Determine if the sequence of numbers is a post order traversal of a binary tree The question is: given a sequence of numbers, find an algorithm that determines if the sequence of numbers is in post order traversal of a binary search trees. 

Up to now, I have understood the following:


In the post order traversal of the binary tree it follows Left, Right, Root. So the Left value has to be less than the Right value. 
The last element of the sequence is the root, assuming the sequence was in the post order traversal. 


I do not know how to progress further with this. Also, is there a way to create a Divide and Conquer algorithm for this?
Probably you consider binary search trees, otherwise the exercise is a little useless.

You already concluded that your input has postorder: post-left-subtree, post-right-subtree, root.
Now the value of the root determines which values belong left, and which values belong right. So you are right: this is divide and conquer. Split the numbers according to the subtrees, and repeat for each of the two subtrees.

If a split of the input does not have the form post-left-subtree &lt; root &lt; post-right-subtree, you know what to conclude from that.

An example. The sequence is 1, 5, 9, 7, 3, 13, 17, 15, 11.
So the root is 11. And we can split the sequence accordingly into left and right subtrees: 1, 5, 9, 7, 3 &lt; 11 &lt; 13, 17, 15. Continue with the left and right subsequences.

Another sequence is 1, 5, 13, 9, 7, 3, 17, 15, 11. No split 'at' 11 possible.