Permutations with Divisibility

• Algorithms and Data Structures: TheAlgorist.com
  
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• Low Level Design: LowLevelDesign.io
  

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Problem Statement:

Suppose you have n integers labeled 1 through n.
A permutation of those n integers perm (1-indexed) is considered a "Divisible Permutation" if for every i (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, return the number of the "Divisible Permutations" that you can construct.

Example 1:
Input: n = 2
Output: 2
Explanation:
The first beautiful arrangement is [1,2]:

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

The second beautiful arrangement is [2,1]:

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

Example 2:
Input: n = 1
Output: 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:

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Java Code:

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Python Code:

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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:

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