Tesla Algorithm Interview: Minimum Operations to Reduce to 1

Tesla's algorithmic interviews emphasize dynamic programming and greedy thinking. This article demonstrates how to optimize from brute force recursion to dynamic programming using the "Minimum Operations" problem. oavoservice helps you master optimization techniques.

📋 Problem Description

Given an integer n, you can perform the following operations:

1. If n is even, divide by 2.
2. If n is odd, add 1 or subtract 1.

Return the minimum number of operations to reduce n to 1.

Example:

Input: n = 15
Output: 5
Explanation: 15 -> 16 -> 8 -> 4 -> 2 -> 1

🎯 Core Concepts

1. Dynamic Programming - Optimal Substructure
2. Greedy Strategy - Local Optimal Choice
3. Bit Manipulation - Efficient Parity Check
4. Memoization - Avoid Re-computation

💡 Solution Strategy (oavoservice Guidance)

Method 1: Recursion + Memoization

def minOperations(n, memo={}):
    if n == 1:
        return 0
    if n in memo:
        return memo[n]
    
    if n % 2 == 0:
        result = 1 + minOperations(n // 2, memo)
    else:
        result = 1 + min(
            minOperations(n + 1, memo),
            minOperations(n - 1, memo)
        )
    
    memo[n] = result
    return result

Time Complexity: O(log n) Space Complexity: O(log n)

Method 2: Greedy (Optimal)

For odd numbers, should we +1 or -1?

• If n ends in 01 (binary), -1 makes it divisible by 4.
• If n ends in 11 (binary), +1 makes it divisible by 4 (except for 3).

def minOperations_greedy(n):
    ops = 0
    while n > 1:
        if n % 2 == 0:
            n //= 2
        else:
            if n == 3 or n % 4 == 1:
                n -= 1
            else:
                n += 1
        ops += 1
    return ops

Time Complexity: O(log n) Space Complexity: O(1)

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Pattern Recognition - Quickly identify optimal strategies Optimization Guidance - Full path from brute force to optimal Code Implementation - Ensure concise and high-performance code Follow-up Prep - Handling variants

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Tags: #Tesla #DynamicProgramming #Greedy #BitManipulation #VOHelp #InterviewPrep #1point3acres

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