**Recursion** in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration).

Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration). Recursive algorithms have two cases: a recursive case and base case. Any function that calls itseld is recursive.

**Examples of recursive functions:**

- Factorial: n! = n x (n -1) x (n-2) x ... x 1
- Fibonacci: 1,1,2,3,5,8 ,...
- Multiplication (3 x 2): 3 + 3
- Multiplication (2 x 3): 2 + 2 + 2
- Summations from i = 1 to 5: 1 + 2 + 3 + 4 + 5
- n^2 + (n-1) ^2 + (n-2)^2 + ... + 1
- 1 + 10 + 100 + 1000 + 10000 + .....
- 1 + 1 + 1 + ... + 1
- 0 + 1 + 2 + 3 + ... + n
- func( 0 ) = 0 , func(n) = func(n-1) + n

Recursion is useful for tasks that can be defined in terms of similar subtasks, for example search, sort , and traversal problems often have simple recursive solutions. At some point the function encounters a subtask that it can perform without calling itself.

**Directly recursive:**method that calls itself**Indirectly recursive:**method that calls another method and eventually results in the original method call**Tail recursive method:**recursive method in which the last statement executed is the recursive call**Infinite recursion:**case where every recursive call results in another recursive call

Factorial numbers defined recursively example:

factorial(0) = 1;

factorial(n) = n * factorial(n-1);

0! = 1

1! = 1 * 1 = 1

2! = 2 * 1 * 1 = 2

3! = 3 * 2 * 1 * 1 = 6

4! = 4 * 3 * 2 * 1 * 1 = 24

/*

*This is a Tower of hanoi recursive program

* written in javascript

*This program will tell you the correct

* moves to make for any number of disks 'n'

* in this case n = 4

*/

function move(n, a, b, c) {

if (n > 0) {

move(n-1, a, c, b);

console.log("Move disk from " + a + " to " + c);

move(n-1, b, a, c);

}

}

move(4, "A", "B", "C");

Learn how to change a recursive function into a recurrence relation

Download PDFMultiplication can be thought of as a recursive function. Multiplication is simply adding the number 'X' 'Y' times or vice versa. For example if I multiplied 5 by 3 (e.g. 5 * 3) the way multiplication works, we get 5 + 5 + 5 = 15 or 3 + 3 +3+ 3+ 3= 15 both are correct ways to do multiplication. This works perfectly for positive integers, but what if the we wanted to multiply 5 * 0 = 0 or 0 * 5 =0 and 5 * 1 = 5 or 1 * 5 = 5, that will be our base case also known as the stopping or non-recursive case.

So what will the recursive program look like ? Base case if input X or input Y is 0 we will return 0, if X is 1 then we return Y , if Y is 1then we return X. Both X and Y are our input parameter variables. You look at the multiplication function next to this paragraph to see how we would multiply two positive numbers recursively. **Note:** you cannot use this function for negative values.

int Multiply(int X, int Y){

if( X == 0 || Y== 0)

return 0;

if(X == 1)

return Y;

if(Y == 1)

return X;

returnY + Multiply(X -1, Y);

}

In this video I show how to write a recursive power function in C programming.

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Learn how to use recursion to multiply two numbers

Download PDF/* C Program for a recursive fibonacci function */ #include< stdio.h > int Fibonacci(int); main() { int n, i = 0, c; scanf("%d",&n); printf("Fibonacci series\n"); for ( c = 1 ; c <= n ; c++ ) { printf("%d\n", Fibonacci(i)); i++; } return 0; } int Fibonacci(int n) { if ( n == 0 ) return 0; else if ( n == 1 ) return 1; else return ( Fibonacci(n-1) + Fibonacci(n-2) ); }