## Traversing a Binary Tree

 Traversing a binary tree comes in handy when you would like to do a print out of all the data elements in the tree. We demonstrate three types of traversals in our tutorial. All traversal descriptions refer to: Figure 1.1:Ā Sorted Binary Tree These three types are as follows:

###### Pre order traversal:
A pre order traversal prints the contents of a sorted tree, in pre order. In other words, the contents of the root node are printed first, followed by left subtree and finally the right subtree. So in Figure 1.1, a pre order traversal would result in the following string: FCADJHIK.
 ```PreOrder (T) If T < > Null then print (T.data) else print(‘empty tree’) If T.lp < > null then PreOrder(T.lp) If T.rp < > null then preorder (T.rp) end. ``` ###### In order traversal:

An in order traversal prints the contents of a sorted tree, in order. In other words, the lowest in value first, and then increasing in value as it traverses the tree. The order of a traversal would be 'a' to 'z' if the tree uses strings or characters, and would be increasing numerically from 0 if the tree contains numerical values. So in Figure 1.1, an in order traversal would result in the following string: ACDFHIJK.

 ```InOrder (T) If T < > null print (‘empty tree’) If T.lp < > null then InOrder(T.lp) print (T.data) If T.rp < > null then InOrder (T.lp) end. ``` ###### Post order traversal:

A post order traversal prints the contents of a sorted tree, in post order. In other words, the contents of the left subtree are printed first, followed by right subtree and finally the root node. So in Figure 1.1, a post order traversal would result in the following string: ADCIHKJF.

 ```PostOrder (T) If T = null then print (‘empty tree’) If T.lp < > null then PostOrder(T.lp) If T.rp < > null then PostOrder(T.lp) Print(T.data) end. ``` If the word right is replaced by left and vice versa in the above definitions the result is called the Converse of the definition. (I.e. ConversePreOrder – Process the root, the right subtree and then the left subtree)