Find the Minimum and Maximum Height of a Binary Search Tree

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In the last challenge we described a scenario in which a tree could become unbalanced. To understand the concept of balance, let's take a look at another tree property: height. Height in a tree represents the distance from the root node to any given leaf node. Different paths in a highly branched tree structure may have different heights, but for a given tree there will be a minimum and maximum height. If the tree is balanced, these values will differ at most by one. This means that in a balanced tree, all the leaf nodes exist within the same level, or if they are not within the same level they are at most one level apart.

The property of balance is important for trees because it is what determines the efficiency of tree operations. As we explained in the last challenge, we face worst case time complexity for heavily unbalanced trees. Self-balancing trees are commonly used to account for this issue in trees with dynamic data sets. Common examples of these include AVL trees, red-black trees, and B-trees. These trees all contain additional internal logic which re-balance the tree when insertions or deletions create a state of imbalance.

Note: A similar property to height is depth, which refers to how far a given node is from the root node.