If a CBT is stored using array , then what is the parent node of element stored at index 11?

Break Down the Problem

1. Identify the structure of a Complete Binary Tree (CBT) when represented as an array.
2. Determine the parent node's index based on the given index of the child node (11).

Relevant Concepts

• In an array representation of a binary tree:
  • For a given node at index $i$:
    • The parent node can be found at index $\frac{i - 1}{2}$ (using integer division).

Analysis and Detail

1. The child node is at index 11.
2. Apply the parent node formula: $\text{Parent Index} = \left\lfloor \frac{11 - 1}{2} \right\rfloor = \left\lfloor \frac{10}{2} \right\rfloor = 5$

Verify and Summarize

• The calculated index for the parent node, which is 5, is correct according to the formula used for computing the parent index.

Final Answer

The parent node of the element stored at index 11 is at index 5.