HDU 4010 Query on The Trees

HDU_4010

    这个题目由于需要Cut和Join，所以需要用link-cut-tree来写。

    无论是Cut还是Join，都涉及到一个基本的操作，就是把一个节点变成根(makeroot)，如果能把makeroot这个操作写成功的话，Cut和Join就比较好完成了。

    实际上在进行access(x)的操作之后，如果我们想将x作为根，只需要将这条路径上的边的父子关系都“反向”即可，那么便只要将x旋转到根，然后将这棵splay以及其子树上左右儿子的位置交换，也就是打一个rev(reverse)的标记就可以了。

    此外，对于一些细节也需要注意，比如某些操作中x如果和y相等的话是否需要特判一下。

#include<stdio.h>
#include<string.h>
#define MAXD 300010
#define MAXM 600010
#define INF 0x7fffffff
int N, first[MAXD], e, next[MAXM], v[MAXM], q[MAXD];
struct Splay
{
    int pre, ls, rs, key, max, rev, add;
    bool root;
    void update(); void pushdown(); void zig(int ); void zag(int ); void splay(int );
    void renew()
    {
        root = true;
        pre = ls = rs = 0;
        rev = add = 0;
    }
}sp[MAXD];
int Max(int x, int y)
{
    return x > y ? x : y;
}
void Splay::update()
{
    max = Max(Max(sp[ls].max, sp[rs].max), key);
}
void makeadd(int cur, int delta)
{
    if(cur)
        sp[cur].add += delta, sp[cur].key += delta, sp[cur].max += delta;
}
void Swap(int &x, int &y)
{
    int t;
    t = x, x = y, y = t;
}
void makerev(int cur)
{
    sp[cur].rev ^= 1;
    Swap(sp[cur].ls, sp[cur].rs);
}
void Splay::pushdown()
{
    if(add)
        makeadd(ls, add), makeadd(rs, add), add = 0;
    if(rev)
        makerev(ls), makerev(rs), rev = 0;
}
void Splay::zig(int x)
{
    int y = rs, fa = pre;
    rs = sp[y].ls, sp[rs].pre = x;
    sp[y].ls = x, pre = y;
    sp[y].pre = fa;
    if(root)
        root = false, sp[y].root = true;
    else
        sp[fa].rs == x ? sp[fa].rs = y : sp[fa].ls = y;
    update();
}
void Splay::zag(int x)
{
    int y = ls, fa = pre;
    ls = sp[y].rs, sp[ls].pre = x;
    sp[y].rs = x, pre = y;
    sp[y].pre = fa;
    if(root)
        root = false, sp[y].root = true;
    else
        sp[fa].rs == x ? sp[fa].rs = y : sp[fa].ls = y;
    update();
}
void Splay::splay(int x)
{
    int y, z;
    for(pushdown(); !root;)
    {
        y = pre;
        if(sp[y].root)
            sp[y].pushdown(), pushdown(), sp[y].rs == x ? sp[y].zig(y) : sp[y].zag(y);
        else
        {
            z = sp[y].pre;
            sp[z].pushdown(), sp[y].pushdown(), pushdown();
            if(sp[z].rs == y)
            {
                if(sp[y].rs == x)
                    sp[z].zig(z), sp[y].zig(y);
                else
                    sp[y].zag(y), sp[z].zig(z);
            }
            else
            {
                if(sp[y].ls == x)
                    sp[z].zag(z), sp[y].zag(y);
                else
                    sp[y].zig(y), sp[z].zag(z);
            }
        }
    }
    update();
}
void access(int x)
{
    int fx;
    for(fx = x, x = 0; fx != 0; x = fx, fx = sp[x].pre)
    {
        sp[fx].splay(fx);
        sp[sp[fx].rs].root = true;
        sp[fx].rs = x, sp[x].root = false;
        sp[fx].update();
    }
}
void makeroot(int x)
{
    access(x);
    sp[x].splay(x);
    makerev(x);
}
void prepare()
{
    int i, j, x, rear = 0;
    sp[0].max = -INF;
    q[rear ++] = 1;
    sp[1].renew(), sp[1].max = sp[1].key;
    for(i = 0; i < rear; i ++)
    {
        x = q[i];
        for(j = first[x]; j != -1; j = next[j])
            if(v[j] != sp[x].pre)
            {
                sp[v[j]].renew(), sp[v[j]].pre = x, sp[v[j]].max = sp[v[j]].key;
                q[rear ++] = v[j];
            }
    }
}
void add(int x, int y)
{
    v[e] = y;
    next[e] = first[x], first[x] = e ++;
}
void init()
{
    int i, x, y;
    memset(first, -1, sizeof(first));
    e = 0;
    for(i = 1; i < N; i ++)
    {
        scanf("%d%d", &x, &y);
        add(x, y), add(y, x);
    }
    for(i = 1; i <= N; i ++)
        scanf("%d", &sp[i].key);
    prepare();
}
void Join(int x, int y)
{
    if(x == y)
    {
        printf("-1\n");
        return ;
    }
    makeroot(x);
    makeroot(y);
    if(sp[x].pre == 0)
        sp[y].pre = x;
    else
        printf("-1\n");
}
void Cut(int x, int y)
{
    makeroot(x);
    access(y);
    sp[y].splay(y);
    if(sp[x].pre == 0)
        printf("-1\n");
    else
    {
        int t = sp[y].ls;
        sp[t].root = true, sp[t].pre = 0, sp[y].ls = 0;
        sp[y].update();
    }
}
void Change(int x, int y, int z)
{
    int fy;
    makeroot(y);
    makeroot(x);
    if(sp[y].pre == 0)
        printf("-1\n");
    else
    {
        access(x);
        for(fy = y, y = 0; fy != 0; y = fy, fy = sp[y].pre)
        {
            sp[fy].splay(fy);
            if(sp[fy].pre == 0)
            {
                makeadd(sp[fy].rs, z), makeadd(y, z);
                sp[fy].key += z;
            }
            sp[sp[fy].rs].root = true;
            sp[fy].rs = y, sp[y].root = false;
            sp[fy].update();
        }
    }
}
void Query(int x, int y)
{
    int fy;
    if(x == y)
    {
        sp[x].splay(x);
        printf("%d\n", sp[x].key);
        return ;
    }
    makeroot(y);
    makeroot(x);
    if(sp[y].pre == 0)
        printf("-1\n");
    else
    {
        access(x);
        for(fy = y, y = 0; fy != 0; y = fy, fy = sp[y].pre)
        {
            sp[fy].splay(fy);
            if(sp[fy].pre == 0)
                printf("%d\n", Max(Max(sp[sp[fy].rs].max, sp[y].max), sp[fy].key));
            sp[sp[fy].rs].root = true;
            sp[fy].rs = y, sp[y].root = false;
            sp[fy].update();
        }
    }
}
void solve()
{
    int i, x, y, z, m, op;
    scanf("%d", &m);
    for(i = 0; i < m; i ++)
    {
        scanf("%d%d%d", &op, &x, &y);
        if(op == 1)
            Join(x, y);
        else if(op == 2)
            Cut(x, y);
        else if(op == 3)
        {
            scanf("%d", &z);
            Change(y, z, x);
        }
        else
            Query(x, y);
    }
}
int main()
{
    while(scanf("%d", &N) == 1)
    {
        init();
        solve();
        printf("\n");
    }
    return 0;
}