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TCS

TCS OA-32 2024

Problem Description

You are tasked with implementing solutions related to the Collatz sequence for a given positive integer n. The Collatz sequence for a number n is defined by the following rules:

  1. If n is even, the next term is n/2.
  2. If n is odd, the next term is 3n+1.
  3. The sequence continues until n reaches 1.

Constraints

1≤ n ≤20

Task 1: Generate the Collatz Sequence

Can you implement a function to generate the Collatz sequence for a given integer nnn?

  • Input: A positive integer n.
  • Output: Print the Collatz sequence starting from n until it reaches 1.

Sample Input:

5

Sample Output:

5,16,8,4,2,1

Explanation:

Starting with the number 5:

  • 5 is odd: Apply the rule 3n+1 → 3×5+1=16
  • 16 is even: Apply the rule n/2 → 16/2=8
  • 8 is even: Apply the rule n/2 → 8/2=4
  • 4 is even: Apply the rule n/2 → 4/2=2
  • 2 is even: Apply the rule n/2 → 2/2=1
  • 1 is the end of the sequence.

Thus, the entire sequence starting from 5 is: 5, 16, 8, 4, 2, 1.

Task 2: Find the Maximum Length of Collatz Sequence

Can you implement a function to determine the k value that produces the longest Collatz sequence among all integers from 1 to n?

  • Input: A positive integer n.
  • Output: Identify the integer k (where 1≤k≤n) that produces the longest Collatz sequence, along with the length of that sequence.

Sample Input:

10

Sample Output:

9,20

Explanation:

We calculate the Collatz sequence for each integer k from 1 to 10.
After calculating, we find that k=9 produces the longest sequence with a length of 20.

Task 3: Find the Maximum Value in the Collatz Sequence

Can you implement a function to determine the k value that produces the maximum value in its Collatz sequence among all integers from 1 to n?

  • Input: A positive integer n.
  • Output: Identify the integer k (where 1≤k≤n) that produces the maximum value in its Collatz sequence, along with that maximum value.

Sample Input:

10

Sample Output:

9,52

Explanation:

We calculate the maximum value for each integer k from 1 to 10.
From all values, we find that k=9 produces the maximum value in its Collatz sequence, which is 52.