Hopefully this lesson will give you an inception of what recursion is.

a method of computer programming in which a function can call itself* *source - Wikipedia

Base Case (also called Terminating Case) This is checked for at the beginning of the method and is the case where you simply return from the method and do not make any more recursive calls Recursive Call This is the point in the method where the method calls itself. It can be done more than once. Change usually a or a increment/decrement, this is how the input variables change from one recursive call to the next.

Without a well thought out base case and change of the variables, it is very easy for recursion to turn into an infinite loop of the method continuously calling itself over and over. When this happens, the program will crash due to memory restrictions since a method call will create duplicates of variables

int factorialLoop(int n){ int factorial = 1; //factorial to be returned //goes through each number from n to 1 //multiplies each number in the sequence for(int m = n; m >= 1; m--){ factorial *= m; } return factorial; //returns total }

int factorialRecur(int n){ if (n==1){ //terminating case return 1; }else{ //recursive call return n * factorialRecur(n-1); } } Remember for factorials that n! = n * (n-1)! So we can design our function to call itself in the form f(n) = n * f(n-1) But where do we stop? Remember that n! = 1*2*3*…*(n-2)*(n-1)*n So as we progress from n to n-1, we must stop when we reach 1.

factorialRecur(4) 4 * = 24 factorialRecur(3) 3 * =6 factorialRecur(2) 2 * = 2 factorialRecur(1) 1

A set of dolls of decreasing sizes placed one inside another.

open() Returns doll inside isAShell() Answers whether the doll is a shell getSize() Returns the size of the doll

doublegetSmallestSize(NestingDoll doll){ Nesting_Doll doll_inside; if( !doll.isAShell() ){ //terminating case return doll.Get_Size() ; }else{ //recursive call return getSmallestSize(doll.Open()); } }

1 Recursive call in a method will give it a Big O of n. Ex: 1 Recursive call with a tree depth of 5:

2 Recursive call in a method will give it a Big O of 2 n. Ex: 2 Recursive call with a tree depth of 5:

Some algorithms are recursive in nature so they are easier to program Some algorithms are more efficiently done recursively Some algorithms can only be programed recursively But a lot of the recursive methods you will start out programing are none these three but are easier to program