We can construct a binary tree if we are given at least two traversal results. The first traversal must be the in-order traversal and the second can be either pre-order or post-order traversal. The in-order traversal result will be used to determine the left and the right child nodes, and the pre-order/post-order can be used to determine the root node. For example, consider the traversal results given below:

In–order Traversal: D B E A F C G

Pre–order Traversal: A B D E C F G

Here, we have the in-order traversal sequence and pre-order traversal sequence. Follow the steps given below to construct the tree:

Step 1 Use the pre-order sequence to determine the root node of the tree. The first element would be the root node.

Step 2 Elements on the left side of the root node in the in-order traversal sequence form the left sub-tree of the root node. Similarly, elements on the right side of the root node in the in-order traversal sequence form the right sub-tree of the root node

Step 3 Recursively select each element from pre-order traversal sequence and create its left and right sub-trees from the in-order traversal sequence. Look at Fig. 9.20 which constructs the tree from its traversal results. Now consider the in-order traversal and post-order traversal sequences of a given binary tree. Before constructing the binary tree, remember that in post-order traversal the root node is the last node. Rest of the steps will be the same as mentioned above Fig. 9.21.

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