Recursion tree

Definition

A recursion tree is a visual representation of the recursive calls made by a function. It helps in understanding and analyzing the flow and complexity of recursive algorithms.

5 Must Know Facts For Your Next Test

1. A recursion tree illustrates how a recursive function splits into subproblems.
2. Each node in the tree represents an instance of the function call.
3. The depth of the recursion tree indicates the maximum number of nested calls.
4. Recursion trees are used to derive time complexities for recursive functions, often using methods like the Master Theorem.
5. Leaf nodes in a recursion tree usually represent base cases where no further recursive calls are made.

Review Questions

• What does each node represent in a recursion tree?
• How can a recursion tree help in determining the time complexity of a recursive algorithm?
• What do leaf nodes typically signify in a recursion tree?

Related terms

Base Case: The condition under which a recursive function returns without making any further calls.

Recursive Function: A function that calls itself within its own definition.

Master Theorem: $$\text{A formula used to determine the asymptotic behavior of recurrences commonly found in divide-and-conquer algorithms.}$$