# Insert children of a specified node in a binary tree and retrieve all leaves of a binary tree.

I am trying to use a binary tree to store data. When different cases happens at some step, I will need to create two children from the current node.

I also need to collect all information on the leaves (nodes with no children). I use the following definition of binary trees:

```
from sage.misc.binary_tree import BinaryTree
T = BinaryTree();
```

I can insert node the following way:

```
t.insert(0,[1,2,4]);
t.insert(1,[4,5]);
t.insert(2,[5,0]);
```

But I couldn't find a way to visualize the tree. Also I don't know how to add two children of one certain node. For example, if `0`

is the root (it seems so), `1`

is its left child and `2`

is its right child (which I am not sure), how do I make sure I add two children for the node `2`

?

I also looked at this page: (http://doc.sagemath.org/html/en/refer...). I couldn't see how to insert a node with values in it, or how to retrieve information of leaves.

Do I have to define my own tree structure?

Thank you for your help!

The first line

points to an other BinaryTree then the above linked one. (Which has no method

`insert`

.) After some good minutes with the cython (!?) code for it on my machine atwhich is mirrored in html at

http://doc.sagemath.org/html/en/reference/data_structures/sage/misc/binary_tree.html

i could not realize how such a BinaryTree "tree" differs from and a python dictionary where we remove most of the functionality, except the basic one. (And make the constructors very tricky and with unwanted side effects. If in a dictionary the last value declaration for a key wins, for a "BinaryTree"... The nodes seem to be the keys. But i am still missing the father-child functionality and ...)

After further searching for lines of code using the same import, i had to resign while founding that the "tree" should be not a kind of a dictionary, but a kind of a spartan map:

https://groups.google.com/forum/#!msg/sage-support...

Yes, you are right. I didn't link the one with "insert" since it does not provide me the functionality I was looking for. So I found another one, which does not have "insert", and still cannot do anything since it does not provide a value for each node. Now I decide I should just make a "recursive list" to achieve my goal. It seems Sage does not have a good Binary Tree implementation, at least for my purpose. Thank you for your time!