[CROATIAN2009] OTOCI

[题目链接]

         https://www.lydsy.com/JudgeOnline/problem.php?id=1180

[算法]

         动态树维护森林连通性

         时间复杂度 : O(NlogN ^ 2)

[代码]

         

#include<bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 10;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

int n;
int val[MAXN];

struct Link_Cut_Tree
{
        struct Node
        {
                int father , son[2] , value , cnt;
                bool tag;
        }    a[MAXN];
        inline void init()
        {
                for (int i = 1; i <= n; i++)
                {
                        a[i].value = a[i].cnt = val[i];
                        a[i].tag = false;
                        a[i].father = a[i].son[0] = a[i].son[1] = 0;
                }
        }
        inline void update(int x)
        {
                a[x].cnt = a[a[x].son[0]].cnt + a[a[x].son[1]].cnt + a[x].value;
        }
        inline void pushdown(int x)
        {
                if (a[x].tag)
                {
                        swap(a[x].son[0] , a[x].son[1]);
                        a[a[x].son[0]].tag ^= 1;
                        a[a[x].son[1]].tag ^= 1;
                        a[x].tag = false;
                }
        }
        inline bool get(int x)
        {
                pushdown(a[x].father);
                return a[a[x].father].son[1] == x;
        }
        inline bool nroot(int x)
        {
                return a[a[x].father].son[0] == x | a[a[x].father].son[1] == x;
        }
        inline void rotate(int x)
        {
                int f = a[x].father , g = a[f].father;
                int tmpx = get(x) , tmpf = get(f);
                int w = a[x].son[tmpx ^ 1];
                if (nroot(f)) a[g].son[tmpf] = x;
                a[x].son[tmpx ^ 1] = f;
                a[f].son[tmpx] = w;
                if (w) a[w].father = f;
                a[f].father = x;
                a[x].father = g;
                update(f);    
        }
        inline void splay(int x)
        {
                int y = x , z = 0;
                static int st[MAXN];
                st[++z] = y;
                while (nroot(y)) y = st[++z] = a[y].father;
                while (z) pushdown(st[z--]);
                while (nroot(x))
                {
                        int y = a[x].father , z = a[y].father;
                        if (nroot(y))
                                rotate((a[z].son[0] == y) ^ (a[y].son[0] == x) ? x : y);
                        rotate(x);
                }
                update(x);
        }
        inline void access(int x)
        {
                for (int y = 0; x; x = a[y = x].father)
                {
                        splay(x);
                        a[x].son[1] = y;
                        update(x);
                }
        }
        inline void make_root(int x)
        {
                access(x);            
                splay(x);
                a[x].tag ^= 1;
                pushdown(x);
        }
        inline int find_root(int x)
        {
                access(x);
                splay(x);
                while (a[x].son[0])
                {
                        pushdown(x);
                        x = a[x].son[0];
                }
                return x;
        }
        inline void link(int x , int y)
        {
                make_root(x);
                if (find_root(y) != x) a[x].father = y;
        }
        inline void split(int x , int y)
        {
                make_root(x);
                access(y);
                splay(y);
        }
        inline int query(int x , int y)
        {
                split(x , y);
                return a[y].cnt;
        }
        inline bool connected(int x , int y)
        {    
                return (find_root(x) == find_root(y));
        }
        inline void modify(int u , int x)
        {
                splay(u);
                a[u].value = x;
                update(u);
        }
} LCT;

template <typename T> inline void chkmax(T &x,T y) { x = max(x,y); }
template <typename T> inline void chkmin(T &x,T y) { x = min(x,y); }
template <typename T> inline void read(T &x)
{
    T f = 1; x = 0;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
    for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
    x *= f;
}
int main()
{
        
        scanf("%d" , &n);
        for (int i = 1; i <= n; i++) scanf("%d" , &val[i]);
        LCT.init();
        int q;
        scanf("%d" , &q);
        while (q--)
        {
                char type[10];
                scanf("%s" , type);
                if (type[0] == 'b')
                {
                        int u , v;
                        scanf("%d%d" , &u , &v);
                        if (LCT.connected(u , v)) 
                        {
                                printf("no\n");
                        } else 
                        {
                                printf("yes\n");
                                LCT.link(u , v);
                        }
                } else if (type[0] == 'p')
                {
                        int u , x;
                        scanf("%d%d" , &u , &x);
                        LCT.modify(u , x);
                } else
                {
                        int u , v;
                        scanf("%d%d" , &u , &v);
                        if (!LCT.connected(u , v)) printf("impossible\n");
                        else printf("%d\n" , LCT.query(u , v));
                }
        }
        
        return 0;
    
}