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Recursion Recursion means "defining a problem in terms of itself". This can be a very powerful tool in writing algorithms. Recursion comes directly from Mathematics, where there are many examples of expressions written in terms of themselves.

For example, the Fibonacci sequence is defined as: For example, we can define the operation "find your way home" as: If you are at home, stop moving.

Take one step toward home. Here the solution to finding your way home is two steps three steps. Secondly, we do a very simple action that makes our situation simpler to solve.

Finally, we redo the entire algorithm. The above example is called tail recursion. This is where the very last statement is calling the recursive algorithm. Tail recursion can directly be translated into loops.

How would you write a recursive "algorithm" for finding Temple Square? Function "Find Temple Square": The maximum value in a list is either the first number or the biggest of the remaining numbers. Here is how we would write the pseudocode of the algorithm: The recursive call, is where we use the same algorithm to solve a simpler version of the problem.

The base case is the solution to the "simplest" possible problem For example, the base case to adding a list of numbers would be if the list had only one number Add three numbers Adding three numbers is equivalent to adding the first two numbers, and then adding these two numbers again.

All recursive algorithm must have the following three stages: This information is "held" by the computer on the "activation stack" i.

Consider a rectangle grid of rooms, where each room may or may not have doors on the North, South, East, and West sides. How do you find your way out of a maze? Here is one possible "algorithm" for finding the answer: For every door in the current room, if the door leads to the exit, take that door.

The "trick" here is of course, how do we know if the door leads to a room that leads to the exit? What is the recursive part about the above algorithm?

Its the "door leads out of the maze". How do we know if a door leads out of the maze? We know because inside the next room going through the doorwe ask the same question, how do we get out of the maze?

What happens is the computer "remembers" all the "what ifs". What if I take the first door, what if I take the second door, what if I take the next door, etc.

And for every possible door you can move through, the computer remembers those what ifs, and for every door after that, and after that, etc, until the end is found.

Here is a close to actual code implementation. Some Computer related examples include: Adding a list of numbers, Computing the Fibonacci sequence, computing a Factorial, and Sudoku.

Summing a list of numbers: What is a recursive solution to summing up a list of numbers? Lets write a recursive function to compute the Nth number in the Fibonacci sequence. This algorithm, while elegant is really inefficient. The problem here is the computer must re-evaluate the same Fibonacci number over and over again.

So when it comes time to evaluate fib 6we are going to evaluate fib 5 over again, and then evaluate fib 4 even more times. Sorting How can you sort a list of numbers using recursion?Awk, C#, C++, E, merd, PHP5, Python, Ruby, Tcl, Vimscript, YCP == Python == /= Haskell == \= Oz == \== Classic REXX, Prolog = /= Ada =!= Maple, XPath.

Find all the books, read about the author, and more. Recursion is a kind of tricky and smart construction which allows a function to call itself.

The Matlab programming language supports it, so a function can call itself during its own execution. Recursive algorithms can be directly implemented in Matlab. In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.

Typically, a fold is presented with a combining function, a top. This gives me D = [6 5 4 7 9] as expected. The problem is, I'm supposed to use a while loop and make it a recursive function to do the same thing.

A function handle is a MATLAB ® data type that stores an association to a function. Indirectly calling a function enables you to invoke the function regardless of where you call it from.

Indirectly calling a function enables you to invoke the function regardless of where you call it from.

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