num[v];            if(son[u] == -1 || num[v] > num[son[u]])                son[u] = v;        }    }}void getpos(int u,int sp) //第二遍dfs求出top和p{    top[u] = sp;    p[u] = pos++;    fp[p[u]] = u;    if(son[u] == -1) return;    getpos(son[u],sp);    for(int i = head[u] ; i != -1; i = edge[i].next)    {        int v = edge[i].to;        if(v != son[u] && v != fa[u])            getpos(v,v);    }}//线段树struct Node{    int l,r;    int Max;} segTree[MAXN*3];void build(int i,int l,int r){    segTree[i].l = l;    segTree[i].r = r;    segTree[i].Max = 0;    if(l == r)return;    int mid = (l+r)/2;    build(i<<1,l,mid);    build((i<<1)|1,mid+1,r);}void push_up(int i){    segTree[i].Max = max(segTree[i<<1].Max,segTree[(i<<1)|1].Max);}void update(int i,int k,int val) // 更新线段树的第k个值为val{    if(segTree[i].l == k && segTree[i].r == k)    {        segTree[i].Max = val;        return;    }    int mid = (segTree[i].l + segTree[i].r)/2;    if(k <= mid)update(i<<1,k,val);    else update((i<<1)|1,k,val);    push_up(i);}int query(int i,int l,int r)  //查询线段树中[l,r] 的最大值{    if(segTree[i].l == l && segTree[i].r == r)        return segTree[i].Max;    int mid = (segTree[i].l + segTree[i].r)/2;    if(r <= mid)return query(i<<1,l,r);    else if(l > mid)return query((i<<1)|1,l,r);    else return max(query(i<<1,l,mid),query((i<<1)|1,mid+1,r));}int find(int u,int v)//查询u->v边的最大值{    int f1 = top[u], f2 = top[v];    int tmp = 0;    while(f1 != f2)    {        if(deep[f1] < deep[f2])        {            swap(f1,f2);            swap(u,v);        }        tmp = max(tmp,query(1,p[f1],p[u]));        u = fa[f1];        f1 = top[u];    }    if(u == v)return tmp;    if(deep[u] > deep[v]) swap(u,v);    return max(tmp,query(1,p[son[u]],p[v]));}int e[MAXN][3];int main(){    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);    int T;    int n;    scanf("%d",&T);    while(T--)    {        init();        scanf("%d",&n);        for(int i = 0; i < n-1; i++)        {            scanf("%d%d%d",&e[i][0],&e[i][1],&e[i][2]);            addedge(e[i][0],e[i][1]);            addedge(e[i][1],e[i][0]);        }        dfs1(1,0,0);        getpos(1,1);        build(1,0,pos-1);        for(int i = 0; i < n-1; i++)        {            if(deep[e[i][0]] > deep[e[i][1]])                swap(e[i][0],e[i][1]);            update(1,p[e[i][1]],e[i][2]);        }        char op[10];        int u,v;        while(scanf("%s",op) == 1)        {            if(op[0] == 'D')break;            scanf("%d%d",&u,&v);            if(op[0] == 'Q')                printf("%d\n",find(u,v));//查询u->v路径上边权的最大值            else update(1,p[e[u-1][1]],v);//修改第u条边的长度为v        }    }    return 0;}

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