What characterizes a complete binary tree?

A complete binary tree is characterized by the property that all levels are fully filled except possibly for the last level, which is filled from left to right. This means that if the last level is not completely filled, all nodes must still be as far left as possible.

This structure ensures a balanced tree, which is crucial for many operations such as insertion and deletion, because it helps maintain optimal time complexity for these processes. By ensuring that every level, except possibly the last, is fully populated, the complete binary tree remains efficient in terms of height, typically leading to a logarithmic height relative to the number of nodes.

The other qualities mentioned in the other choices provide characteristics of different types of trees. For example, a tree where each node has exactly two children is referred to as a full binary tree, not a complete binary tree. Additionally, while it is true that all nodes connect to a single root, this is a property of all trees, not uniquely of complete binary trees. Lastly, having at least one child applies to trees in general but does not specifically define a complete binary tree.