Amazon Interview Tips: Real Questions Answers & OA Interviews

Imagine you are now a software engineer at Amazon, responsible for managing a cluster of servers in a data center. In order to cope with user traffic at different times of the day, we need to dynamically adjust the operating state of the servers. Each server cluster can be represented by a number that represents its current operational energy level, which can range from 0 (completely off) to any positive integer (running at high energy).

At first, all server clusters have an energy consumption level of 0.

Now you get a list of expected energy levels for some future time period, e.g.: expected_energy_levels = [3, 5, 2, 0, 6]

Meaning: The first cluster (index 0) consumes 3. The second cluster (index 1) consumes 5. And so on.

What can you do?

You cannot adjust the energy level of a particular server cluster on its own. For efficient management, you do this by selecting a segment of consecutive server clusters at a time and then increasing the energy level of that segment by 1 unit at the same time.

For example: You can select clusters 2 through 4 (indexes 1 through 3) and increase the energy consumption by 1 unit together. Or you can add 1 unit to the 5th cluster (index 4) only. Or increase 1 unit for all clusters ......

In summary: a single operation can only increase the energy consumption for a segment of consecutive clusters by 1 unit for each cluster.

Your goal is: Find out: the minimum number of operations needed to change the energy consumption of all server clusters from [all 0s] to the list of target energy levels given by your boss.

This question is typical in that it simulates a resource scheduling problem that we would encounter in real life at Amazon. Essentially, we are taking a cluster of servers from a **"zero energy" state** to a predetermined energy goal by performing a batch of "boost energy" operations. What we are looking for is the minimum number of operations.

This topic is actually a practical business scenario of the "interval plus one" problem we just discussed. Its core logic is exactly the same as that of the previous road-paving question.

Let's analyze this again and take the example of expected_energy_levels = [3, 5, 2, 0, 6].

• Initial state: energy consumption of all server clusters is [0, 0, 0, 0, 0, 0].

• We want to realize [3, 5, 2, 0, 6].

• Consider that if I need to raise the energy consumption of cluster[0] from 0 to 3, then I need at least 3 operations, and all of these operations must cover cluster[0]. These operations can be any length from cluster[0] to the right.

• The point is that when we look at the energy levels of the clusters from left to right, if the expected energy consumption expected_energy_levels[i] of the current cluster is higher than the expected energy consumption expected_energy_levels[i-1] of the previous cluster, it means that that extra portion of the energy boost will inevitably require a new, independent batch operation to accomplish. Why? Because the previous batch operations for clusters i-1 or earlier could only bring cluster[i] up to expected_energy_levels[i-1] at best. To reach higher expected_energy_levels[i], there must be a new energy boost operation starting at i or further to the right.

• So, we can summarize a greedy strategy: we traverse the list of desired energy consumption, and each time we encounter a higher energy requirement than the previous cluster, we count this **"increment "** in the total number of operations. Because these increments cannot be "whored out" by previous operations, they must be made up by new operations.

• The specific steps of the algorithm are as follows:

  1. Initialize total_operations = 0.
  2. For the first cluster (indexed 0): it needs expected_energy_levels[0] lifts to reach the target. So, total_operations plus expected_energy_levels[0].
  3. Starting at i = 1, traverse to expected_energy_levels.length - 1:
     
     • If expected_energy_levels[i] is larger than expected_energy_levels[i-1], it means that starting from cluster[i], we need to perform expected_energy_levels[i] - expected_ energy_levels[i-1] operations. These operations are independent and must be counted in the total. So, total_operations += (expected_energy_levels[i] - expected_energy_levels[i-1]).
     • If expected_energy_levels[i] is less than or equal to expected_energy_levels[i-1], then the energy consumption of cluster[i] can be overridden by the previous operations that raised cluster[i-1] to a higher energy consumption. There is no need to start a new operation starting from cluster[i].

Let's actually run this example with expected_energy_levels = [3, 5, 2, 0, 6]:

1. Initialize total_operations = 0.
2. i = 0: expected_energy_levels[0] = 3. total_operations = 0 + 3 = 3. (Imagine that we performed 3 energy boost operations on a segment of the cluster starting at cluster[0].)
3. i = 1: expected_energy_levels[1] = 5, and expected_energy_levels[0] = 3. 5 > 3. total_operations += (5 - 3) = 2. total_operations = 3 + 2 = 5 now. (This means that 2 new energy boost operations have been performed starting from cluster[1].)
4. i = 2: expected_energy_levels[2] = 2, and expected_energy_levels[1] = 5. 2 <= 5. No additional operations are required, and total_operations remain 5. (The energy requirement of 2 for cluster[2] can be met by overriding the previous operation of cluster[1] to 5.) ] to 5 can be satisfied by the previous operation of overriding cluster[1] to 5.)
5. i = 3: expected_energy_levels[3] = 0, while expected_energy_levels[2] = 2. 0 <= 2. No additional operations are needed, total_operations stays 5.
6. i = 4: expected_energy_levels[4] = 6, while expected_energy_levels[3] = 0. 6 > 0. total_operations += (6 - 0) = 6. total_operations = 5 + 6 = 11 now. ( Starting from cluster[4], 6 new energy boost operations are performed.)

Finally, we conclude that a minimum of 11 operations are required to reach the target energy state.

The time complexity of this method is linear, i.e. $o(N)$, where N is the number of server clusters. The space complexity is $o(1)$, because it only requires a few variables to store intermediate states. This efficient and logical solution is ideal in an efficiency-oriented scenario like Amazon.