To find the number of steps to reach 1 from a given integer n using the Collatz conjecture rules (divide by 2 if even, multiply by 3 and add 1 if odd), you can employ either an iterative or a recursive approach.
Iterative Approach:
Use a while loop that continues as long as n is not equal to 1. Inside the loop, check if n is even or odd and apply the corresponding rule. Increment a step counter in each iteration. This is straightforward and avoids potential stack overflow issues with very large inputs.
Recursive Approach:
Define a function that takes n as input. The base case is when n equals 1, returning 0 steps. Otherwise, apply the Collatz rule based on whether n is even or odd, and recursively call the function with the new value of n, adding 1 to the result of the recursive call. Memoization (caching) can be used to store results for previously computed numbers, significantly optimizing performance for repeated calculations or overlapping subproblems.
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