How to think in recursive way?

Question

In order to understand the advanced algorithm concepts like greedy methods and dynamic programming, one first need to be well versed in recursion.

I am relatively new to

Answer 1

Let's take a simple task. Printing numbers from 1 to 10. I'll use Python2.7 here.

for i in range(1,11):
    print i

Now let's try to do the same, using recursion.

>>> def print_me(n):
    if n > 0:
        print_me(n - 1)
        print n
    else:
        return

>>> print_me(10)
1
2
3
4
5
6
7
8
9
10

So how do we think of it ?

• Step1: Think of my boundaries. I need two . 1 and 10. Next.
• Step2: The print statement. That's our motive. To print numbers. And we want it from 1 to 10. So I need to print 1 first.

• Step3: We start by writing a function that does the job of printing a number passed as an argument. Let's think of just, the main task.

  def print_me(n): print n

• Step 4: I want the function to return, if n < 1.

  def print_me(n): if n > 0: print n else: return

• Step 5: Now I want to pass numbers, from 1 to 10 to this function, but we don't want a loop of 1 to 10 , and then pass it to our function. We want it to be done recursively.

What is recursion? In plain words, the repeated application of a recursive procedure or definition.

So in order to make it recursive, we need to call the function itself. And we want to pass our range of 1 to 10.

def print_me(n):
    if n > 0:
        print_me(n - 1)
        print n
    else:
        return

Summarizing: All recursive calls must obey 3 important rules:

1. A recursive algorithm, MUST have a base case.
2. A recursive algorithm, MUST change its state and move toward the base case.
3. A recursive algorithm MUST call itself, recursively.

Source : interactivepython

Another program in Javascript to find factorial:

function factorial(n){
    if (n == 1)
        {
        return 1;
        }
    else {
        return n * factorial(n-1);
        }
}