Height, Depth, and Size
Explore the key measurements of height, depth, and size in binary trees. Understand how these metrics describe tree structure, impact traversal and search operations, and influence performance. Learn recursive methods to compute each measurement to build foundational skills in managing tree data structures effectively.
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In a binary tree, we often need more than just the node values. We also need ways to describe the tree’s structure. Three of the most important measurements are height, depth, and size. These help us understand how large the tree is, how far a node is from the top, and how far a node is from the bottom.
These ideas are important in recursion, traversal, binary search trees, heaps, and performance analysis. A tree with the same values can behave very differently depending on its height and shape. That is why these measurements matter.
Depth of a node
The depth of a node is the number of edges from the root to that node. It tells us how far a node is from the top of the tree.
The root always has depth 0. Its children have depth 1. Their children have depth 2, and so on. So depth increases as we move downward in the tree.
Consider this binary tree:
In this tree, A has depth B and C have depth A. The nodes D, E, and F all have depth
Depth is useful for determining a node’s level. It helps in level-order processing and in understanding how deeply a value lies in the tree.
Height of a node
The height of a node is the number of edges on the longest path from that node down to a leaf. It ...