# factorial recursive algorithm

Factorial for any number N is equivalent to N * N-1 * N-2…1. Here’s a Simple Program to find factorial of a number using both recursive and iterative methods in C Programming Language. If so, in line 6, we determine the result of the function as n multiplied by the value of the function factorial (the same function as the one we currently define) for n minus 1 (4). Challenge: Recursive factorial. Our mission is to provide a free, world-class education to anyone, anywhere. We can write a recurrence relation for the total amount of work done. Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720. As a base case, you do one unit of work when the algorithm is run on an input of size 1, so In the base case there'd be some hard coded value based on the algorithm you are writing, while at the end you'd want to return the result of the recursive call, perhaps plus or times some other value . Let's start off with the analysis of this algorithm. Suppose the user entered 6. = n * (n-1)! n! Properties of recursive algorithms. Hence for factorial of N, a stack of size N will be implicitly allocated for storing the state of the function calls. We've done a reduction of the factorial problem to a smaller instance of the same problem. Lesson learned: Be careful of the recursive algorithm, they can grow exponential. Recursive Solution: Factorial can be calculated using following recursive formula. Using recursion to determine whether a word is a palindrome. The factorial of an integer can be found using a recursive program or an iterative program. ‘N’ multiplied by ‘N-1’ multiplied by ‘N-2’ and so on till ‘1’. Initially, multiplyNumbers() is called from main() with 6 passed as an argument. Suppose three recursive calls are made, what is the order of growth. The space complexity of recursive factorial implementation is O(n) Example: Binary Representation. Let's pick apart the code: Recursive nature of the factorial algorithm To understand how factorial calculation is recursive in nature, let us first define a function factorial such that n! In line 5 we check if n is greater than 1 - block (3) of the algorithm. At this point, the function factorial calls itself. This Program prompts user for entering any integer number, finds the factorial of input number and displays the output on screen. factorial(0) => 1 factorial(3) 3 * factorial(2) 3 * 2 * factorial(1) 3 * 2 * 1 * factorial(0) 3 * 2 * 1 * 1 => 6 This looks good. The following program demonstrates a recursive program to find the factorial of a number − Example When the value of n is less than 1, there is no recursive call and the factorial is returned ultimately to the main() function. In each recursive call, the value of argument n is decreased by 1. Now factorial(x) is x * (x-1)!, aka someArg times the return result of calling factorial with x-1. ... Properties of recursive algorithms. This idea of reducing a problem to itself is known as recursion. Especial if the problem size is measured by the level of the recursive tree and the operation count is total number of nodes. I.e. Write a C Program to find factorial by recursion and iteration methods. Properties of recursive algorithms. Factorial Algorithm in Lisp/Scheme Below you’ll find a recursive and an iterative version of the Factorial algorithm in Lisp/Scheme, based on the book Structure and Interpretation of Computer Programs (SICP). = 1 if n = 0 or n = 1 Up Next. Recursion that only contains a single self-reference is known as single recursion, while recursion that contains multiple self-references is known as multiple recursion. This is the currently selected item. Then, 5 is passed to multiplyNumbers() from the same function (recursive call).

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