[AHOI 2005] 航线规划

[题目链接]

https://www.lydsy.com/JudgeOnline/problem.php?id=1969

[算法]

首先离线 ， 将删边操作转化为加边操作

不妨首先将这张图按边-双连通分量(e-DCC)缩点 ， 缩点后形成了一棵树

树链剖分 + 线段树即可

时间复杂度 : O(NlogN ^ 2)

[代码]

#include<bits/stdc++.h>
using namespace std;
#define MAXN 200010

struct query
{
        int type , u , v;
} que[MAXN];
struct edge
{
        int to , nxt;
} e[MAXN << ] , ec[MAXN << ];

int n , m , timer , cnt , tot , q , len;
int head[MAXN] , chead[MAXN] , low[MAXN] , dfn[MAXN] , belong[MAXN] ,
        size[MAXN] , fa[MAXN] , son[MAXN] , top[MAXN] , depth[MAXN] , u[MAXN] , v[MAXN] , ans[MAXN];
map< pair<int , int> , int> mp;
bool is_bridge[MAXN << ] , des[MAXN << ];

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 = ; x = ;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
    for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';
    x *= f;
}
struct Segment_Tree
{
        struct Node
        {
                int l , r , sum;
                int tag;
        } Tree[MAXN << ];
        inline void build(int index , int l , int r)
        {
                Tree[index].l = l;
                Tree[index].r = r;
                Tree[index].tag = ;
                if (l == r)
                {
                        if (l != ) Tree[index].sum = ;
                        return;
                }
                int mid = (l + r) >> ;
                build(index <<  , l , mid);
                build(index <<  |  , mid +  , r);
                update(index);
        }
        inline void pushdown(int index)
        {
                Tree[index << ].sum = Tree[index <<  | ].sum = ;
                Tree[index << ].tag = Tree[index <<  | ].tag = ;
                Tree[index].tag = ;
        }
        inline void update(int index)
        {
                Tree[index].sum = Tree[index << ].sum + Tree[index <<  | ].sum;
        }
        inline void modify(int index , int l , int r)
        {
                if (Tree[index].l == l && Tree[index].r == r)
                {
                        Tree[index].sum = ;
                        Tree[index].tag = ;
                        return;
                }
                if (Tree[index].tag) pushdown(index);
                int mid = (Tree[index].l + Tree[index].r) >> ;
                if (mid >= r) modify(index <<  , l , r);
                else if (mid +  <= l) modify(index <<  |  , l , r);
                else
                {
                        modify(index <<  , l , mid);
                        modify(index <<  |  , mid +  , r);
                }
                update(index);
        }
        inline int query(int index , int l , int r)
        {
                if (Tree[index].l == l && Tree[index].r == r)
                        return Tree[index].sum;
                if (Tree[index].tag) pushdown(index);
                int mid = (Tree[index].l + Tree[index].r) >> ;
                if (mid >= r) return query(index <<  , l , r);
                else if (mid +  <= l) return query(index <<  |  , l , r);
                else return query(index <<  , l , mid) + query(index <<  |  , mid +  , r);
        }
} SGT;
inline void addedge(int u , int v)
{
        ++tot;
        e[tot] = (edge){v , head[u]};
        head[u] = tot;
}
inline void addcedge(int u , int v)
{
        ++tot;
        ec[tot] = (edge){v , chead[u]};
        chead[u] = tot;
}
inline void tarjan(int u , int t)
{
        low[u] = dfn[u] = ++timer;
        for (int i = head[u]; i; i = e[i].nxt)
        {
                int v = e[i].to;
                if (!dfn[v])
                {
                        tarjan(v , i);
                        chkmin(low[u] , low[v]);
                        if (low[v] > dfn[u])
                                is_bridge[i] = is_bridge[i ^ ] = true;
                }    else if (i != (t ^ )) chkmin(low[u] , dfn[v]);
        }
}
inline void dfs(int u , int id)
{
        belong[u] = id;
        for (int i = head[u]; i; i = e[i].nxt)
        {
                int v = e[i].to;
                if (!belong[v] && !is_bridge[i]) dfs(v , id);
        }
}
inline void dfs1(int u)
{
        size[u] = ;
        son[u] = ;
        for (int i = chead[u]; i; i = ec[i].nxt)
        {
                int v = ec[i].to;
                if (v == fa[u]) continue;
                depth[v] = depth[u] + ;
                fa[v] = u;
                dfs1(v);
                size[u] += size[v];
                if (son[u] ==  || size[v] > size[son[u]]) son[u] = v;
        }
}
inline void dfs2(int u , int tp)
{
        dfn[u] = ++timer;
        top[u] = tp;
        if (son[u]) dfs2(son[u] , tp);
        for (int i = chead[u]; i; i = ec[i].nxt)
        {
                int v = ec[i].to;
                if (v == fa[u] || v == son[u]) continue;
                dfs2(v , v);
        }
}
inline void modify(int u , int v)
{
        u = belong[u] , v = belong[v];
        int tu = top[u] , tv = top[v];
        while (tu != tv)
        {
                if (depth[tu] > depth[tv])
                {
                        swap(u , v);
                        swap(tu , tv);
                }
                SGT.modify( , dfn[tv] , dfn[v]);
                v = fa[tv]; tv = top[v];
        }
        if (dfn[u] > dfn[v]) swap(u , v);
        if (dfn[u] +  <= dfn[v]) SGT.modify( , dfn[u] +  , dfn[v]);
}
inline int query(int u , int v)
{
        u = belong[u] , v = belong[v];
        int tu = top[u] , tv = top[v];
        int ret = ;
        while (tu != tv)
        {
                if (depth[tu] > depth[tv])
                {
                        swap(u , v);
                        swap(tu , tv);
                }
                ret += SGT.query( , dfn[tv] , dfn[v]);
                v = fa[tv]; tv = top[v];
        }
        if (dfn[u] > dfn[v]) swap(u , v);
        if (dfn[u] +  <= dfn[v]) ret += SGT.query( , dfn[u] +  , dfn[v]);
        return ret;
}

