g0501_0600.s0543_diameter_of_binary_tree.complexity.md Maven / Gradle / Ivy

Go to download

Show more of this group Show more artifacts with this name
Show all versions of leetcode-in-java Show documentation

Java-based LeetCode algorithm problem solutions, regularly updated

The newest version!

**Time Complexity (Big O Time):**

The time complexity of the program is determined by the depth-first traversal of the binary tree. Specifically, the time complexity is governed by the `diameterOfBinaryTreeUtil` function, which recursively traverses the tree.

In each call to `diameterOfBinaryTreeUtil`, the program visits each node once. Therefore, the time complexity of visiting all nodes in the binary tree is O(n), where 'n' is the number of nodes in the tree.

Hence, the overall time complexity of the program is O(n), where 'n' is the number of nodes in the binary tree.

**Space Complexity (Big O Space):**

The space complexity of the program is determined by the function call stack during the recursive traversal of the binary tree.

1. The space used by the call stack is proportional to the height of the binary tree. In the worst case, when the tree is completely unbalanced (a skewed tree), the height of the tree can be 'n' (where 'n' is the number of nodes), resulting in a space complexity of O(n).

2. Additionally, the program uses a single integer variable `diameter` to keep track of the maximum diameter found during the traversal. This variable requires constant space, O(1).

Therefore, the overall space complexity of the program is O(n), where 'n' is the number of nodes in the binary tree. The dominant factor in the space complexity is the call stack space used during the recursion.

In summary, the provided program has a time complexity of O(n) and a space complexity of O(n), where 'n' is the number of nodes in the binary tree. It efficiently finds the diameter of the binary tree by performing a depth-first traversal.