Understanding the range postorder pattern

A binary search tree follows the binary search property where all nodes in the left subtree of a node are smaller than it, while all nodes in the right subtree are greater than it. This property allows for the efficient searching of values in the tree. However, some binary search tree problems require us to find and process not just a single node but all nodes whose value lies in a specified range. Some problems go a step further and may require aggregating these processed values over some function into a single value. Such problems can be efficiently solved using the range postorder technique.

In this lesson, we will learn more about using the range postorder technique to solve binary search tree problems and how to identify a problem as a range postorder pattern problem.

The range postorder technique

Consider we are given a binary search tree, and a range of values denoted by low and high, and we need to process all the nodes with values within this range using the aggregated value of the function f over all nodes in their left and right subtree that also lie within the range.

Another way to look at the problem is to imagine that we have a transformed tree that only has nodes within the specified range and that we need to process every node in this transformed tree using the aggregated value of a function f over all nodes in its left and right subtrees.