We discussed an implementation of a min priority queue as a min heap, which had two key properties.1. The min heap property: the key at a node is at most the keys of its children.2. The heap is represented by a complete binary tree.What is the purpose of the complete binary tree property? Select all that apply.It ensures that the minimum key is at the root of the tree.It allows a simple representation of the tree by a vector in a memory efficient manner.It permits us to tell if a given key is contained in the heap in time 𝑂(log⁡𝑛)O(logn).When the heap has 𝑛n elements it insures that the height of the tree is at most log⁡𝑛logn, which in turn means push and pop can be done in time 𝑂(log⁡𝑛)O(logn).Submit

The purpose of the complete binary tree property in a min heap implementation of a min priority queue is:

1. It allows a simple representation of the tree by a vector in a memory efficient manner. This is because a complete binary tree can be easily represented as an array. Each element in the array represents a node; the parent-child relationship can be defined by the indices of the elements.

2. When the heap has 𝑛 elements it ensures that the height of the tree is at most log⁡𝑛, which in turn means push and pop can be done in time 𝑂(log⁡𝑛). This is because in a complete binary tree, all levels are fully filled except possibly for the last level, which is filled from left to right. This property ensures that the tree remains balanced, and the height of the tree remains logarithmic in the number of elements, ensuring that operations like push and pop can be done in logarithmic time.

The complete binary tree property does not ensure that the minimum key is at the root of the tree. This is ensured by the min heap property. Also, it does not permit us to tell if a given key is contained in the heap in time 𝑂(log⁡𝑛). Searching for a specific key in a heap is not a logarithmic time operation.