∗ April 1960 1 Introduction A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. Introduction to Recursion Handout written by Jerry Cain. Applying the recurrence relation again and again, we have a1 = 2a0 +1 a2 = 2a1 +1 = 2(2a0 +1)+1 = 22a 0 +2+1 a3 = 2a2 +1 = 2(2 2a 0 +2+1)+1 = 23a 0 +2 2 +2+1 a4 = 2a3 +1 = 2(2 3a 0 +2 2 +2+1)+1 = 24a 0 +2 3 +22 +2+1 an = 2 na 0 +2 n¡1 +2n¡2 +¢¢¢+2+1 = 2na 0 +2 n ¡1: Let a0 = 0. A recursion trace closely mirrors the programming language’s execution of the recursion. The classic introductory Either today or Friday, we'll start working through one of computer science’s neatest ideas: support for recursion. • First rule of code optimization: • Don’t optimize it..yet. 1 Leonardo da Vinci 1452 –1519 La Giaconda ( Mona Lisa ) Louvre, Paris. Recursion in Java Recursion: Recursion is the process of defining something in terms of itself. • "cultural experience“ - A different way of thinking on problems. Modern compilers can often optimize the code and eliminate recursion. Why learn recursion ? The value a n could be the number of elements in a set or the probability of a certain event. Recursion Examples of Recursive Functions Tower of Hanoi 1 2 A B C A B C A B C 3 Two recursive problems of size n 1 to be solved. • Sample problem: printing the … Here is the basic idea: Suppose we are interested in computing a sequence a n, for n= 0;1;2;:::. Every node in T extends to an infinite path in T. T has a perfect subtree. • In Python, each time a function is called, a structure known as an activation record or frame is created to store information about the progress of that invocation of the function. Some Recursion Practice Problems Jon Fast jonathan.fast@msu.montana.edu April 13, 2014 1 Intro I’ve taken the liberty of putting some interesting (intermediate to challeng-ing) recursion problems together to help all of you in Computer Coding practice solving some more challenging problems. as follows. Recursion often does the trick whenever the problem to be solved can be broken down into smaller (but otherwise identical) sub-problems. • Unless you write super-duper optimized code, recursion is good • Mastering recursion is essential to … 14.1 Using Recursion Some problems in combinatorics and probability can be solved using recursive methods. Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I John McCarthy, Massachusetts Institute of Technology, Cambridge, Mass. • Recursion has an overhead (keep track of all active frames). Recursion and Recursive Backtracking Computer Science E-119 Harvard Extension School Fall 2012 David G. Sullivan, Ph.D. Iteration • When we encounter a problem that requires repetition, we often use iteration – i.e., some type of loop. If A is an infinite path in T and A is 11 1, then A is recursive. Chapter 3: Recursion • Theory – Introduce recursive definitions in Prolog – Go through four examples – Show that there can be mismatches between the declarative and procedural meaning of a Prolog program • Exercises – Exercises of LPN chapter 3 – Practical work The Base case is moving the disk with largest diameter. Panjer and Wang [21] show that, for non-degenerate severity distributions, the numerical stability of Panjer’s recursion with claim number distribution in the Panjer(a,b,k) class only depends on the values of a and b. Try … Non-Recursive It is not so easy: There is a recursive subtree T of 2

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