Understanding recursion [closed]

Answer 1

Children implicitly use recursion, for instance:

Road trip to Disney World

Are we there yet?(no)

Are we there yet?(Soon)

Are we there yet?(Almost...)

Are we there yet?(SHHHH)

Are we there yet?(!!!!!)

At which point the child falls asleep...

This countdown function is a simple example:

function countdown()
      {
      return (arguments[0] > 0 ?
        (
        console.log(arguments[0]),countdown(arguments[0] - 1)) : 
        "done"
        );
      }
countdown(10);

Hofstadter's Law applied to software projects is also relevant.

The essence of human language is, according to Chomsky, the ability of finite brains to produce what he considers to be infinite grammars. By this he means not only that there is no upper limit on what we can say, but that there is no upper limit on the number of sentences our language has, there's no upper limit on the size of any particular sentence. Chomsky has claimed that the fundamental tool that underlies all of this creativity of human language is recursion: the ability for one phrase to reoccur inside another phrase of the same type. If I say "John's brother's house", I have a noun, "house", which occurs in a noun phrase, "brother's house", and that noun phrase occurs in another noun phrase, "John's brother's house". This makes a lot of sense, and it's an interesting property of human language.

References

• Recursion and Human Thought

Answer 2

I think this very simple method should help you understand recursion. The method will call itself until a certain condition is true and then return:

function writeNumbers( aNumber ){
 write(aNumber);
 if( aNumber > 0 ){
  writeNumbers( aNumber - 1 );
 }
 else{
  return;
 }
}

This function will print out all numbers from the first number you'll feed it till 0. Thus:

writeNumbers( 10 );
//This wil write: 10 9 8 7 6 5 4 3 2 1 0
//and then stop because aNumber is no longer larger then 0

What bassicly happens is that writeNumbers(10) will write 10 and then call writeNumbers(9) which will write 9 and then call writeNumber(8) etc. Until writeNumbers(1) writes 1 and then calls writeNumbers(0) which will write 0 butt will not call writeNumbers(-1);

This code is essentially the same as:

for(i=10; i>0; i--){
 write(i);
}

Then why use recursion you might ask, if a for-loop does essentially the same. Well you mostly use recursion when you would have to nest for loops but won't know how deep they are nested. For example when printing out items from nested arrays:

var nestedArray = Array('Im a string', 
                        Array('Im a string nested in an array', 'me too!'),
                        'Im a string again',
                        Array('More nesting!',
                              Array('nested even more!')
                              ),
                        'Im the last string');
function printArrayItems( stringOrArray ){
 if(typeof stringOrArray === 'Array'){
   for(i=0; i<stringOrArray.length; i++){ 
     printArrayItems( stringOrArray[i] );
   }
 }
 else{
   write( stringOrArray );
 }
}

printArrayItems( stringOrArray );
//this will write:
//'Im a string' 'Im a string nested in an array' 'me too' 'Im a string again'
//'More nesting' 'Nested even more' 'Im the last string'

This function could take an array which could be nested into a 100 levels, while you writing a for loop would then require you to nest it 100 times:

for(i=0; i<nestedArray.length; i++){
 if(typeof nestedArray[i] == 'Array'){
  for(a=0; i<nestedArray[i].length; a++){
   if(typeof nestedArray[i][a] == 'Array'){
    for(b=0; b<nestedArray[i][a].length; b++){
     //This would be enough for the nestedAaray we have now, but you would have
     //to nest the for loops even more if you would nest the array another level
     write( nestedArray[i][a][b] );
    }//end for b
   }//endif typeod nestedArray[i][a] == 'Array'
   else{ write( nestedArray[i][a] ); }
  }//end for a
 }//endif typeod nestedArray[i] == 'Array'
 else{ write( nestedArray[i] ); }
}//end for i

As you can see the recursive method is a lot better.

Answer 3

http://javabat.com is a fun and exciting place to practice recursion. Their examples start fairly light and work through extensive (if you want to take it that far). Note: Their approach is learn by practicing. Here is a recursive function that I wrote to simply replace a for loop.

The for loop:

public printBar(length)
{
  String holder = "";
  for (int index = 0; i < length; i++)
  {
    holder += "*"
  }
  return holder;
}

Here is the recursion to do the same thing. (notice we overload the first method to make sure it is used just like above). We also have another method to maintain our index (similar to the way the for statement does it for you above). The recursive function must maintain their own index.

public String printBar(int Length) // Method, to call the recursive function
{
  printBar(length, 0);
}

public String printBar(int length, int index) //Overloaded recursive method
{
  // To get a better idea of how this works without a for loop
  // you can also replace this if/else with the for loop and
  // operationally, it should do the same thing.
  if (index >= length)
    return "";
  else
    return "*" + printBar(length, index + 1); // Make recursive call
}

To make a long story short, recursion is a good way to write less code. In the latter printBar notice that we have an if statement. IF our condition has been reached, we will exit the recursion and return to the previous method, which returns to the previous method, etc. If I sent in a printBar(8), I get ********. I am hoping that with an example of a simple function that does the same thing as a for loop that maybe this will help. You can practice this more at Java Bat though.

Answer 4

To understand recursion, all you have to do is look on the label of your shampoo bottle:

function repeat()
{
   rinse();
   lather();
   repeat();
}

The problem with this is that there is no termination condition, and the recursion will repeat indefinitely, or until you run out of shampoo or hot water (external termination conditions, similar to blowing your stack).

Answer 5

Ouch. I tried to figure out the Towers of Hanoi last year. The tricky thing about TOH is it's not a simple example of recursion - you have nested recursions which also change the roles of towers on each call. The only way I could get it to make sense was to literally visualize the movement of the rings in my mind's eye, and verbalize what the recursive call would be. I would start with a single ring, then two, then three. I actually ordered the game on the internet. It took me maybe two or three days of cracking my brains to get it.

Answer 6

Think a worker bee. It tries to make honey. It does its job and expects other worker bees to make rest of the honey. And when the honeycomb is full, it stops.

Think it as magic. You have a function that has the same name with the one you are trying to implement and when you give it the subproblem, it solves it for you and the only thing you need to do is to integrate the solution of your part with the solution it gave you.

For example, we want to calculate the length of a list. Lets call our function magical_length and our magical helper with magical_length We know that if we give the sublist which does not have the first element, it will give us the length of the sublist by magic. Then only thing we need to think is how to integrate this information with our job. The length of the first element is 1 and magic_counter gives us the length of sublist n-1, therefore total length is (n-1) + 1 -> n

int magical_length( list )
  sublist = rest_of_the_list( list )
  sublist_length = magical_length( sublist ) // you can think this function as magical and given to you
  return 1 + sublist_length

However this answer is incomplete because we didn't consider what happens if we give an empty list. We thought that the list we have always has at least one element. Therefore we need to think about what should be the answer if we are given an empty list and answer is obviously 0. So add this information to our function and this is called base/edge condition.

int magical_length( list )
  if ( list is empty) then
    return 0
  else
    sublist_length = magical_length( sublist ) // you can think this function as magical and given to you
    return 1 + sublist_length