在C ++中使用BFS的最短路径

Question

I have to write an algorithm to find the shortest path in an unweighted graph. I found out that the best way to find the shortest path in an unweighted graph is to simply perform a BFS and stop once the destination is reached. The problem is I don't know how to keep track of the path that led to that destination.

So far I've thought about creating a new path list for every new node that is discovered, but I can't figure out how to implement that.

This code seems to be working so far as visiting every node goes (it's a bit messy, sorry):

void shortestPath(string start, string finish, list< list<string> > adjList){

    queue< list< list<vertex*> >::iterator >    myQueue;
    list< list<vertex*> > listVertices = initializeVertices(start, adjList);
    list< list<vertex*> >::iterator aux = extractList(start, listVertices);

    myQueue.push(aux);

    while(myQueue.size() > 0){

        list< list<vertex*> >::iterator vert = myQueue.front();

        for(list<vertex*>::iterator it = vert->begin(); it != vert->end(); it++){
            if((*it)->color == "white"){
                (*it)->color = "gray";
                myQueue.push(extractList((*it)->name, listVertices));
            }

        }

        list<vertex*>::iterator vertAux = vert->begin();
        (*vertAux)->color = "black";
        myQueue.pop();
    }
}

Any ideas?

Answer 1

You can store the shortest path tree by keeping, for each vertex v , the name of v 's parent in the shortest path tree. Then you can reconstruct whichever shortest path you want by following these parent pointers until you get to the source vertex.

Answer 2

Add vertex *parent to your vertex class whatever that is, and add one more input *vertex to your push function and change this line:

myQueue.push(extractList((*it)->name, listVertices));

to this:

myQueue.push(extractList((*it)->name, listVertices),*vert);

after you myQueue.pop(); check if poped node is your destination if it is, break from while loop and start from your destination and with a loop print(or whatever you do) every node->parent and then node = node->parent until your reach the source.

Answer 3

//Breadth first Search Shortest Path
//It is implemented using Queue Linked list representation
//It is used to pind the shortest path from destination to the source

#include<iostream>
#include<stdio.h>
#include<stdlib.h>

using namespace std;

typedef struct queue1{
    int info;
    struct queue1 *next;
}node;

void createqueue(node **front1,node **rear1){
    *front1=*rear1=NULL;
}

void pushqueue(node **front1, node **rear1,int item){
    node *ptr;
    ptr=(node *)malloc(sizeof(node));
    ptr->info=item;
    ptr->next=NULL;

    if((*front1)==NULL)
        *front1=*rear1=ptr;
    else{
        (*rear1)->next=ptr;
        *rear1=ptr;
    }
}

int popqueue(node **front1){

int item;
    node *ptr;
    ptr=*front1;
    item=ptr->info;
    *front1=ptr->next;

return item;
}

int peekqueue(node *front1){
    return front1->info;
}

bool isEmpty(node *front1){
    if(front1==NULL)
        return true;
return false;
}

int main(){

    int graph[7][7]={
                {0,1,1,0,0,0,0},
                {1,0,0,1,1,0,0},
                {1,0,0,0,0,1,1},
                {0,1,0,0,0,0,0},
                {0,1,0,0,0,0,0},
                {0,0,1,0,0,0,0},
                {0,0,1,0,0,0,0},
             };

    int src;
    cout << "Following is Breadth First Traversal (starting from vertex 0) \n";
    cin>>src;

    int parent[10];
    parent[src]=-1; //Source is the root node

    cout<<"Breadth First Search\n";

node *front1;
node *rear1;
int choice,element,temp;

createqueue(&front1,&rear1);
pushqueue(&front1,&rear1,src);

bool visited[7];

for(int i=0;i<7;i++) //Mark all nodes as visited as false
    visited[i]=false;


    while(!isEmpty(front1)){
        src=popqueue(&front1);
        cout<<src<<"\t";
        if(!visited[src]){
            for(int i=0;i<7;i++){
                if(graph[src][i] && !visited[i]){
                    parent[i]=src;        //TO get the predessecor of the node which will help in backtracking
                    pushqueue(&front1,&rear1,i);
                }
            }
        visited[src]=true;
        }
    }

int destination;
cout<<"\nEnter destination = \n";
cin>>destination;

int j=destination;
cout<<"Path from "<<j<<" to root node is as follows\n";

//Backtrack from destination to root node
do{
    cout<<""<<j<<"\t";
    j=parent[j];
}while(j!=-1);

cout<<"Thank You\n";

return 0;
}