What is the space complexity of a recursive traversal of a binary tree?

What is the space complexity of a recursive traversal of a binary tree?

Step 1: Understand what space complexity means. It refers to the amount of memory required by an algorithm as the input size grows.
Step 2: Recognize that a binary tree is a data structure with nodes, where each node has at most two children.
Step 3: Know that a recursive traversal means visiting each node in the tree using a function that calls itself.
Step 4: Realize that each time a function is called, it uses some space in memory, which is stored in a call stack.
Step 5: In the worst case, the maximum depth of the call stack will be equal to the height of the tree.
Step 6: For a balanced binary tree, the height is log(n), but for an unbalanced tree (like a linked list), the height can be n.
Step 7: Therefore, in the worst case, the space used by the call stack can be O(n), where n is the number of nodes in the tree.
Step 8: Conclude that the space complexity of a recursive traversal of a binary tree is O(n) due to the call stack.

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