# efficiency of recursion

Emphasis of iteration:! In total, we get T(n) = k 2 + T(n-1). Recursion is such an elegant and powerful technique that a lot of effort has been invested in creating compilers that can optimize it and make its use competitive with iteration. Recursion can reduce time complexity. You count the lines of code, and if there are any loops, you multiply by the length. Example: Recursive Algorithm for Fibonacci Numbers. Problem size is n, the sequence number for the Fibonacci number. Solve a complicated task one piece at a time, and combine the results. A recursive function, then, is a function that calls itself. Recursion vs. Iteration Roughly speaking, recursion and iteration perform the same kinds of tasks:! 2. Recurrence relation Efficient Recursion This section contains extra material that is not part of the course but supplements it with essential insights about recursion and its efficient use. Recursion is a useful way of defining things that have a repeated similar structural form like tree traversal. They divide the input into one or more subproblems. This also includes the constant time to perform the previous addition. Feb. 28, 1996. Basic operation is the sum in recursive call. What this means is, the time taken to calculate fib(n) is equal to the sum of time taken to calculate fib(n-1) and fib(n-2). 4. Also, recursion … Cons Analysis of the recursive Fibonacci program: We know that the recursive equation for Fibonacci is = + +. 3. If we are only looking for an asymptotic estimate of the time complexity, we don’t need to specify the actual values of the constants k 1 and k 2. Pros and Cons of recursive programming Pros. Algorithm F(n) if n ≤ 1 then return n. else return F(n-1) + F(n-2) 1. This recursive call will perform T(n-1) operations. Recursion can lead to more readable and efficient algorithm descriptions. Recursion adds clarity and reduces the time needed to write and debug code. No difference between worst and best case. Things to notice: Base case --- array ``vanishing'' Recursively searches sub-arrays Sub-arrays delimited by first, last; Mid +/- 1 used in recursive call Similarities to homework program? One recursive implementation of a program to compute the n-th element of the Fibonacci sequence is the C program below. Binary Search. Tom Kelliher, CS18. Recursion, Searching, and Efficiency. However, recursive algorithms are not that intuitive. Analyzing the running time of non-recursive algorithms is pretty straightforward. When dealing with recursion, its important to note down what your base and recursive cases are and go from there. You've already figured out the different cases for your problem: If n == 0; If 8 is in the ones digit place (n % 10 == 8) On this post, we are going to learn how to get the big O notation for most recursive algorithms. These different cases will essentially become the structure of your function. Recursion adds clarity and reduces the time needed to write and debug code. Instead, we let k 1 = k 2 = 1. Programming involves recursive thinking, and it can help us to write shorter and more efficient code when used appropriately. View Lesson 3 The efficiency of recursion.pdf from AA 1The efficiency of Recursion AP COMPUTER SCIENCE Introduction Recursion can be a powerful tool to solve complex algorithms. Unlock Content Over 83,000 lessons in all major subjects Tree traversal then return n. else return F ( n-1 ) operations this post, let... We efficiency of recursion that the recursive equation for Fibonacci is = + + divide the input into one or more.. Cases are and go from there it can help us to write shorter more. With recursion, its important to note down what your base and recursive cases are go. 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