[ZJOI 2012] 网络

Posted 2021-01-28 evenbao

[题目链接]

           https://www.lydsy.com/JudgeOnline/problem.php?id=2816

[算法]

         对每种颜色的边建一棵LCT ， 维护联通性即可

         时间复杂度 : O(C * NlogN ^ 2)

[代码]

          

#include<bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 10;
const int MAXC = 15;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

int n , m , c , k;
int u[MAXN] , v[MAXN] , w[MAXN] , val[MAXN] , cnt[MAXC][MAXN];
map< pair<int , int> , int> mp;

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;
}

struct Link_Cut_Tree
{
        struct Node
        {
                int father , son[2] , value , mx;
                bool tag;        
        }    a[MAXN];
        inline void init()
        {
                for (int i = 1; i <= n; i++)
                {
                        a[i].father = 0;
                        a[i].son[0] = a[i].son[1] = 0;
                        a[i].value = a[i].mx = val[i];
                        a[i].tag = false;
                }
        }
        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 void update(int x)
        {
                a[x].mx = a[x].value;
                if (a[x].son[0]) chkmax(a[x].mx , a[a[x].son[0]].mx);
                if (a[x].son[1]) chkmax(a[x].mx , a[a[x].son[1]].mx);
        }
        inline bool get(int x)
        {
                pushdown(x);
                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)) st[++z] = y = 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 void link(int x , int y)
        {
                make_root(x);
                if (find_root(y) != x) a[x].father = y;
        }
        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 cut(int x , int y)
        {
                make_root(x);
                if (find_root(y) == x && a[x].father == y && !a[x].son[1])
                {
                        a[x].father = a[y].son[0] = 0;
                        update(y);
                }
        }
        inline void split(int x , int y)
        {
                make_root(x);
                access(y);
                splay(y);
        }
        inline void modify(int x , int y)
        {
                splay(x);
                a[x].value = y;
                update(x);
        }
        inline bool connected(int x , int y)
        {
                return (find_root(x) == find_root(y));
        }
        inline int query(int x , int y)
        {
                split(x , y);
                return a[y].mx;
        }
} T[MAXC];

int main()
{
        
        read(n); read(m); read(c); read(k);
        for (int i = 1; i <= n; i++) read(val[i]);
        for (int i = 0; i < c; i++) T[i].init(); 
        for (int i = 1; i <= m; i++)
        {
                read(u[i]); read(v[i]); read(w[i]);
                mp[make_pair(u[i] , v[i])] = mp[make_pair(v[i] , u[i])] = w[i];
                T[w[i]].link(u[i] , v[i]);    
                ++cnt[w[i]][u[i]]; ++cnt[w[i]][v[i]];
        } 
        for (int i = 1; i <= k; i++)
        {
                int type;
                read(type);
                if (type == 0)
                {
                        int x , y;
                        read(x); read(y);
                        for (int i = 0; i < c; i++) T[i].modify(x , y);        
                }    else if (type == 1)
                {
                        int u , v , w;
                        read(u); read(v); read(w);
                        if (!mp.count(make_pair(u , v))) 
                        {
                                printf("No such edge.
");
                                continue;
                        } else
                        {
                                int value = mp[make_pair(u , v)];
                                if (value == w) 
                                {
                                        printf("Success.
");
                                        continue;
                                }
                                if (cnt[w][u] >= 2 || cnt[w][v] >= 2)
                                {
                                        printf("Error 1.
");
                                        continue;
                                }
                                if (T[w].connected(u , v))
                                {
                                        printf("Error 2.
");
                                        continue;
                                }
                                printf("Success.
");
                                T[value].cut(u , v);
                                --cnt[value][u]; --cnt[value][v];
                                T[w].link(u , v);
                                mp[make_pair(u , v)] = mp[make_pair(v , u)] = w;
                                ++cnt[w][u]; ++cnt[w][v];
                        } 
                } else
                {
                        int w , u , v;
                        read(w); read(u); read(v);
                        if (!T[w].connected(u , v)) printf("-1
");
                        else printf("%d
" , T[w].query(u , v));
                }
        }
        
        return 0;
    
}