习题7-4　切断圆环链（Cutting Chains, ACM/ICPC World Finals 2000, UVa818）

#include <iostream>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <algorithm>
#include <sstream>
#include <utility>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <cctype>
#define CLEAR(a, b) memset(a, b, sizeof(a))
#define IN() freopen("in.txt", "r", stdin)
#define OUT() freopen("out.txt", "w", stdout)
#define LL long long
#define mod 1000000007
#define INF 10000007
#define eps 1e-5
#define PI 3.1415926535898
using namespace std;
//-------------------------CHC------------------------------//
const int maxn = 20;
int n;
vector<int> G[maxn];
bool cut[maxn], vis[maxn];
int component, cut_num;

void calc_cut(int subset) {
CLEAR(cut, 0);
cut_num = 0;
for (int i = 0; i < n; ++i) {
if ((1 << i) & subset) cut[n - i] = true, ++cut_num;
}
}

bool too_much() {
for (int i = 1; i <= n; ++i) {
if (cut[i]) continue;
int deg = 0;
for (int j = 0; j < G[i].size(); ++j)
if (!cut[G[i][j]]) ++deg;
if (deg > 2) return true;
}
return false;
}

bool dfs(int u, int f) {
vis[u] = true;
for (int i = 0; i < G[u].size(); ++i) {
int v = G[u][i];
if (!cut[v] && v != f) {
if (vis[v]) return true;
else if (dfs(v, u)) return false;
}
}
return false;
}

bool have_circle() {
CLEAR(vis, 0);
component = 0;
for (int i = 1; i <= n; ++i)
if (!vis[i] && !cut[i]) {
if (dfs(i, -1)) return true;
component++;
}
return false;
}

int main() {
int kase = 1;
while (~scanf("%d", &n) && n) {
for (int i = 0; i < maxn; ++i) G[i].clear();
int u, v;
while (scanf("%d%d", &u, &v)) {
if (u == -1 || v == -1) break;
G[u].push_back(v);
G[v].push_back(u);
}
for (int i = 1; i <= n; ++i) {
sort(G[i].begin(), G[i].end());
G[i].resize(unique(G[i].begin(), G[i].end()) - G[i].begin());
}
int ans = n;
for (int i = 0; i < (1 << n); ++i) {
calc_cut(i);
if (too_much() || have_circle()) continue;
if(component <= cut_num + 1) ans = min(ans, cut_num);
}
printf("Set %d: Minimum links to open is %d\n", kase++, ans);
}
return 0;
}