Western Governors University (WGU) ICSC2100 C949 Data Structures and Algorithms I Practice Exam

In a max heap, the defining characteristic is that every parent node must be greater than or equal to its child nodes. This property is essential for maintaining the structure and ordering of the heap. Therefore, the correct assertion is that parent nodes in a max heap are always greater than their children.

This arrangement guarantees that the maximum value within the heap is always at the root (the topmost parent node). This property is what allows for efficient operations, such as retrieving the maximum element (which can be done in constant time) or maintaining the heap structure during insertions or deletions in logarithmic time.

Other options fall short of accurately representing the properties of a max heap. Stating that parent nodes are always less than their children or have no relation to them fails to capture the fundamental ordering requirement of the data structure. Additionally, saying that they can be equal to children overlooks the fact that, while it is possible for a parent to equal a child in value in certain cases, the emphasis is on the greater than condition as a defining feature of the max heap property.