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:  Sorted Binary Tree

These three types are as follows:

Pre order traversal:

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, an in 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)