Final answer:
Heaps are efficiently implemented as arrays because they are complete binary trees, allowing for compact storage and straightforward parent-child index calculations which facilitate heap operations.
Step-by-step explanation:
The feature of heaps that allows them to be efficiently implemented using an array is that heaps are complete binary trees. This means that every level of the tree, except possibly the last one, is completely filled, and all nodes are as far left as possible. This property is beneficial because it ensures that when we represent a heap using an array, there is no wasted space due to missing elements in the tree structure, allowing for compact and efficient storage.
In a complete binary tree, the left child of a node at position i can be found at position 2i+1 and the right child at position 2i+2 in the array. The parent of any node other than the root, which is at position i, can be found at position (i-1)/2. These simple mathematical relations between the indices in the array make traversing the heap and performing heap operations like insertions and deletions efficient.