# Recursion

What is Recursion?
The process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called as recursive function. Using recursive algorithm, certain problems can be solved quite easily. Examples of such problems are Towers of Hanoi (TOH), Inorder/Preorder/Postorder Tree Traversals, DFS of Graph, etc.

What is base condition in recursion?
In recursive program, the solution to base case is provided and solution of bigger problem is expressed in terms of smaller problems.

```int fact(int n)
{
if (n < = 1) // base case
return 1;
else
return n*fact(n-1);
}
```

In the above example, base case for n < = 1 is defined and larger value of number can be solved by converting to smaller one till base case is reached.

Why Stack Overflow error occurs in recursion?
If base case is not reached or not defined, then stack overflow problem may arise. Let us take an example to understand this.

```int fact(int n)
{
// wrong base case (it may cause
// stack overflow).
if (n == 100)
return 1;

else
return n*fact(n-1);
}```

If fact(10) is called, it will call fact(9), fact(8), fact(7) and so on but number will never reach 100. So, the base case is not reached. If the memory is exhausted by these functions on stack, it will cause stack overflow error.

What is the difference between direct and indirect recursion?
A function fun is called direct recursive if it calls the same function fun. A function fun is called indirect recursive if it calls another function say fun_new and fun_new calls fun directly or indirectly. Difference between direct and indirect recursion has been illustrated in Table 1.

```
// An example of direct recursion
void directRecFun()
{
// Some code....

directRecFun();

// Some code...
}

// An example of indirect recursion
void indirectRecFun1()
{
// Some code...

indirectRecFun2();

// Some code...
}
void indirectRecFun2()
{
// Some code...

indirectRecFun1();

// Some code...
}```

What is difference between tailed and non-tailed recursion?
A recursive function is tail recursive when recursive call is the last thing executed by the function. Please refer tail recursion article for details.

How memory is allocated to different function calls in recursion?
When any function is called from main(), the memory is allocated to it on stack. A recursive function calls itself, the memory for called function is allocated on top of memory allocated to calling function and different copy of local variables is created for each function call. When the base case is reached, the function returns its value to the function by whom it is called and memory is de-allocated and the process continues.

Let us take the example how recursion works by taking a simple function.

```// A C++ program to demonstrate working of
// recursion
#include<bits/stdc++.h>
using namespace std;

void printFun(int test)
{
if (test < 1)
return;
else
{
cout << test << " ";
printFun(test-1);    // statement 2
cout << test << " ";
return;
}
}

int main()
{
int test = 3;
printFun(test);
}
```

Output :

`3 2 1 1 2 3`

When printFun(3) is called from main(), memory is allocated to printFun(3) and a local variable test is initialized to 3 and statement 1 to 4 are pushed on the stack as shown in below diagram. It first prints ‘3’. In statement 2, printFun(2) is called and memory is allocated to printFun(2) and a local variable test is initialized to 2 and statement 1 to 4 are pushed in the stack. Similarly, printFun(2) calls printFun(1) and printFun(1) calls printFun(0). printFun(0) goes to if statement and it return to printFun(1). Remaining statements of printFun(1) are executed and it returns to printFun(2) and so on. In the output, value from 3 to 1 are printed and then 1 to 3 are printed. The memory stack has been shown in below diagram.

What are the disadvantages of recursive programming over iterative programming?
Note that both recursive and iterative programs have same problem solving powers, i.e., every recursive program can be written iteratively and vice versa is also true. Recursive program has greater space requirements than iterative program as all functions will remain in stack until base case is reached. It also has greater time requirements because of function calls and return overhead.

What are the advantages of recursive programming over iterative programming?
Recursion provides a clean and simple way to write code. Some problems are inherently recursive like tree traversals, Tower of Hanoi, etc. For such problems it is preferred to write recursive code. We can write such codes also iteratively with the help of stack data structure. For example refer Inorder Tree Traversal without Recursion, Iterative Tower of Hanoi.

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