Road Construction 【POJ - 3352】【Tarjan边双连通】

题目链接

  题意：给一个无向连通图，至少添加几条边使得去掉图中任意一条边不改变图的连通性（即使得它变为边双连通图）。

  思路：就是去求一个缩点之后求度为1的点的个数，然后用(ans + 1)/2就可以得到最后的答案了。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#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
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
const int maxN = 1e3 + 7;
int N, M, head[maxN], cnt;
struct Eddge
{
    int nex, to;
    Eddge(int a=-1, int b=0):nex(a), to(b) {}
}edge[maxN<<1];
inline void addEddge(int u, int v)
{
    edge[cnt] = Eddge(head[u], v);
    head[u] = cnt++;
}
inline void _add(int u, int v) { addEddge(u, v); addEddge(v, u); }
int dfn[maxN], low[maxN], Belong[maxN], Index, Bcnt, Stap[maxN], Stop, du[maxN];
bool inStack[maxN];
void Tarjan(int u, int fa)
{
    dfn[u] = low[u] = ++Index;
    inStack[u] = true;
    Stap[++Stop] = u;
    int v;
    for(int i=head[u]; ~i; i=edge[i].nex)
    {
        v = edge[i].to;
        int child = 0;
        if(v == fa && !child) { child++; continue; }
        if(!dfn[v])
        {
            Tarjan(v, u);
            low[u] = min(low[u], low[v]);
        }
        else if(inStack[v] && low[u] > dfn[v]) low[u] = dfn[v];
    }
    if(dfn[u] == low[u])
    {
        Bcnt++;
        do
        {
            v = Stap[Stop--];
            Belong[v] = Bcnt;
            inStack[v] = false;
        }
        while(u != v);
    }
}
inline void init()
{
    cnt = Index = Stop = Bcnt = 0;
    memset(head, -1, sizeof(head));
    for(int i=1; i<=N; i++) dfn[i] = du[i] = 0;
    for(int i=1; i<=N; i++) inStack[i] = false;
}
int main()
{
    while(scanf("%d%d", &N, &M) != EOF)
    {
        init();
        for(int i=1, u, v; i<=M; i++)
        {
            scanf("%d%d", &u, &v);
            _add(u, v);
        }
        for(int i=1; i<=N; i++) if(!dfn[i]) Tarjan(i, -1);
        for(int u=1; u<=N; u++)
        {
            for(int i=head[u], v; ~i; i=edge[i].nex)
            {
                v = edge[i].to;
                if(Belong[u] == Belong[v]) continue;
                du[Belong[v]]++;
            }
        }
        int ans = 0;
        for(int i=1; i<=Bcnt; i++)
        {
            if(du[i] == 1) ans++;
        }
        printf("%d\n", (ans + 1)/2);
    }
    return 0;
}