A max-heap is a heap where the value of each parent is greater than or equal to the value of its children. Which of the following is a max-heap?

A binary max-heap must satisfy two properties [1]:

1. Shape Property (Complete Binary Tree): All levels of the tree are completely filled except possibly the last level, which is filled strictly from left to right [1].

2. Max-Heap Property: The key/value stored in each node must be greater than or equal to the keys stored in its children ($A[\text{parent}(i)] \ge A[i]$) [1].

Let us evaluate the options:

• (A) The tree is not a complete binary tree because the right child of node $6$ is missing a left child, but node $5$ has a left child $1$ on the next level, violating the complete binary tree structure [1].

• (B) It is a complete binary tree where every level is fully filled, and for every node, the parent value is greater than or equal to its children:

  • $10 \ge 8$ and $10 \ge 6$

  • $8 \ge 4$ and $8 \ge 5$

  • $6 \ge 1$ and $6 \ge 2$

  Therefore, (B) is a valid max-heap [1].

• (C) Node $5$ has a right child $8$, where $5 < 8$, violating the max-heap property.

• (D) The root is $5$, which has a right child $8$ ($5 < 8$), violating the max-heap property.

Thus, (B) is the correct option.