Maximum Energy Boost From Two Drinks

Maximum Energy Boost From Two Drinks - Problem

Imagine you're a professional athlete preparing for the most important competition of your career! 🏃‍♂️💪

A futuristic sports scientist has provided you with two different energy drinks A and B, each offering varying energy boosts throughout the day. You have n hours to prepare, and you must drink exactly one energy drink per hour to maximize your total energy boost.

Here's the catch: switching between drinks isn't instant! If you want to switch from one energy drink to another, your body needs one full hour to cleanse your system - meaning you get zero energy boost during that transition hour.

Your Goal: Determine the maximum total energy boost you can achieve over n hours. You can start with either drink A or drink B.

Input: Two integer arrays energyDrinkA and energyDrinkB of length n, representing energy boosts per hour.

Output: The maximum total energy boost possible.

Input & Output

example_1.py — Basic case

$ Input: energyDrinkA = [1, 3, 1], energyDrinkB = [3, 1, 1]

› Output: 5

💡 Note: Start with B (3), switch to A in hour 2 but get 0 due to switching penalty, then get A (1) in hour 3. Total: 3 + 0 + 1 = 4. Or start with B (3), continue with B (1), continue with B (1). Total: 3 + 1 + 1 = 5. The maximum is 5.

example_2.py — No switching optimal

$ Input: energyDrinkA = [4, 1, 1], energyDrinkB = [1, 1, 3]

› Output: 7

💡 Note: Start with A (4), switch to B (penalty = 0), then B (3). Total: 4 + 0 + 3 = 7. This beats staying with one drink throughout.

example_3.py — Single hour

$ Input: energyDrinkA = [5], energyDrinkB = [3]

› Output: 5

💡 Note: With only one hour, choose the higher energy drink A with value 5.

Constraints

n == energyDrinkA.length == energyDrinkB.length
1 ≤ n ≤ 10⁵
1 ≤ energyDrinkA[i], energyDrinkB[i] ≤ 10⁵

Visualization

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Asked in

G Google 42 a Amazon 38 f Meta 29 ⊞ Microsoft 31

The optimal solution uses dynamic programming to track the maximum energy possible ending with each drink type. At each hour, we calculate the maximum energy by either continuing with the same drink (no penalty) or switching drinks (with one-hour penalty). The key insight is that we only need to maintain two values: maximum energy ending with drink A and maximum energy ending with drink B. This gives us O(n) time and O(1) space complexity.

Common Approaches

✓ Hash Map

⏱️ Time: N/A Space: N/A

Brute Force (Recursive Exploration)

⏱️ Time: O(2^n) Space: O(n)

Generate all possible sequences of drink choices, considering the switching penalty. For each hour, try both drinks and recursively calculate the maximum energy from remaining hours.

Dynamic Programming (Optimal)

⏱️ Time: O(n) Space: O(1)

Use dynamic programming to efficiently compute the maximum energy boost. At each hour, maintain the maximum energy possible ending with drink A and ending with drink B, considering the switching penalty.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Smart Actions

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