HDU3394 Railway(点双连通分量)
题意:
给出一个无向图,求出它的冲突边数和多余边数,冲突边就是那些同时存在于多个环中的边,而多余边是不在任何一个环中的边.。
要点:
多余边很明显就是桥,我们可以推断除冲突边只能在点双连通分量中,感觉边双应该也行,主要就是求出分量后看分量中点数n和边数m的关系,如果n<m,整个分量中所有的边都是冲突边,因为总是一个大环分成几个内部小环,大环跟内部小环肯定冲突。
#include<iostream>
#include<cstring>
#include<algorithm>
#include<vector>
#include<stack>
using namespace std;
const int maxn = 10000 + 10;
vector<int> g[maxn], bcc[maxn];
int dfs_clock, bcc_cnt,n,m,ans1,ans2;
int pre[maxn], bccno[maxn];
typedef pair<int, int> Pair;
stack<Pair> s;
void solve()//冲突边计算
{
for (int u = 1; u <= bcc_cnt; u++)
{
int sum = 0;
bool vis[maxn];
memset(vis, false, sizeof(vis));
for (int i = 0; i < bcc[u].size(); i++)
vis[bcc[u][i]] = true;
for (int i = 0; i < bcc[u].size(); i++)
{
int x = bcc[u][i];
for (int j = 0; j < g[x].size(); j++)
if (vis[g[x][j]])
sum++;
}
sum /= 2;
if (sum>bcc[u].size())
ans2 += sum;
}
}
int dfs(int u, int fa)
{
int lowu = pre[u] = ++dfs_clock;
for (int i = 0; i < g[u].size(); i++)
{
int v = g[u][i];
Pair e = make_pair(u, v);
if (!pre[v])
{
s.push(e);
int lowv = dfs(v, u);
lowu = min(lowu, lowv);
if (lowv >= pre[u])
{
if (lowv > pre[u])
ans1++;//桥数增加也就是多余边
bcc_cnt++;
bcc[bcc_cnt].clear();
while (1)
{
Pair x = s.top(); s.pop();
if (bccno[x.first] != bcc_cnt)
{
bcc[bcc_cnt].push_back(x.first);
bccno[x.first] = bcc_cnt;
}
if (bccno[x.second] != bcc_cnt)
{
bcc[bcc_cnt].push_back(x.second);
bccno[x.second] = bcc_cnt;
}
if (x.first == u&&x.second == v)
break;
}
}
}
else if (pre[v] < pre[u] && v != fa)
{
s.push(e);
lowu = min(lowu, pre[v]);
}
}
return lowu;
}
void find_bcc()
{
memset(pre, 0, sizeof(pre));
memset(bccno, 0, sizeof(bccno));
dfs_clock = bcc_cnt = 0;
for (int i = 0; i < n; i++)
if (!pre[i])
dfs(i, -1);
}
int main()
{
while (scanf("%d%d", &n, &m) == 2 && n)
{
ans1 = ans2 = 0;
for (int i = 0; i < maxn; i++)
{
g[i].clear();
bcc[i].clear();
}
int x, y;
for (int i = 1; i <= m; i++)
{
scanf("%d%d", &x, &y);
g[x].push_back(y);
g[y].push_back(x);
}
find_bcc();
solve();
printf("%d %d\n", ans1, ans2);
}
return 0;
}