HDU 5409 CRB and Graph【dfs序+RMQ】

超、凢脫俗 2022-08-04 13:56 102阅读 0赞

先用trajan缩环变成了一棵树  
然后删除了一条边就将树分成了两个部分，一个是删除的那边下面的子树，一个是剩余部分。那么要查询的是两个部分中最大的点的值，和不大于它的最小的点的值。

这样一想就有点像树链剖分啊，树形DP一样求出一颗子树的某个最大值。 又想到是分离出一颗子树，那么就是想到一些dfs序可以对子树进行区间求值。

那么就想到可以预处理出dfs序列，将树的值转化为一个区间值。去掉一颗子树，就是将区间分成三段（可能是两段）。

|\_\_\_\_（A）\_\_\_\_|\_\_\_\_子树（B）\_\_\_\_|\_\_\_（C）\_\_\_\_|

求出A,C段最大值中小的那个，和B中最大值。求出最大值。就是答案中的  ansfirst 。  
那么  anssecond 就是  ansfirst\+1 ，因为假设  ansfirst\+1 和  ansfirst 在同一个区间内，那么一定取不到  ansfirst ，所以  ansfirst\+1 一定是在被分离的区间内，就是答案。

至于区间最大值，因为不会修改就用RMQ求~树上每个节点的最大值就是连通块里的最大节点值。

// whn6325689
    // Mr.Phoebe
    // http://blog.csdn.net/u013007900
    #include <algorithm>
    #include <iostream>
    #include <iomanip>
    #include <cstring>
    #include <climits>
    #include <complex>
    #include <fstream>
    #include <cassert>
    #include <cstdio>
    #include <bitset>
    #include <vector>
    #include <deque>
    #include <queue>
    #include <stack>
    #include <ctime>
    #include <set>
    #include <map>
    #include <cmath>
    #include <functional>
    #include <numeric>
    #pragma comment(linker, "/STACK:1024000000,1024000000")
    
    
    using namespace std;
    
    #define eps 1e-9
    #define PI acos(-1.0)
    #define INF 0x3f3f3f3f
    #define LLINF 1LL<<62
    #define speed std::ios::sync_with_stdio(false);
    
    typedef long long ll;
    typedef unsigned long long ull;
    typedef long double ld;
    typedef pair<ll, ll> pll;
    typedef complex<ld> point;
    typedef pair<int, int> pii;
    typedef pair<pii, int> piii;
    typedef vector<int> vi;
    
    #define CLR(x,y) memset(x,y,sizeof(x))
    #define CPY(x,y) memcpy(x,y,sizeof(x))
    #define clr(a,x,size) memset(a,x,sizeof(a[0])*(size))
    #define cpy(a,x,size) memcpy(a,x,sizeof(a[0])*(size))
    #define debug(a) cout << #a" = " << (a) << endl;
    #define debugarry(a, n) for (int i = 0; i < (n); i++) { cout << #a"[" << i << "] = " << (a)[i] << endl; }
    
    #define mp(x,y) make_pair(x,y)
    #define pb(x) push_back(x)
    #define lowbit(x) (x&(-x))
    
    #define MID(x,y) (x+((y-x)>>1))
    #define ls (idx<<1)
    #define rs (idx<<1|1)
    #define lson ls,l,mid
    #define rson rs,mid+1,r
    
    template<class T>
    inline bool read(T &n)
    {
        T x = 0, tmp = 1;
        char c = getchar();
        while((c < '0' || c > '9') && c != '-' && c != EOF) c = getchar();
        if(c == EOF) return false;
        if(c == '-') c = getchar(), tmp = -1;
        while(c >= '0' && c <= '9') x *= 10, x += (c - '0'),c = getchar();
        n = x*tmp;
        return true;
    }
    template <class T>
    inline void write(T n)
    {
        if(n < 0)
        {
            putchar('-');
            n = -n;
        }
        int len = 0,data[20];
        while(n)
        {
            data[len++] = n%10;
            n /= 10;
        }
        if(!len) data[len++] = 0;
        while(len--) putchar(data[len]+48);
    }
    //-----------------------------------
    