int main()
{

        read(n); read(m);
        for (int i = ; i <= m; i++)
        {
                read(u[i]);
                read(v[i]);
                mp[make_pair(u[i] , v[i])] = mp[make_pair(v[i] , u[i])] = i;
        }
        while (true)
        {
                int C , A , B;
                read(C);
                if (C == -) break;
                read(A); read(B);
                if (C == ) des[mp[make_pair(A , B)]] = true;
                que[++q].type = C; que[q].u = A; que[q].v = B;
        }
        tot = ;
        for (int i = ; i <= m; i++)
        {
                if (!des[i])
                {
                        addedge(u[i] , v[i]);
                        addedge(v[i] , u[i]);
                }
        }
        for (int i = ; i <= n; i++)
                if (!dfn[i]) tarjan(i , );
        for (int i = ; i <= n; i++)
                if (!belong[i]) dfs(i , ++cnt);
        tot = ;
        for (int i = ; i <= m; i++)
        {
                if (des[i]) continue;
                if (belong[u[i]] != belong[v[i]])
                {
                        addcedge(belong[u[i]] , belong[v[i]]);
                        addcedge(belong[v[i]] , belong[u[i]]);
                }
        }
        timer = ;
        memset(dfn ,  , sizeof(dfn));
        dfs1();
        dfs2( , );
        SGT.build( ,  , timer);
        for (int i = q; i >= ; i--)
        {
                if (que[i].type == ) modify(que[i].u, que[i].v);
                else ans[++len] = query(que[i].u , que[i].v);
        }
        reverse(ans +  , ans + len + );
        for (int i = ; i <= len; i++) printf("%d\n" , ans[i]);

        return ;

}