Summary

A complete_binary_tree fills all levels except possibly the last, and the last level is filled left_to_right. Nodes are stored naturally in level_order. This makes an array_representation simple and compact, with parent and child positions found by simple formulas. The height_logarithmic property is about O(log n). Common use: heap implementations. Simple insert places a node at the next open slot; delete often swaps with the last node, preserving the balanced_shape.