Starting with any positive integer N, we define the Collatz sequence corresponding to N as the numbers formed by the following operations:
If N is even, N→ N/2
if N is odd, N→ 3N+ 1
It is conjectured but not yet proven that no matter which positive integer we start with; we always end up with 1.
For example, 10 → 5 → 16 → 8 → 4 → 2 → 1. You have to give the maximum collatz sequence length among all the numbers from 1 to N(both included).
Example 1:
Input: N = 1
Output: 1
Explaination: Here N can have only one
value 1.
Example 2:
Input: N = 3
Output: 8
Explaination: For N= 3 we need to check
sequence length when sequence starts with
1, 2, and 3.
when sequence starts with 1, it's : 1
length = 1
when sequence starts with 2, it's : 2->1,
length = 2
when sequence starts with 3, it's :
3->10->5->16->8->4->2->1, length = 8.
Your Task:
You do not need to read input or print anything. Your task is to complete the function collatzLength()which takes N as input parameter and returns the maximum collatz sequence length.
Expected Time Complexity:O(N)
Expected Auxiliary Space: O(N)
Constraints:
1 < N < 10^{6}

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