# methods of visiting the nodes on a level of a tree

• January 23rd, 2010, 12:52 PM
para15000
methods of visiting the nodes on a level of a tree
Hello
I know of only one method of visiting the elements on one level of a tree. This method is not very efficient. This is the way I do it(PHP implementation):
Code:

```private function NextNode(&\$node,\$curlevel,\$desiredlevel,&\$nodesnr=null)         {             if(\$node == null)                 return;             \$curlevel++;             if(\$curlevel == \$desiredlevel)             {                 \$this->Visit(\$node);                 if(\$nodesnr!==null)                     \$nodesnr++;             }             \$this->NextNode(\$node->left,\$curlevel,\$desiredlevel,\$nodesnr);             \$this->NextNode(\$node->right,\$curlevel,\$desiredlevel,\$nodesnr);         }```
I travese all the nodes of the tree in depth(inorder) and I check if teh level is equal to my desired level and if so I visit that node. I also keep track on the number of nodes but that is not relevant to the question.
This is inefficient because it goes throgh the entire tree.

Does anyone know of a better(more efficient) sollution?
• January 24th, 2010, 01:52 AM
nuzzle
Re: methods of visiting the nodes on a level of a tree
Quote:

Originally Posted by para15000
Does anyone know of a better(more efficient) sollution?

One way is to stop going deeper when you've reached the desired level. You just put in a return at the end of the if-statement where you check that the current level equals the desired level.

Another way is to traverse the tree once and build a linked list of tree nodes for each level. You can keep the linked lists in an array at the index corresponding to the level. When you want a certain level it's just to pick the linked list for that level in the array.
• January 24th, 2010, 11:37 AM
para15000
Re: methods of visiting the nodes on a level of a tree
Quote:

Originally Posted by nuzzle
One way is to stop going deeper when you've reached the desired level. You just put in a return at the end of the if-statement where you check that the current level equals the desired level.

I don't see what you mean. If put a return at the end of the if statement after I chekc the level then only the first of the nodes on that level will be returned. I want to return all of them. Maby I don't understand exactly what you mean ...

Quote:

Originally Posted by nuzzle
Another way is to traverse the tree once and build a linked list of tree nodes for each level. You can keep the linked lists in an array at the index corresponding to the level. When you want a certain level it's just to pick the linked list for that level in the array.

This I did but not with a linked list I am using a object-oriented approach so I just stored the level of a node inside the each node object when I build the tree. So I already thought of this ... sorry I forgot to say. Or is this not related to what you meant
• January 24th, 2010, 02:00 PM
nuzzle
Re: methods of visiting the nodes on a level of a tree
Quote:

Originally Posted by para15000
I don't see what you mean. If put a return at the end of the if statement after I chekc the level then only the first of the nodes on that level will be returned. I want to return all of them. Maby I don't understand exactly what you mean ...

It should look like this,
Code:

```            if(\$curlevel == \$desiredlevel)             {                 \$this->Visit(\$node);                 if(\$nodesnr!==null)                     \$nodesnr++;                 return;             }```
This will stop the recursion from going deeper than desiredlevel but the recursion will continue throughout the tree so that all nodes at the desiredlevel depth will be visited.

Quote:

This I did but not with a linked list I am using a object-oriented approach so I just stored the level of a node inside the each node object when I build the tree. So I already thought of this ... sorry I forgot to say. Or is this not related to what you meant
Storing the level inside each node is not what I'm talking about. I'm talking about keeping all nodes belonging to a certain level in a separate data structure outside the tree. It could be a linked list or an array or whatever. I has nothing to do with whether you're using OO or not.

You get two data structures. The tree itself and a list of nodes for each tree level. You pick the list for a certain level and when you scan it you get all nodes belonging to this level.
• January 24th, 2010, 03:14 PM
para15000
Re: methods of visiting the nodes on a level of a tree
Quote:

Originally Posted by nuzzle
Code:

```            if(\$curlevel == \$desiredlevel)             {                 \$this->Visit(\$node);                 if(\$nodesnr!==null)                     \$nodesnr++;                 return;             }```

Yes you are right this is a good improvement. It doesn't prevent all the nodes from being visited. THank you.

Quote:

Originally Posted by nuzzle
Storing the level inside each node is not what I'm talking about. I'm talking about keeping all nodes belonging to a certain level in a separate data structure outside the tree. It could be a linked list or an array or whatever. I has nothing to do with whether you're using OO or not.

You get two data structures. The tree itself and a list of nodes for each tree level. You pick the list for a certain level and when you scan it you get all nodes belonging to this level.

I see.And this would also be done when the tree is constructed? Right?
• January 24th, 2010, 05:28 PM
nuzzle
Re: methods of visiting the nodes on a level of a tree
Quote:

Originally Posted by para15000
Yes you are right this is a good improvement. It doesn't prevent all the nodes from being visited.

No it doesn't, but you don't have to visit any nodes below desiredlevel and that can be a substantial saving considering that the bulk of the nodes tend to be at the deepest levels.

Quote:

I see.And this would also be done when the tree is constructed? Right?
That's a possibility but in principle it can be done at any time. And of course if the tree is changed structurally the "level lists" must be updated to reflect that.

This solution is the fastest because you visit only exactly the nodes at desiredlevel. The drawback is that it requires an additional data structure which needs to be updated each time the tree changes. To what extent this is a problem depends on how often the tree is changed of course. If it never changes the only cost is the extra data structure.