Lec-32 What is recursion? A mathematical look
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Recursion is a problem-solving technique that involves dividing a problem into smaller subproblems which can also be further divided until they can be solved directly. It is defined in terms of itself through recursive algorithms and includes concepts like recursive data structures, such as linked lists and trees, which reference themselves. The document provides examples and definitions of recursion, illustrating its application in computer science.
Lec-32 What is recursion? A mathematical look
- 2. Recursion Basic problem solving technique is to divide a problem into smaller subproblems These subproblems may also be divided into smaller subproblems When the subproblems are small enough to solve directly the process stops A recursive algorithm is a problem solution that has been expressed in terms of two or more easier to solve subproblems
- 3. What is recursion? A procedure that is defined in terms of itself In a computer language a function that calls itself
- 4. Recursion Recursion A recursive definition is one which is defined in terms of itself. Examples: • A phrase is a "palindrome" if the 1st and last letters are the same, and what's inside is itself a palindrome (or empty or a single letter) • Rotor • Rotator • 12344321
- 5. N = 1 is a natural number if n is a natural number, then n+1 is a natural number • The definition of the natural numbers: Recursion Recursion
- 6. 1. Recursive data structure: A data structure that is partially composed of smaller or simpler instances of the same data structure. For instance, a tree is composed of smaller trees (subtrees) and leaf nodes, and a list may have other lists as elements. a data structure may contain a pointer to a variable of the same type: struct Node { int data; Node *next; }; 2. Recursive procedure: a procedure that invokes itself 3. Recursive definitions: if A and B are postfix expressions, then A B + is a postfix expression. Recursion in Computer Science Recursion in Computer Science
- 7. Recursive Data Structures Recursive Data Structures Linked lists and trees are recursive data structures: struct Node { int data; Node *next; }; struct TreeNode { int data; TreeNode *left; TreeNode * right; }; Recursive data structures suggest recursive algorithms.