Tarjanの強連結成分（SCC）の反復バージョンを実装しようとしています。これは、便宜上ここに複製されています（出典： 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)
私の反復バージョンは、次のノード構造体を使用しています。
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
};
反復バージョンで行ったことは次のとおりです。
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;
}
}
}
}
私の反復バージョンが実行され、再帰バージョンと同じ出力が得られます。問題は、反復バージョンが遅いことです。理由はわかりません。誰かが私の実装についての洞察を私に与えることができますか？再帰的アルゴリズムを繰り返し実装するためのより良い方法はありますか？