递归算法的迭代版本速度较慢

Question

我正在尝试实现 Tarjan 强连接组件（SCC）的迭代版本，为方便起见，在此处复制（来源：http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm）。

Input: Graph G = (V, E)

index = 0                         // DFS node number counter 
S = empty                         // An empty stack of nodes
forall v in V do
  if (v.index is undefined)       // Start a DFS at each node
    tarjan(v)                     // we haven't visited yet

procedure tarjan(v)
  v.index = index                 // Set the depth index for v
  v.lowlink = index
  index = index + 1
  S.push(v)                       // Push v on the stack
  forall (v, v') in E do          // Consider successors of v
    if (v'.index is undefined)    // Was successor v' visited?
        tarjan(v')                // Recurse
        v.lowlink = min(v.lowlink, v'.lowlink)
    else if (v' is in S)          // Was successor v' in stack S? 
        v.lowlink = min(v.lowlink, v'.lowlink )
  if (v.lowlink == v.index)       // Is v the root of an SCC?
    print "SCC:"
    repeat
      v' = S.pop
      print v'
    until (v' == v)

我的迭代版本使用以下 Node 结构。

struct Node {
    int id; //Signed int up to 2^31 - 1 = 2,147,483,647
    int index;
    int lowlink;        
    Node *caller;                    //If you were looking at the recursive version, this is the node before the recursive call
    unsigned int vindex;             //Equivalent to the iterator in the for-loop in tarjan
    vector<Node *> *nodeVector;      //Vector of adjacent Nodes 
};

以下是我对迭代版本所做的操作：

 void Graph::runTarjan(int out[]) {  //You can ignore out. It's a 5-element array that keeps track of the largest 5 SCCs
        int index = 0;
tarStack = new stack<Node *>();
    onStack = new bool[numNodes];
  for (int n = 0; n < numNodes; n++) {
    if (nodes[n].index == unvisited) {
      tarjan_iter(&nodes[n], index);
    }
  }
}

void Graph::tarjan_iter(Node *u, int &index) {
    u->index = index;
    u->lowlink = index;
    index++;
    u->vindex = 0; 
    tarStack->push(u);
    u->caller = NULL;           //Equivalent to the node from which the recursive call would spawn.
    onStack[u->id - 1] = true;
    Node *last = u;
    while(true) {
        if(last->vindex < last->nodeVector->size()) {       //Equivalent to the check in the for-loop in the recursive version
            Node *w = (*(last->nodeVector))[last->vindex];
            last->vindex++;                                   //Equivalent to incrementing the iterator in the for-loop in the recursive version
            if(w->index == unvisited) {
                w->caller = last;                     
                w->vindex = 0;
                w->index = index;
                w->lowlink = index;
                index++;
                tarStack->push(w);
                onStack[w->id - 1] = true;
                last = w;
            } else if(onStack[w->id - 1] == true) {
                last->lowlink = min(last->lowlink, w->index);
            }
        } else {  //Equivalent to the nodeSet iterator pointing to end()
            if(last->lowlink == last->index) {
                numScc++;
                Node *top = tarStack->top();
                tarStack->pop();
                onStack[top->id - 1] = false;
                int size = 1;

                while(top->id != last->id) {
                    top = tarStack->top();
                    tarStack->pop();
                    onStack[top->id - 1] = false;
                    size++;
                }
                insertNewSCC(size);  //Ranks the size among array of 5 elements
            }

            Node *newLast = last->caller;   //Go up one recursive call
            if(newLast != NULL) {
                newLast->lowlink = min(newLast->lowlink, last->lowlink);
                last = newLast;
            } else {   //We've seen all the nodes
                break;
            }
        }
    }
}

我的迭代版本运行并提供与递归版本相同的输出。问题是迭代版本较慢，我不确定为什么。谁能给我一些关于我的实施的见解？有没有更好的方法来迭代实现递归算法？

Answer 1

递归算法使用堆栈作为存储区域。在迭代版本中，您使用一些向量，它们本身依赖于堆分配。众所周知，基于堆栈的分配非常快，因为它只是移动堆栈末尾指针的问题，而堆分配可能要慢得多。迭代版本较慢并不完全令人惊讶。

一般来说，如果手头的问题非常适合仅堆栈递归模型，那么无论如何，递归。