UVA 11994 Happy Painting!

UVA_11994

    这个题目思维上的障碍比较少，因为实际上都是link-cut-tree的基本的操作，还有一个更为复杂的link-cut-tree的题目——HDU_4010。

    在维护路径上边的颜色的数量时，由于颜色的种类只有30个，因此可以用一个整数的30个二进制位来存储颜色的种类。

#include
#include<string.h>
#define MAXD 50010
int N, M;
struct Splay
{
    int pre, ls, rs, col, set, to, size;
    bool root;
    void pushdown(); void update(); void zig(int x); void zag(int x); void splay(int x);
    void init()
    {
        root = true;
        size = to = pre = ls = rs = col = set = 0;
    }
}sp[MAXD];
inline void same(int x, int c)
{
    if(x) sp[x].to = sp[x].col = c, sp[x].set = 1 << c;
}
inline void Splay::pushdown()
{
    if(to)
    {
        same(ls, to), same(rs, to);
        to = 0;
    }
}
inline void Splay::update()
{
    set = sp[ls].set | sp[rs].set | 1 << col;
    size = sp[ls].size + sp[rs].size + 1;
}
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 cut(int x)
{
    access(x), sp[x].splay(x);
    sp[sp[x].ls].root = true, sp[sp[x].ls].pre = 0, sp[x].ls = 0;
    sp[x].update();
}
void join(int x, int y, int c)
{
    access(y), sp[y].splay(y);
    sp[x].splay(x);
    if(sp[y].pre != 0) return ;
    cut(x);
    sp[x].pre = y, sp[x].col = c;
    sp[x].update();
}
void init()
{
    int i, x;
    for(i = 1; i <= N; i ++)
    {
        scanf("%d", &x);
        sp[i].init(), sp[i].pre = x;
    }
    for(i = 1; i <= N; i ++)
    {
        scanf("%d", &x);
        sp[i].col = x, sp[i].set = 1 << x, sp[i].size = 1;
    }
    sp[0].init();
}
void paint(int x, int y, int c)
{
    int fx;
    access(y), sp[y].splay(y);
    for(fx = x, x = 0; fx != 0; x = fx, fx = sp[x].pre)
    {
        sp[fx].splay(fx);
        if(sp[fx].pre == 0)
        {
            if(sp[y].pre != 0 || fx == y) same(sp[fx].rs, c), same(x, c);
        }
        sp[sp[fx].rs].root = true, sp[fx].rs = x, sp[x].root = false;
        sp[fx].update();    
    }    
}
void count(int x, int y)
{
    int fx;
    access(y), sp[y].splay(y);
    for(fx = x, x = 0; fx != 0; x = fx, fx = sp[x].pre)
    {
        sp[fx].splay(fx);
        if(sp[fx].pre == 0)
        {
            if(sp[y].pre == 0 && fx != y) printf("0 0\n");
            else
            {
                int cnt = 0, t = sp[sp[fx].rs].set | sp[x].set;
                for(int i = 1; i <= 30; i ++) if(t & 1 << i) ++ cnt;
                printf("%d %d\n", sp[sp[fx].rs].size + sp[x].size, cnt);
            }
        }
        sp[sp[fx].rs].root = true, sp[fx].rs = x, sp[x].root = false;
        sp[fx].update();    
    }    
}
void solve()
{
    int i, op, x, y, c;
    for(i = 0; i < M; i ++)
    {
        scanf("%d", &op);
        if(op == 1)
        {
            scanf("%d%d%d", &x, &y, &c);
            if(x == y) continue;
            join(x, y, c);
        }    
        else if(op == 2)
        {
            scanf("%d%d%d", &x, &y, &c);
            if(x == y) continue;
            paint(x, y, c);    
        }
        else
        {
            scanf("%d%d", &x, &y);
            if(x == y) printf("0 0\n");
            else count(x, y);    
        }
    }
}
int main()
{
    while(scanf("%d%d", &N, &M) == 2)
    {
        init();
        solve();    
    }
    return 0;    
}