# Design an algorithm that uses BFS to output the shortest path from vertex u to V in the graph G (non-weighted undirected connectivity graph G is stored with adjacency table)

Source: Internet
Author: User

thought: Figure G is a non-weighted undirected connectivity graph. The length of an edge is counted as 1, so the shortest path to the vertex u and Vertex v is the vertex sequence with the least number of sides of vertex u and Vertex v. Using the breadth-first traversal algorithm, the breadth traversal from U is similar to a layer-by-layer outward expansion from the vertex u, and when the vertex v is first found, the queue includes the recent path from vertex u to vertex v, and then uses the queue output path (inverse path), so it is designed as a non-cyclic queue.

The corresponding algorithm is as follows:

typedef struct

{

int data; //Vertex number

int parent; //position of the previous vertex

} QUEUE; //non-circular queue type

void ShortPath (Agraph *g,int u, int v)

{

The shortest inverse path of the output from vertex u to vertex v

Arcnode *p;

int w,i;

QUEUE QU[MAXV]; //non-circular queue

int front=-1,rear=-1; //queue tail pointer

int VISITED[MAXV];

for (i=0;i<g->n;i++)//Access flag set initial value 0

visited[i]=0;

rear++;

Qu[rear].data=u; //vertex u into Team

Qu[rear].parent=-1;

Visited[u]=1;

while (front<=rear)//queue is not empty when looping

{

front++;

W=qu[front].data; //out of the team vertex W

if (w==v)//The inverse of the output path when V is found and exits

{

I=front; //Output reverse path via queue

while (Qu[i].parent!=-1)

{

printf ("%2d", qu[i].data);

I=qu[i].parent;

}

printf ("%2d\n", qu[i].data);

Break

}

while (P!=null)

{

{

rear++; //Put the non-visited adjacency points of W into the team

Qu[rear].parent=front;

}

p=p->nextarc;

}

}

}

As you can see, the results of finding the shortest inverse path for vertices 0 to 3 are as follows:

"0": 1->4->^

"1": 0->2->3->^

"2": 1->2->^

"3": 1->2->^

"4": 0->2->^

Shortest inverse path of vertex 0 to Vertex 3:3 1 0

Design an algorithm that uses BFS to output the shortest path from vertex u to V in the graph G (non-weighted undirected connectivity graph G is stored with adjacency table)

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