FIND MINIMUM LIGHT BULBS TO SATISFY (HARD TREE PROBLEM)

https://practice.geeksforgeeks.org/problems/f7bfa137576243795abb0595962d61b632bbad21/1

Given N nodes of a tree and a list of edges. Find the minimum number of nodes to be selected to light up all the edges of the tree.
An edge lights up when at least one node at the end of the edge is selected.

Example 1:
Input:
N = 6
edges[] = {(1,2), (1,3), (2,4), (3,5), (3,6)}
Output: 2
Explanation: Selecting nodes 2 and 3 lights
up all the edges.

Example 2:
Input:
N = 3
arr[] = {(1,2), (1,3)}
Output: 1
Explanation: Selecting Node 1
lights up all the edges.

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class Solution{
  private:
    vector<vector<int>> adj;
  public:
    int res=0;
    bool helper(int src, int par){
        bool SELECT_ROOT=false;
        for(auto nei: adj[src]){
            if(nei!=par){
                bool isChildSelected=helper(nei,src);
                if(isChildSelected==false){
                    SELECT_ROOT=true; // WE CANNOT BREAK OUT YET, WE NEED TO CHECK ALL CHILDREN BEFORE EXITING
                }
            }
        }
        if(SELECT_ROOT==true){
            res++;
        }
        return SELECT_ROOT;
    }

    int countVertex(int N, vector<vector<int>>edges){
        adj.resize(N+1);
        res=0;
        for(auto edge: edges){
            adj[edge[0]].push_back(edge[1]);
            adj[edge[1]].push_back(edge[0]);
        }
        helper(1,-1);
        return res;
    }
};