How to trace the path in a Breadth-First Search

Question

How do you trace the path of a Breadth-First Search  such that in the following example     If searching for key 11  return the shortest list connecting 1 to 11    1  4  7  11

User · Answer

I thought I d try code this up for fun   graph              1     2    3    4             2     5    6             5     9    10             4     7    8             7     11    12              def bfs graph  forefront  end         assumes no cycles      next forefront     node  path         node  for i  path in forefront if i in graph for node in graph i        for node path in next forefront          if node  end              return path     else          return bfs graph next forefront end   print bfs graph    1   1     11       gt  gt  gt    1  4  7  11   If you want cycles you could add this   for i  j in for front    allow cycles  add this code     if i in graph          del graph i

User · Answer

I like both  Qiao first answer and  Or s addition  For a sake of a little less processing I would like to add to Or s answer     In  Or s answer keeping track of visited node is great  We can also allow the program to exit sooner that it currently is  At some point in the for loop the current neighbour will have to be the end  and once that happens the shortest path is found and program can return   I would modify the the method as follow  pay close attention to the for loop  graph     1   2  3  4   2   5  6   3   10   4   7  8   5   9  10   7   11  12   11   13          def bfs graph to search  start  end           queue     start           visited   set        while queue            Gets the first path in the queue         path   queue pop 0             Gets the last node in the path         vertex   path -1             Checks if we got to the end         if vertex    end              return path           We check if the current node is already in the visited nodes set in order not to recheck it         elif vertex not in visited                enumerate all adjacent nodes  construct a new path and push it into the queue             for current neighbour in graph to search get vertex                       new path   list path                  new path append current neighbour                  queue append new path                    No need to visit other neighbour  Return at once                 if current neighbour    end                     return new path                 Mark the vertex as visited             visited add vertex    print bfs graph  1  13    The output and everything else will be the same  However  the code will take less time to process  This is especially useful on larger graphs  I hope this helps someone in the future

User · Answer

You should have look at http   en wikipedia org wiki Breadth-first search first      Below is a quick implementation  in which I used a list of list to represent the queue of paths     graph is in adjacent list representation graph              1     2    3    4             2     5    6             5     9    10             4     7    8             7     11    12              def bfs graph  start  end         maintain a queue of paths     queue            push the first path into the queue     queue append  start       while queue            get the first path from the queue         path   queue pop 0            get the last node from the path         node   path -1            path found         if node    end              return path           enumerate all adjacent nodes  construct a new path and push it into the queue         for adjacent in graph get node                   new path   list path              new path append adjacent              queue append new path   print bfs graph   1    11       Another approach would be maintaining a mapping from each node to its parent  and when inspecting the adjacent node  record its parent  When the search is done  simply backtrace according the parent mapping   graph              1     2    3    4             2     5    6             5     9    10             4     7    8             7     11    12              def backtrace parent  start  end       path    end      while path -1     start          path append parent path -1        path reverse       return path   def bfs graph  start  end       parent          queue          queue append start      while queue          node   queue pop 0          if node    end              return backtrace parent  start  end          for adjacent in graph get node                   if node not in queue                   parent adjacent    node    lt  lt  lt  lt  lt  record its parent                  queue append adjacent   print bfs graph   1    11     The above codes are based on the assumption that there s no cycles

User · Answer

I liked qiao s first answer very much  The only thing missing here is to mark the vertexes as visited  Why we need to do it  Lets imagine that there is another node number 13 connected from node 11  Now our goal is to find node 13  After a little bit of a run the queue will look like this     1  2  6    1  3  10    1  4  7    1  4  8    1  2  5  9    1  2  5  10     Note that there are TWO paths with node number 10 at the end  Which means that the paths from node number 10 will be checked twice  In this case it doesn t look so bad because node number 10 doesn t have any children   But it could be really bad  even here we will check that node twice for no reason    Node number 13 isn t in those paths so the program won t return before reaching to the second path with node number 10 at the end  And we will recheck it    All we are missing is a set to mark the visited nodes and not to check them again   This is qiao s code after the modification   graph         1   2  3  4       2   5  6       3   10       4   7  8       5   9  10       7   11  12       11   13      def bfs graph to search  start  end       queue     start       visited   set        while queue            Gets the first path in the queue         path   queue pop 0             Gets the last node in the path         vertex   path -1             Checks if we got to the end         if vertex    end              return path           We check if the current node is already in the visited nodes set in order not to recheck it         elif vertex not in visited                enumerate all adjacent nodes  construct a new path and push it into the queue             for current neighbour in graph to search get vertex                       new path   list path                  new path append current neighbour                  queue append new path                 Mark the vertex as visited             visited add vertex    print bfs graph  1  13    The output of the program will be    1  4  7  11  13    Without the unneccecery rechecks

User · Answer

Very easy code  You keep appending the path each time you discover a node    graph               A   set   B    C               B   set   A    D    E               C   set   A    F               D   set   B               E   set   B    F               F   set   C    E               def retunShortestPath graph  start  end        queue     start  start        visited   set        while queue          vertex  path   queue pop 0          visited add vertex          for node in graph vertex               if node    end                  return path    end              else                  if node not in visited                      visited add node                      queue append  node  path    node

[python] How to trace the path in a Breadth-First Search?

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