Tesla Coding Interview — Minimum Operations to Reduce Integer to 1 | Greedy + Bit Manipulation | Optimal Strategy

Problem:
Given an integer n, you may perform only the following operations:

1. If n is divisible by 2, you may perform:
   n = n / 2
2. You may increment n by 1:
   n = n + 1

Your goal is to compute the smallest number of operations required to reduce n to 1.

Example:

n = 1
→ output = 0

This is a classic greedy + bit-manipulation problem.
Two operations are allowed:

• If n is even, dividing by 2 is always optimal.
• If n is odd, we must choose between:
  • n + 1
  • (implicitly) n - 1 through repeated divides

The key insight comes from binary representation:

• For odd numbers, using +1 is only better when it leads to more trailing zeroes in binary (meaning more subsequent /2 operations).
• Special case:
  n = 3 → always choose n - 1 path (i.e., go to 2).

This produces an O(log n) time greedy solution.

This problem tests whether the candidate knows:

• How to analyze binary patterns
• Greedy correctness reasoning
• Minimizing operations on integer reduction
  It’s similar to problems seen in FAANG interviews (e.g., LeetCode 397).

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