What is tail recursion?

Question

Whilst starting to learn lisp, I\'ve come across the term tail-recursive. What does it mean exactly?

Answer 1

The recursive function is a function which calls by itself

It allows programmers to write efficient programs using a minimal amount of code.

The downside is that they can cause infinite loops and other unexpected results if not written properly.

I will explain both Simple Recursive function and Tail Recursive function

In order to write a Simple recursive function

1. The first point to consider is when should you decide on coming out of the loop which is the if loop
2. The second is what process to do if we are our own function

From the given example:

public static int fact(int n){
  if(n <=1)
     return 1;
  else 
     return n * fact(n-1);
}

From the above example

if(n <=1)
     return 1;

Is the deciding factor when to exit the loop

else 
     return n * fact(n-1);

Is the actual processing to be done

Let me the break the task one by one for easy understanding.

Let us see what happens internally if I run fact(4)

1. Substituting n=4

public static int fact(4){
  if(4 <=1)
     return 1;
  else 
     return 4 * fact(4-1);
}

If loop fails so it goes to else loop so it returns 4 * fact(3)

2. In stack memory, we have 4 * fact(3)

   Substituting n=3

public static int fact(3){
  if(3 <=1)
     return 1;
  else 
     return 3 * fact(3-1);
}

If loop fails so it goes to else loop

so it returns 3 * fact(2)

Remember we called ```4 * fact(3)``

The output for fact(3) = 3 * fact(2)

So far the stack has 4 * fact(3) = 4 * 3 * fact(2)

3. In stack memory, we have 4 * 3 * fact(2)

   Substituting n=2

public static int fact(2){
  if(2 <=1)
     return 1;
  else 
     return 2 * fact(2-1);
}

If loop fails so it goes to else loop

so it returns 2 * fact(1)

Remember we called 4 * 3 * fact(2)

The output for fact(2) = 2 * fact(1)

So far the stack has 4 * 3 * fact(2) = 4 * 3 * 2 * fact(1)

3. In stack memory, we have 4 * 3 * 2 * fact(1)

   Substituting n=1

public static int fact(1){
  if(1 <=1)
     return 1;
  else 
     return 1 * fact(1-1);
}

If loop is true

so it returns 1

Remember we called 4 * 3 * 2 * fact(1)

The output for fact(1) = 1

So far the stack has 4 * 3 * 2 * fact(1) = 4 * 3 * 2 * 1

Finally, the result of fact(4) = 4 * 3 * 2 * 1 = 24

The Tail Recursion would be

public static int fact(x, running_total=1) {
    if (x==1) {
        return running_total;
    } else {
        return fact(x-1, running_total*x);
    }
}

1. Substituting n=4

public static int fact(4, running_total=1) {
    if (x==1) {
        return running_total;
    } else {
        return fact(4-1, running_total*4);
    }
}

If loop fails so it goes to else loop so it returns fact(3, 4)

2. In stack memory, we have fact(3, 4)

   Substituting n=3

public static int fact(3, running_total=4) {
    if (x==1) {
        return running_total;
    } else {
        return fact(3-1, 4*3);
    }
}

If loop fails so it goes to else loop

so it returns fact(2, 12)

2. In stack memory, we have fact(2, 12)

   Substituting n=2

public static int fact(2, running_total=12) {
    if (x==1) {
        return running_total;
    } else {
        return fact(2-1, 12*2);
    }
}

If loop fails so it goes to else loop

so it returns fact(1, 24)

3. In stack memory, we have fact(1, 24)

   Substituting n=1

public static int fact(1, running_total=24) {
    if (x==1) {
        return running_total;
    } else {
        return fact(1-1, 24*1);
    }
}

If loop is true

so it returns running_total

The output for running_total = 24

Finally, the result of fact(4,1) = 24