The Human Approach to Merging Trees

Imagine you have two different trees. To combine them into one tree, you'd naturally start by looking at the top piece of each puzzle—the root. You'd combine these roots to create a new root for the merged tree.

Then, you'd proceed down each branch, combining corresponding pieces (nodes) from each tree. If a branch exists in one tree but not the other, you'd simply include the existing branch in the new tree. If a branch exists in both trees, you'd combine them to form a new branch.

Running Through Examples to Identify Patterns

Example 1

• Tree 1: A single node with value 3
• Tree 2: A single node with value 1
• Merged Tree: A single node with value (3 + 1 = 4)

Example 2

• Tree 1:
  • Root: 3
  • Left child: 5
• Tree 2:
  • Root: 1
  • Right child: 4
• Merged Tree:
  • Root: (3 + 1 = 4)
  • Left child: 5 (from Tree 1)
  • Right child: 4 (from Tree 2)

Example 3

• Tree 1:
  • Root: 2
  • Left child: 3
  • Right child: 4
• Tree 2:
  • Root: 1
  • Left child: 4
  • Right child: 5
• Merged Tree:
  • Root: (2 + 1 = 3)
  • Left child: (3 + 4 = 7)
  • Right child: (4 + 5 = 9)

Observations

1. Roots Merge: The root of the merged tree is the sum of the roots of the individual trees.
2. Branching Logic: If a node exists in one tree but not in the other, the node from the existing tree is included in the merged tree.
3. Recursive Nature: The process for merging the children of two nodes looks suspiciously similar to the process for merging the roots. This suggests a recursive solution.

Armed with these observations, we can confidently proceed to code our brute-force solution.