Important Sisters【HDU-4694】【Dominator Tree】

题目链接

  有N个妹妹，然后从N号妹妹开始发消息，现在每个妹妹都想知道消息是什么，但是消息只有M条有向路径来传播，然后现在询问每个点u，从N号妹妹到她的路径上有哪些必经点，将这些必经点的点序号求和后输出。

  所以，这就是一个一般图上的Dominator Tree问题，一般图的支配树问题，直接建支配树，然后求一个“深度”即可。然后因为是多组输入，记得初始化。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
#define pii pair<int, int>
#define MP(a, b) make_pair(a, b)
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 5e4 + 7, maxM = 2e5 + 7;
int N, M;
namespace Graph
{
    int head[maxN], cnt;
    struct Eddge
    {
        int nex, to;
        Eddge(int a=-1, int b=0):nex(a), to(b) {}
    } edge[maxM];
    inline void addEddge(int u, int v)
    {
        edge[cnt] = Eddge(head[u], v);
        head[u] = cnt++;
    }
    inline void init()
    {
        cnt = 0;
        for(int i=1; i<=N; i++) head[i] = -1;
    }
};
using namespace Graph;
namespace Dominator
{
    int tim;
    int dfn[maxN], rid[maxN], fa[maxN], sdom[maxN], idom[maxN];
    int fo[maxN], vo[maxN];
    vector<int> pre[maxN], bkt[maxN];
    int findf(int p)
    {
        if(fo[p]==p) return p;
        int r = findf(fo[p]);
        if(sdom[vo[fo[p]]]<sdom[vo[p]]) vo[p] = vo[fo[p]];
        return fo[p] = r;
    }
    inline int eval(int p)
    {
        findf(p);
        return vo[p];
    }
    void dfs(int p)
    {
        rid[dfn[p]=++tim] = p; sdom[p] = dfn[p];
        for(int i=head[p]; ~i; i=edge[i].nex) if(!dfn[edge[i].to])
        {
            dfs(edge[i].to);
            fa[edge[i].to] = p;
        }
    }
    void work()
    {
        int p;
        dfs(N);
        for(int i=tim; i>=2; i--)
        {
            p = rid[i];
            for(int k : pre[p]) if(dfn[k]) sdom[p] = min(sdom[p], sdom[eval(k)]);
            bkt[rid[sdom[p]]].push_back(p);
            int fp = fa[p];
            fo[p] = fa[p];
            for(int v : bkt[fp])
            {
                int u = eval(v);
                idom[v] = sdom[u] == sdom[v] ? fp : u;
            }
            bkt[fp].clear();
        }
        for(int i=2; i<=tim; i++) { p = rid[i]; idom[p] = idom[p] == rid[sdom[p]] ? idom[p] : idom[idom[p]]; }
        for(int i=2; i<=tim; i++) { p = rid[i]; sdom[p] = rid[sdom[p]]; }
    }
    inline void link(int a, int b)
    {
        addEddge(a, b);
        pre[b].push_back(a);
    }
    void init()
    {
        tim = 0;
        for(int i=1; i<=N; i++)
        {
            dfn[i] = idom[i] = 0;
            fo[i] = vo[i] = i;
            pre[i].clear();
            bkt[i].clear();
        }
    }
};
using namespace Dominator;
vector<int> E[maxN];
ll siz[maxN];
void last_dfs(int u)
{
    siz[u] += u;
    for(int v : E[u])
    {
        siz[v] = siz[u];
        last_dfs(v);
    }
}
int main()
{
    while(scanf("%d%d", &N, &M) != EOF)
    {
        Graph::init();
        Dominator::init();
        for(int i=1, u, v; i<=M; i++)
        {
            scanf("%d%d", &u, &v);
            link(u, v);
        }
        work();
        for(int i=1; i<=N; i++) { E[i].clear(); siz[i] = 0; }
        for(int i=1; i<N; i++) E[idom[i]].push_back(i);
        siz[N] = 0;
        last_dfs(N);
        for(int i=1; i<=N; i++) printf("%lld%c", siz[i], i == N ? '
' : ' ');
    }
    return 0;
}