从节点数组和边缘向量获取所有子树的最有效方法是什么？

Question

Assume that there are nodes as array and undirected edges as vector like this:

int nodes[n] = {1, 2, 3, ... ,n };
vector<pair<int, int>> edges;

edges.push_back(std::make_pair(0, 2));
edges.push_back(std::make_pair(2, 4));

where each element of array is value and n is the number of array. Following above code, there are two edges. One is from 0 to 2. The other one is from 2 to 4. These numbers indicate index of array. In this case, size of largest sub-tree is 3 that 0-2-4 and size of smallest sub-tree is 1 obviously.

I solved this like below:

1. Sort edges vector
2. Choose one permutation in edges
3. Repeat 2 until exploring all possible cases

However I am not sure this is efficient way. How can I get all sub-trees in the problem domain like this? is there any general and efficient way?

Answer 1

I solved this problem using BFS (Breadth First Search) based on edge information. To avoid making cyclic graph and keep nodes as tree, I use set . And I also apply sort before searching. It is useful to reduce time complexity.

void BFS(set<int> nodes, vector<pair<int,int>>& edges, vector<set<int>>& result) {
    result.push_back(nodes);
    int lastNode = *max_element(nodes.begin(), nodes.end());
    auto findIt = find_if(edges.begin(), edges.end(), [](const pair<int, int>& element){ return element.first == lastNode});
    if(findIt != edges.end()) {
        nodes.insert((*findIt).second);
        BFS(nodes, edges, result);
    }
}

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

vector<set<int>> result;
for(auto it : edges) {
    set<int> nodes;
    nodes.insert((*it).first);
    nodes.insert((*it).second);
    BFS(nodes, edges, result);
}