hihocoder1127 二分图三·二分图最小点覆盖和最大独立集

Posted 2021-01-15 wangyiming

思路：

对于不存在孤立点的图，|最大匹配| + |最小边覆盖| = |V|，|最大独立集| + |最小顶点覆盖| = |V|。对于二分图而言，|最大匹配| = |最小顶点覆盖|。（V是图的顶点集合）

实现：

 1 #include <iostream>
 2 #include <cstring>
 3 #include <vector>
 4 using namespace std;
 5 
 6 const int MAXN = 1005;
 7 vector<int> G[MAXN];
 8 int n, m;
 9 bool used[MAXN];
10 int match[MAXN];
11 
12 bool dfs(int v)
13 {
14     used[v] = true;
15     for (int i = 0; i < G[v].size(); i++)
16     {
17         int u = G[v][i];
18         int w = match[u];
19         if (w == -1 || !used[w] && dfs(w))
20         {
21             match[v] = u;
22             match[u] = v;
23             return true;
24         }
25     }
26     return false;
27 }
28 
29 int max_match()
30 {
31     int res = 0;
32     for (int i = 1; i <= n; i++)
33     {
34         if (match[i] == -1)
35         {
36             memset(used, 0, sizeof(used));
37             if (dfs(i))
38                 res++;
39         }
40     }
41     return res;
42 }
43 
44 int main()
45 {
46     cin >> n >> m;
47     int a, b;
48     for (int i = 0; i < m; i++)
49     {
50         cin >> a >> b;
51         G[a].push_back(b);
52         G[b].push_back(a);
53     }
54     memset(match, -1, sizeof(match));
55     int ans = max_match();
56     cout << ans << endl;
57     cout << n - ans << endl;
58     return 0;
59 }