C++ 中的 Bron Kerbosch 算法 [英] Bron Kerbosch algorithm in c++

问题描述

我一直在练习我的 C++ 算法知识，并且卡在了标准的 BK 实现上.该算法输出太多派系，我似乎不明白为什么.我将图表示为邻接表:

I've been practicing my C++ algorithm knowledge, and got stuck on the standard BK implementation. The algorithm outputs way too many cliques, and I doesn't seem to figure out why. I represented the graph as an adjacency list:

vector< list<int> > adjacency_list;

我的 BK 函数看起来像:

My BK function looks like:

void graph::BronKerbosch(vector<int> R, vector<int> P, vector<int> X){

  if (P.empty() && X.empty()){
    result_cliques.insert(R);
  }

  for (int node : P){

    vector<int> intersection = {}, intersectionX = {};

    //N(P)
    for (int nodeP : adjacency_list[node]){
      for (int node2 : P){
        if (nodeP == node2){
          intersection.push_back(nodeP);
        }   
      }

      //N(X)
      for (int node3 : X){
        if (nodeP == node3){
          intersectionX.push_back(nodeP);
        }
      }
    }

    R.push_back(node);
    BronKerbosch(R,intersection,intersectionX);
    P.erase(remove(P.begin(),P.end(),node),P.end());
    X.push_back(node);    

  }
}

我称之为:

void graph::run_BronKerbosch(){

  vector<int> R,P,X;

  for (int i=1; i < adjacency_list.size(); i++) {
    P.push_back(i);
  }

  BronKerbosch(R,P,X);

  cout << "................\nClassic: " << result_cliques.size() << endl;
  for (auto clique : result_cliques){
    cout << "(";
    for (int node : clique){
      cout << node <<" ";
    }    
    cout << ")\n";    
  } 

}

我正在尝试实现算法的基本版本，但我似乎在这里遗漏了一个细节.问题出在:

I am trying to implement the basic version of the algorithm, but I seem to be missing a detail here. Is the problem in:

for (int node : P){

我应该以某种方式在第一个循环中使用 P 的副本吗?(我在相关问题中看到过这一点)

Should I somehow use a copy of P for this first loop? (I've seen this in a related issue)

感谢您的帮助.

推荐答案

是的，您应该复制一份，除非您提前预留空间以保证不会重新分配¹.(请注意，C++ foreach 实现在幕后归结为一堆迭代器.)

Yes you should take a copy, unless you reserve space in advance so you can guarantee there is no reallocation¹. (Note that the C++ foreach implementation boils down to a bunch of iterators under the hood.)

如果我是你，我会改写为老式的 for 循环，使用 std::size_t(超级学徒² 将使用 std::vector::size_type) 来索引您当前感兴趣的向量元素.当 P<的最后一个元素时终止/code> 已阅读.

I'd recast to an old-fashioned for loop if I were you, iterating over the vector using an std::size_t (the super-pedants² would use a std::vector<int>::size_type) to index the vector element you're currently interested in. Terminate when the final element of P has been read.

参考文献:

¹迭代器失效规则

²C++ for-loop -size_type vs. size_t

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