Understanding the Problem
The task is to convert a given binary tree into a sum tree. In a sum tree, each node’s value is replaced by the sum of values of its left and right subtrees in the original tree. For leaf nodes, since they don’t have children, their value becomes 0.
This transformation is done recursively, which means for each node, we first compute the sum of its left and right subtrees and update the node’s value, then repeat the process for its children.
Step-by-Step Solution with Example
Step 1: Understand Tree Structure
Consider this example binary tree:
10
/ -2 6
/ / 8 -4 7 5
We need to convert this into a sum tree. For every node, we’ll replace its value with the sum of values in its left and right subtrees from the original tree.
Step 2: Process Leaf Nodes
Leaf nodes have no children, so their new value becomes 0
.
Step 3: Process Intermediate Nodes
Now, we go one level up and calculate the new values based on the original values of children.
- -2 has children 8 and -4 → new value = 8 + (-4) = 4
- 6 has children 7 and 5 → new value = 7 + 5 = 12
Step 4: Process Root Node
Finally, we compute the value for the root node.
- 10 has children -2 and 6 → in original tree, their values were -2 and 6 → new value = -2 + 6 = 4
Step 5: Update Tree
After the transformation, the sum tree looks like this:
4
/ 4 12
/ / 0 0 0 0
Edge Cases
Case 1: Tree with Multiple Levels
This is the general case like the example above. Each internal node gets updated based on the sum of its children’s original values. Leaf nodes become 0.
Case 2: Tree with a Single Node
If the tree only has one node, there are no children to sum. Therefore, the single node becomes 0, since it's considered a leaf node.
Case 3: Empty Tree
If the input tree is empty (i.e., the root is null), then the output is also an empty tree or null. This is the base case in our recursion.
Finally
Converting a binary tree to a sum tree requires a post-order traversal, where we visit left and right children before updating the current node. The solution handles all edge cases and maintains correctness by updating nodes only after their subtrees are processed. Always remember to handle base cases like leaf nodes and empty trees to avoid runtime errors.
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