D - Erase Leaves

D - Erase Leaves

https://atcoder.jp/contests/abc333/tasks/abc333_d

 

思路

把这个图看成一棵树， 1作为树根，

统计 1树根关联的 子节点作为根的子树的总节点数，

去除 子树中总节点数最大子的 子树， 其它子树的总节点 记做贡献， 最后+1 （对应1节点）。

 

同时注意一个特殊情况， 1仅有一个子树的情况， 1退化为叶子节点， 只需要一次操作。

 

Code

https://atcoder.jp/contests/abc333/submissions/48592800

/******************************** GRAPH START ***************************************/
// Graph class represents a directed graph
// using adjacency list representation
class Graph {
public:
    map<int, int> nodecnt;
    map<int, bool> visited;
    map<int, vector<int> > adj;

    // function to add an edge to graph
    void addEdge(int v, int w);

    // DFS traversal of the vertices
    // reachable from v
    void DFS(int v);
};

void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w); // Add w to v’s list.
    adj[w].push_back(v); // Add w to v’s list.
}

void Graph::DFS(int v)
{
    // Mark the current node as visited and
    // print it
    visited[v] = true;
//    cout << v << " ";

    if (adj[v].size() == 0){
        nodecnt[v] = 1;
        return;
    }

    // Recur for all the vertices adjacent
    // to this vertex
    list<int>::iterator i;
    long long nodesnum = 1;
    
    for (auto one: adj[v]){
        if (!visited[one]){
            DFS(one);

            nodesnum += nodecnt[one];
        }
    }
    
    nodecnt[v] = nodesnum;
}

/******************************** GRAPH END ***************************************/

/*
https://atcoder.jp/contests/abcxxx/tasks/abcxxx_d
*/

int n;

class Graph g;

int main()
{
    cin >> n;
    
    for(int i=1; i<n; i++){
        int u,v;
        
        cin >> u >> v;
        
        g.addEdge(u, v);
    }
    
    if(g.adj[1].size() == 1){
        cout << 1 << endl;
        return 0;
    }
    
    g.DFS(1);


    vector<int> oneadjnodecnt;
    
    int oneadj_len = g.adj[1].size();
    for(int i=0; i<oneadj_len; i++){
        int oneadj_i = g.adj[1][i];
        int nodes_i = g.nodecnt[oneadj_i];

        oneadjnodecnt.push_back(nodes_i);

//        if (minnodes > nodes_i){
//            minnodes = nodes_i;
//        }
    }

    sort(oneadjnodecnt.begin(), oneadjnodecnt.end());

    int nodenumsum = 0;
    int oneadjnodecnt_len = oneadjnodecnt.size();
    for(int i=0; i<oneadjnodecnt_len-1; i++){
        nodenumsum += oneadjnodecnt[i];
    }

    cout << nodenumsum+1 << endl;

    return 0;
}