How do I think about recursion.

1

I got the idea for problems like factorials or finding sum from 1 to n, where there’s a pattern visible. Like this:

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Source:https://99x.io/blog/recursion-is-not-hard-here-is-the-right-way-to-think

But I’m confused for things like addition. I know the answer but I am unable to figure out how we came to the answer. Could you guys help me on this?

2

Can you give an example of what you mean for addition? Are you trying to add two numbers using a recursive approach?

3

I got for addition of two numbers. Can you describe one for division of two numbers a/b?

For addition, it’s a+b=a-1+1+b
=(a-1)+(b+1)
=Sum(a-1,b+1).
Now I need for division

4

I got for division as well. It’s
(a-b+b)/b
= (a-b)/b + b/b
=1+(a-b)/b/

5

Hey mate,
There are multiple way to call functions repeatedly.

You can for example save the result of a function call to a variable and then call it again e.g.

// call the add function with the previous variable until the last run equals 10
function add (z){ return z + 1 }

let run1 = add(1)
let run2 = add(run1)
let run3 = add(run2)
let run4 = add(run3)
let run5 = add(run4)
let run6 = add(run5)
let run7 = add(run6)
let run8 = add(run7)
let run9 = add(run8)

Or call it in a loop e.g.

function add (z){ return z + 1 }

// while "a" is less 10 make "a" equal to add "a" BUT stop at 10
let a = 1;
while( a < 10 ){ a = add(a) }

Or you have a function call itself from inside itself (recursion) e.g.

// if x equals 10 return x else call recursion with the value of x again
function recursion (x){
  if(x == 10) return x
  else return recursion(x + 1)
}

recursion(1)

The main thing that should concern you is having a break case so you don’t get excessive stacks or an endless loop…