【codeforces 19/11/06 div2】D. 0-1 MST

  1 #include<iostream>
  2 #include<set>
  3 #include<map>
  4 #include<queue>
  5 #include<algorithm>
  6 using namespace std;
  7 
  8 const int maxn = 100010;
  9 int n, m;
 10 set<int>e[maxn];
 11 set<int>node;
 12 int fa[maxn];
 13 int sz[maxn];
 14 
 15 int find(int x)
 16 {
 17     if (fa[x] == x) return x;
 18     fa[x] = find(fa[x]);
 19     return fa[x];
 20 }
 21 
 22 void merge(int a, int b)
 23 {
 24     int fx = find(a);
 25     int fy = find(b);
 26     fa[fx] = find(fy);
 27     sz[fy] += sz[fx];
 28 }
 29 
 30 bool check(int a, int b)
 31 {
 32     return find(a) == find(b);
 33 }
 34 
 35 void dfs(int x)
 36 {
 37     set<int>reach;
 38     for (auto it : node)
 39     {
 40         if (e[x].find(it) == e[x].end())
 41         {
 42             reach.insert(it);
 43         }
 44     }
 45     for (auto it : reach)
 46     {
 47         node.erase(it);
 48     }
 49     for (auto it : reach)
 50     {
 51         dfs(it);
 52     }
 53 }
 54 
 55 int main()
 56 {
 57     cin >> n >> m;
 58     for (int i = 1; i <= n; i++)
 59     {
 60         fa[i] = i;
 61         node.insert(i);
 62     }
 63     for (int i = 1; i <= m; i++)
 64     {
 65         int a, b;
 66         cin >> a >> b;
 67         e[a].insert(b);
 68         e[b].insert(a);
 69     }
 70     /*
 71     //dfs做法
 72     int ans = 0;
 73     for (int i = 1; i <= n; i++)
 74     {
 75         if (node.find(i) != node.end())
 76         {
 77             dfs(i);
 78             ans++;
 79         }
 80     }
 81     */
 82     //正解：并查集
 83     vector<int>g;
 84     for (int i = 1; i <= n; i++)
 85     {
 86         sz[i] = 1;
 87         map<int, int>cnt;
 88         for (auto it : e[i])
 89         {
 90             if (it >= i) continue;
 91             cnt[find(it)]++;
 92         }
 93         for (auto it : g)
 94         {
 95             int t = find(it);
 96             if (check(i, t)) continue;
 97             if (sz[t] > cnt[t])
 98             {
 99                 merge(i, t);
100             }
101         }
102         int fi = find(i);
103         if (fi == i) g.push_back(fi);
104     }
105     int ans = 0;
106     for (int i = 1; i <= n; i++)
107     {
108         if (fa[i] == i) ans++;
109     }
110     cout << ans - 1;
111     return 0;
112 }
113  

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