廣度優先搜尋（BFS）演算法類似於樹中的層次搜尋：

從任意點s出發，先遍歷與s相鄰的點，然後再遍歷於相鄰的點相鄰的點。注意有向圖必須是順方向的鄰接點。

為什麼說廣度優先搜尋可以用來求無權最短路徑呢？因為，廣度優先搜尋每次都會先發現距離s為k的所有頂點，然後才會 發現距離s為k+1的所有頂點。 s為起始點。

void BFS(Graph& g, Vertex& s)
 {
  queue<vertex> q;
  for each vertex v in g
  {
   v.distance = INFINITY;
  }
  s.distance = 0;
  
  q.enqueue(s);
  while (!q.Empty())
  {
   v = dequeue(q);
   for each w adjenct to v
   if (v.distance == INFINITY)
   {
    w.distance = v. distance + 1;       
    w.path = v;
    q.enqueue(w);
   }    
  }    
 }
 對於外面的while迴圈，會執行|V|次，因為每個頂點入隊出隊一次，而裡面的for迴圈會看到一共會執行|E|次，即變長， 所以該演算法時間複雜度為O(|V|+|E|)。
 列印最短路徑：
 void PrintPath(Graph& g, Vertex& target)
 {
  if (target.path is a vertex)
  {
   PrintPath(g, target.path);
  }
  cout << target;
 }

#if 1 #include <iostream> #include <queue> using namespace std; #define MAX_VERTEX_NUM 20 #define INFINITY 2147483647 enum var{Infinity = -1}; struct adjVertexNode { int adjVertexPosition; adjVertexNode* next; }; //注意此結構體大小，因為對齊要求，第一個char位元組陣列要擴充套件成為4個位元組。所以this struct 為12個位元組 struct VertexNode { char data[2]; adjVertexNode* list; int dist; VertexNode *path; }; struct Graph { VertexNode VertexNode[MAX_VERTEX_NUM]; int vertexNum; int edgeNum; }; void CreateGraph (Graph& g) { int i, j, edgeStart, edgeEnd; adjVertexNode* adjNode; cout << "Please input vertex and edge num (vnum enum):" <<endl; cin >> g.vertexNum >> g.edgeNum; cout << "Please input vertex information (v1)/n note: every vertex info end with Enter" <<endl; for (i=0;i<g.vertexNum;i++) { cin >> g.VertexNode[i].data; // vertex data info. g.VertexNode[i].list = NULL; g.VertexNode[i].path = NULL; } cout << "input edge information(start end):" <<endl; for (j=0; j<g.edgeNum; j++) { cin >>edgeStart >>edgeEnd; //連結串列的插入程式。 adjNode = new adjVertexNode; adjNode->adjVertexPosition = edgeEnd-1; // because array begin from 0, so it is j-1 adjNode->next=g.VertexNode[edgeStart-1].list; g.VertexNode[edgeStart-1].list=adjNode; //每增加一條邊，則邊的End頂點的入度加1 } } void PrintAdjList(const Graph& g) { cout << "The adjacent list for graph is:" << endl; for (int i=0; i < g.vertexNum; i++) { cout<< g.VertexNode[i].data << "->"; adjVertexNode* head = g.VertexNode[i].list; if (head == NULL) cout << "NULL"; while (head != NULL) { cout << head->adjVertexPosition + 1 <<" "; head = head->next; } cout << endl; } } void DeleteGraph(Graph &g) { for (int i=0; i<g.vertexNum; i++) { adjVertexNode* tmp=NULL; while(g.VertexNode[i].list!=NULL) { tmp = g.VertexNode[i].list; g.VertexNode[i].list = g.VertexNode[i].list->next; delete tmp; tmp = NULL; } } } #if 1 void BFS(Graph &g,VertexNode &S) { // VertexNode *V = S; queue<VertexNode *>Q; int i; for(i = 0; i < g.vertexNum; i++) { g.VertexNode[i].dist = Infinity; } S.dist = 0; Q.push(&S); while (!Q.empty()) { VertexNode *v = Q.front(); Q.pop(); adjVertexNode *head = v->list; while (head != NULL) { if (g.VertexNode[head->adjVertexPosition].dist == Infinity) { g.VertexNode[head->adjVertexPosition].dist = v->dist + 1; g.VertexNode[head->adjVertexPosition].path = v; Q.push(&g.VertexNode[head->adjVertexPosition]); } head = head->next; } } } #endif #if 1 void PrintGraph(Graph& g, VertexNode* target) { if (target->path != NULL) { //cout << 1 << " "; PrintGraph(g, target->path); cout << " "; } cout << target->data ; } #endif int main(int argc, const char** argv) { Graph g; CreateGraph(g); PrintAdjList(g); BFS(g, g.VertexNode[0]); cout<<"print the shortest path from v1 to v7:"<<endl; PrintGraph(g, &g.VertexNode[6]); DeleteGraph(g); system("pause"); return 0; } #endif