    
    
    const int MAXN = 2e5 + 5;
    
    int head_Tu[MAXN], si_Tu;
    int head_G[MAXN], si_G;
    int par[MAXN], rmax[MAXN];
    int pre[MAXN], dfs_clock;
    int ans_u[MAXN], ans_v[MAXN];
    int in[MAXN], out[MAXN];
    int A[MAXN], dmax[MAXN][30];
    int n, m;
    
    struct edge
    {
        int to, next;
    }Tu[MAXN<<1], G[MAXN<<1];
    
    struct Node
    {
        int u, v;
    } E[MAXN];
    
    void add_Tu(int st, int ed)
    {
        Tu[si_Tu].to = ed;
        Tu[si_Tu].next = head_Tu[st];
        head_Tu[st] = si_Tu++;
    }
    void add_G(int st, int ed)
    {
        G[si_G].to = ed;
        G[si_G].next = head_G[st];
        head_G[st] = si_G++;
    }
    
    void init(int _n)
    {
        for (int i = 0; i <= _n; i++)
            par[i] = rmax[i] = i;
    }
    int Find(int x)
    {
        if (x == par[x]) return x;
        return par[x] = Find(par[x]);
    }
    void unite(int x, int y)
    {
        x = Find(x);
        y = Find(y);
        if (x == y) return ;
        par[x] = y;
        rmax[y] = max(rmax[x], rmax[y]);
    }
    
    int Tarjan(int u, int fa)
    {
        int lowu = pre[u] = ++dfs_clock;
        for (int i = head_Tu[u]; i != -1; i = Tu[i].next)
        {
            int v = Tu[i].to;
            if (v == fa) continue;
            if (pre[v] == 0)
            {
                int lowv = Tarjan(v, u);
                lowu = min(lowu, lowv);
                if (lowv <= pre[u]) unite(u, v);
            }
            else lowu = min(lowu, pre[v]);
        }
        return lowu;
    }
    
    void find_bridge(int _n)
    {
        CLR(pre, 0); dfs_clock = 0;
        for (int i = 1; i <= n; i++)
            if (!pre[i]) Tarjan(i, -1);
    }
    
    void dfs(int u, int fa)
    {
        in[u] = dfs_clock++;
        A[in[u]] = rmax[u];
        for (int i = head_G[u]; i != -1; i = G[i].next)
        {
            int v = G[i].to;
            if (v == fa) continue;
            dfs(v, u);
        }
        out[u] = dfs_clock-1;
    }
    
    void RMQ_init(int _n)
    {
        int N = _n;
        for (int i = 0; i < N; i++) dmax[i][0] = A[i];
        for (int j = 1; (1<<j) <= N; j++)
            for (int i = 0; i + (1<<j) - 1 < N; i++)
                dmax[i][j] = max(dmax[i][j-1], dmax[i + (1<<(j-1))][j-1]);
    }
    int RMQ(int L, int R)
    {
        int k = 0;
        while((1<<(k+1)) <= R-L+1) k++;
        return max(dmax[L][k], dmax[R-(1<<k)+1][k]);
    }
    
    int main()
    {
        //freopen("input.txt", "r", stdin);
    
        int T;
        scanf("%d", &T);
        while(T--)
        {
            scanf("%d%d", &n, &m);
            CLR(head_Tu, -1); si_Tu = 0;
            CLR(head_G, -1); si_G = 0;
            CLR(ans_u, -1); CLR(ans_v, -1);
            CLR(in, -1); CLR(out, -1);
    
            init(n);
            for (int i = 0; i < m; i++)
            {
                scanf("%d%d", &E[i].u, &E[i].v);
                add_Tu(E[i].u, E[i].v);
                add_Tu(E[i].v, E[i].u);
            }
            find_bridge(n);
            for (int i = 0; i < m; i++)
            {
                int u = Find(E[i].u);
                int v = Find(E[i].v);
                if (u == v)
                {
                    ans_u[i] = ans_v[i] = 0;
                }
                else
                    add_G(u, v),add_G(v, u);
            }
            int root = Find(1);
            dfs_clock = 0;
            dfs(root, -1);
            int len = dfs_clock;
            RMQ_init(len);
            //debug(si_G);
            for (int i = 0; i < m; i++)
            {
                int u = Find(E[i].u);
                int v = Find(E[i].v);
                if (in[u] < in[v]) swap(u, v);
                if (u != v)
                {
                    //if(i==8){ cout<<" "; debug(in[u]);debug(out[u]);}
                    int x = RMQ(in[u], out[u]);
                    int y = 0;
                    if (in[u] > 0) y = max(y, RMQ(0, in[u]-1));
                    if (out[u]+1 < len) y = max(y, RMQ(out[u]+1, len-1));
                    //if(i==8){cout<<x<<" "<<y<<endl;}
                    ans_u[i] = min(x, y);
                    ans_v[i] = ans_u[i] + 1;
                }
            }
            for (int i = 0; i < m; i++)
                printf("%d %d\n", ans_u[i], ans_v[i]);
        }
        return 0;
    }