Creating a Leap Tree from the Given Nodes

Constructing a leap tree involves organizing the given nodes into a hierarchical structure that resembles a tree, with each level representing a specific distance or "leap" from the root node. The leap tree is built in the following manner:

Step 1: Identify Nodes and Their Levels

Start by identifying the nodes and assigning them to different levels based on their values. In this case, the given nodes are:

Nodes: 8, 15, 24, 48, 3, 12, 18, 32, 54, 11, 6

Assign them to levels according to the following rule:

• Level 0: Root node (the largest node)
• Level 1: Nodes that differ from the root by a factor of 2
• Level 2: Nodes that differ from Level 1 nodes by a factor of 2, and so on.

Node	Level
48	0 (Root)
24, 32	1
12, 15, 18, 54	2
6, 8, 11, 3	3

Step 2: Organize Nodes into a Tree Structure

Arrange the nodes into a tree structure, with the root at the top and subsequent levels below it. The arrangement should follow the parent-child relationship, where nodes at a lower level are connected to their parent node at a higher level.

               48 (Level 0)
             /      \
            24 (L1)   32 (L1)
           /    \    /   \
          12 (L2) 15 (L2) 18 (L2) 54 (L2)
         /  \   /   / \   / \   /  \
        6 (L3) 8 (L3) 3 (L3) 11 (L3)

Step 3: Connect Nodes with Leaps

The concept of leaps comes into play when moving from one node to another. Leaps represent the difference between nodes at different levels. Specifically, a leap from a node at level $i$ to a node at level $j$ is calculated as follows:

$$ Leap = 2^{j-i} $$

For example, the leap from node 24 (Level 1) to node 12 (Level 2) is calculated as:

$$ Leap = 2^{2-1} = 2^1 = 2 $$

This means that node 12 is obtained by multiplying node 24 by 2. Similarly, leaps can be calculated for other pairs of nodes.

Complete Leap Tree Structure

The final leap tree structure, including the leaps, is illustrated below:

               48 (Level 0)
             /      \
            24 (L1)   32 (L1)
          /    \    /   \       
         12 (L2) 15 (L2) 18 (L2) 54 (L2)   
        /  \   /   / \   / \   /  \
       6 (L3) 8 (L3) 3 (L3) 11 (L3)

Leaps:
- Leap from 48 to 24 or 32: 2
- Leap from 24 to 12 or 15: 2
- Leap from 32 to 18 or 54: 2
- Leap from 12 to 6 or 8: 2
- Leap from 15 to 3 or 11: 2
- Leap from 18 to 6 or 11: 2
- Leap from 54 to 6 or 8: 2

This leap tree efficiently organizes the given nodes into a hierarchical structure, facilitating efficient searching and traversal operations.