Understanding the Problem
In a Binary Search Tree (BST), every node follows a specific rule: the left child contains values less than the node, and the right child contains values greater than the node. This structure helps us find the maximum value efficiently — we just need to follow the right children because the maximum value is always located at the rightmost node of the BST.
Let’s explore this idea with a detailed example and then walk through edge cases that a beginner should be aware of.
Step-by-Step Solution with Example
Step 1: Start at the Root
We begin at the root node of the BST. For example, consider the tree:
4
/ 2 6
/ / 1 3 5 7
The root is 4. Since we are looking for the maximum, we move to the right child.
Step 2: Keep Moving Right
From node 4, we move to 6. Then from 6, we move to 7. Node 7 has no right child, which means it is the rightmost node.
Step 3: Return the Node
Since 7 has no right child, we return 7 as the maximum value in the BST.
Step 4: Code Summary
The logic in code looks like this (pseudo-code):
function findMax(node):
if node is null:
return null
while node.right is not null:
node = node.right
return node.value
Edge Cases
Case 1: Tree has only one node
If the tree has a single node, such as [10]
, that node is both the minimum and the maximum. Since there is no right child, we return 10 directly.
Case 2: Tree is empty
If the input tree is empty, there’s no value to return. In such cases, we return null
or None
depending on the language used. This signals that the tree has no nodes.
Case 3: Right-skewed tree
In a tree like [15, 10, 20, null, null, 18, 25]
, the maximum path is:
15
20
25
We follow the path 15 → 20 → 25, and since 25 has no right child, it’s the maximum value.
Case 4: Tree with missing left children
Even if some left children are missing, it doesn't affect our search for the maximum — we ignore the left side completely. We only care about the rightmost path.
Finally
The beauty of a Binary Search Tree lies in its structure, which allows efficient search operations. To find the maximum value, we only need to traverse the right child nodes until we can go no further. For beginners, remember this simple rule: keep going right until you can't. And don’t forget to check for edge cases like empty trees or single-node trees for a robust solution.
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