Understanding the Problem
A binary tree is considered balanced if, for every node in the tree, the height difference between its left and right subtrees is no more than 1. This ensures that the tree remains approximately balanced in structure, preventing it from becoming skewed like a linked list which would degrade performance in certain operations.
Our goal is to check whether a given binary tree is balanced or not. We need an approach that checks the tree from the bottom up and returns true
if all nodes satisfy the height balance condition.
Step-by-Step Solution with Example
Step 1: Define What We Need
To determine if a binary tree is balanced, we must know the height of each subtree and ensure the difference is no more than 1 for every node. We’ll use a recursive approach to calculate the height of subtrees and check the balance condition simultaneously.
Step 2: Understand the Base Case
If the current node is null
, we return a height of 0. This acts as the base case in our recursion and also helps us handle empty trees properly.
Step 3: Post-order Traversal to Check Balance
We perform a post-order traversal (left → right → root) so that we can calculate the height of left and right subtrees before checking the balance at the current node.
Step 4: Return Special Flag for Unbalanced Subtrees
Instead of just returning the height, we return -1
if we find any unbalanced subtree. This helps us quickly propagate the unbalanced status upward and avoid unnecessary checks.
Step 5: Apply the Logic on an Example
Let’s take the example tree [3, 9, 20, null, null, 15, 7]
.
- Left subtree rooted at 9 has a height of 1.
- Right subtree rooted at 20 has two children: 15 and 7, both leaves. So height is 2.
- Difference at root is 1 ⇒ Balanced.
- All subtrees also satisfy the condition ⇒ Entire tree is balanced.
Step 6: Visualize an Unbalanced Case
Now consider tree [1, 2, 2, 3, 3, null, null, 4, 4]
.
- Left subtree continues deep into levels 4 and 5.
- At one point, difference between heights becomes 2 ⇒ Tree is unbalanced.
We detect this early and bubble up the unbalanced signal.
Edge Cases
- Empty Tree: A
null
tree is considered balanced by definition.
- Single Node: A single node with no children is balanced (height difference is 0).
- Skewed Trees: Trees where all nodes are only on one side (e.g., linked-list like trees) are unbalanced if their depth exceeds 1 without a corresponding opposite side.
Finally
To solve this problem efficiently, we use a recursive function that checks height and balance together. This avoids redundant computation. The key intuition is that a balanced tree should not have any node where one subtree is taller than the other by more than one level. Handling base cases and special flags for early termination ensures optimal performance even for large trees.
Comments
Loading comments...