Permutations with Divisibility

• Algorithms and Data Structures: TheAlgorist.com
  
• System Design: SystemsDesign.Cloud
  
• Low Level Design: LowLevelDesign.io
  
• Frontend Engineering: FrontendEngineering.io
  

---

Problem Statement:

Suppose you have n integers from 1 through n.
A permutation of those n integers is considered a Divisible Permutation if for every i, where 1 <= i <= n, either of the following is true:

• perm[i] is divisible by i.
• i is divisible by perm[i].

Given an integer n, find the total number of the valid Divisible Permutations.

Example 1:
Input: n = 2
Output: 2
Explanation:
The first Divisible Permutation is [1,2]:

• permutation[1] = 1 is divisible by i = 1
• permutation[2] = 2 is divisible by i = 2

The second Divisible Permutation is [2,1]:

• permutation[1] = 2 is divisible by i = 1
• i = 2 is divisible by permutation[2] = 1

Solution:

• NOTE: I highly recommend going through the Backtracking chapters in the order they are given in the Index page to get the most out of it and be able to build a rock-solid understanding.

Prerequisites:

• Backtracking Fundamentals
• Find Permutations using Backtracking

Algorithm:

This is a Premium content.
Please subscribe to the Algorithms course to access the detailed Algorithm discussion.

Java Code:

This is a Premium content.
Please subscribe to Algorithms course to access the code.

Python Code:

This is a Premium content.
Please subscribe to Algorithms course to access the code.




Don't forget to take in-depth look at the other backtracking problems in the below link, because that is what would make you comfortable with using the backtracking template and master the art of Backtracking:

• All Backtracking Problems in one place

Instructor:

If you have any feedback, please use this form: https://thealgorists.com/Feedback.

---

Subscribe to Our Youtube Channel

Follow Us On LinkedIn