recursion:greatest common divisor

[VeronicaM]

All PRs

• I have self-reviewed my code
• I have written tests which cover new and changed functionality
• All tests pass
• I have commented on difficult to understand code

Where Relevant

• I have compared and validated my UI changes against the designs
• I've updated relevant documentation e.g. README

Description

What is this PR about ?

Find the greatest common divisor of two given numbers

What was implemented ?

1. Iterative solution

• Loop from 1 to max, where max is num1 if num1 > num2, or num2 is num2 > num1
• Check if num1 % i === 0 && num2 % i === 0
• check if i is greater than a variable greatest divisor if yes replace it.

Runtime complexity: O(max)
Space complexity: O(1)

This could have been further optimised by

• Using the min instead of max
• looping in reverse from min to 1
• breaking as soon as the condition num1 % i === 0 && num2 % i === 0 returns true
• if no common divisor is found return -1

2. Recursive solution

• Base case:
  • num1 === 0 || num2 === 0
  • num1 === num2 return num1
• recursive case calling the function again with the subtraction of the smaller number from the bigger one.

Runtime complexity and space complexity : O(max/min)

What did you learn ?

• A problem can be written in many different ways, it's important to pay attention to how they compare in terms of performance to each other.
• Taking advantage of math properties helps to simplify the algorithms and remove redundant steps.

What links/documents relate to this PR ?

• Recursion for Coding Interviews in JavaScript on Educative

Testing

Steps required to test

• cd interviews/recursion/greatest-common-divisor
• run node greatest-common-divisor.js

All tests should pass
Test cases can be found in interviews/recursion/greatest-common-divisor/testData