The breadth-first Traversal Algorithm for undirected Connected Graphs

Image breadth firstAlgorithmIt is the basic graph algorithm and also the basis of the minimum spanning tree and single-source shortest path algorithm. Recently, I implemented the breadth-first traversal algorithm, hoping to have a deeper understanding or better understanding of the algorithm. I saw a video about Yu Dan's visit to youmi online the other day. I agree with Yu Dan's point of view. A person's knowledge is very important. The so-called knowledge, from one aspect, is to be personally experienced. This is especially true for algorithms, a discipline that emphasizes both mathematics and programming.

Any algorithm needs to understand the context of the algorithm. You need to ask yourself some questions about the name of the algorithm and solve the problems, what are the important definitions or conditions of these problems. In fact, there is no omnipotent method, but there are indeed algorithms that can solve specific problems under certain condition sets. Here, the breadth-first traversal algorithm targets undirected connected graphs. One is undirected, and the other is connected. I will give you a undirected connected graph and A Start Node. What should I do if I want you to do a breadth-first traversal?

 /*  ** The adjacent matrix is used to represent an undirected connected graph.  */  # Include <Iostream> # Include <Queue> Using   Namespace STD;  # Define Len 10 # Define Infinite 100 # Define Nil-1 Bool  M [Len] [Len];  Enum  Color {white, gray, black}; color [Len];  Int  D [Len];  Int  P [Len];  //  The breadth-first traversal algorithm is implemented using a queue + coloring tag.  Void BFS (Int  S ){  Int  I;  For (I = 0 ; I <Len; ++ I) {color [I] = White; d [I] = Infinite; P [I] = Nil;} color [s] = Gray; d [s] = 0  ; P [s] = Nil; queue <Int > Q; q. Push (s );  While (! Q. Empty ()){  Int U = Q. Front (); cout <U < Endl; q. Pop ();  //  Access all vertices next to u      Int  J;  For (J = 0 ; J <Len; ++ J ){ If (M [u] [J] = True  ){  If (Color [J] = White) {color [J] = Gray; d [J] = D [u] + 1  ; P [J] = U; q. Push (j) ;}} color [u] = Black ;}}  Int  Main (){  Int  I, J; For (I = 0 ; I <Len; ++ I ){  For (J = 0 ; J <Len; ++ J) {M [I] [J] = False  ;} M [  0 ] [ 2 ] = True ; M [ 2 ] [ 0 ] = True ; M [  1 ] [ 7 ] = True ; M [ 7 ] [ 1 ] = True  ; M [  2 ] [ 7 ] = True ; M [ 7 ] [ 2 ] = True  ; M [ 2 ] [ 4 ] = True ; M [ 4 ] [ 2 ] = True  ; M [  7 ] [ 3 ] = True ; M [ 3 ] [ 7 ] = True  ; M [  3 ] [ 4 ] = True ; M [ 4 ] [ 3 ] = True  ; M [  4 ] [ 5 ] = True ; M [ 5 ] [ 4 ] = True  ; M [  5 ] [8 ] = True ; M [ 8 ] [ 5 ] = True  ; M [  8 ] [ 6 ] = True ; M [ 6 ] [ 8 ] = True  ; M [  8 ] [ 9 ] = True ; M [ 9 ] [ 8 ] = True  ; BFS (  0  );  Return   0  ;} 

 

The aboveProgramIs the breadth-first traversal of the following undirected connected graph:

The output result after compilation and running is: