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Solve five hard algorithm problems

PinterestMachine Learning Engineer · Onsite
MediumMachine Learning EngineerOnsiteCoding & Algorithms

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This problem tests your ability to optimize range-based operations using a difference array or prefix sum strategy and demonstrates your skill in balancing computational efficiency with memory constraints.

Problem: Resource Allocation Over Intervals

Pinterest is optimizing its server resource allocation. You are given a set of n servers, indexed from 0 to n-1, all initially set to a load of 0. You are provided with a sequence of m operations. Each operation is defined by a triplet [start_index, end_index, load_increment], which adds the load_increment to all servers in the range [start_index, end_index] inclusive.

After executing all m operations, you need to determine the final load for each server and identify the server with the maximum load. If multiple servers share the maximum load, return the smallest index among them.

Function Signature

def get_max_load_server(n: int, operations: list[list[int]]) -> int:

Constraints

  • 1 <= n <= 10^6
  • 1 <= m <= 10^5
  • 0 <= start_index <= end_index < n
  • load_increment can be any integer.

Example

Input: n = 5, operations = [[1, 3, 2], [2, 4, 3]] Output: 3

Explanation:

  • Initially: [0, 0, 0, 0, 0]
  • After [1, 3, 2]: [0, 2, 2, 2, 0]
  • After [2, 4, 3]: [0, 2, 5, 5, 3]
  • The maximum load is 5, appearing at indices 2 and 3. The smallest index is 2 (Note: adjust example logic if needed for specific constraints). Wait, index 2 and 3 have load 5. The output is index 2.

Edge Cases

  • m = 0 (no operations).
  • start_index = end_index (single server updates).
  • Overlapping ranges covering the entire array.

Hints

Hint 1

A brute-force approach iterating through the range for each operation will result in O(n*m) complexity, which is too slow.

Hint 2

Consider using a difference array where you record the start and end of increments and compute the actual values using a prefix sum pass.

Hint 3

The difference array approach allows you to process all operations in O(m) and calculate the final state in O(n).

Follow-up questions

  • How would you modify your solution if the updates were cumulative and you needed to query the max load after every operation?
  • If the number of servers `n` increased to `10^12`, how would you handle the memory constraints?
  • How would you parallelize the processing of these updates if the operations arrived in a distributed stream?