Count segments and optimize 3-server assignment
Interview Question: Transaction Segments & Server Assignment
This interview consists of two independent programming tasks.
Problem 1: Transaction Segments
You are tasked with analyzing a series of financial transactions. Given an array transactionValues of length n, where transactionValues[i] represents the transaction amount at time i, and an integer k (where 1 ≤ k ≤ n), your goal is to count the number of contiguous subarrays of length exactly k that are strictly increasing.
A contiguous segment transactionValues[l..r] is considered strictly increasing if, for every i such that l ≤ i < r, transactionValues[i] < transactionValues[i + 1] holds true.
Formally, you need to count the number of starting indices s such that 0 ≤ s ≤ n - k and the subarray transactionValues[s], transactionValues[s + 1], ..., transactionValues[s + k - 1] is strictly increasing.
Input:
n: The length of thetransactionValuesarray.k: The required length of the strictly increasing segments.transactionValues: An integer array of lengthnrepresenting transaction amounts.
Output:
- A single integer: The total count of strictly increasing contiguous subarrays of length exactly
k.
Efficiency Requirement:
Design an algorithm that runs efficiently for large n (e.g., up to 2 × 10^5).
Problem 2: Efficient Tasks Across 3 Servers
You are given n software modules, each with an associated difficulty value. The difficulty array has length n, where difficulty[i] is the difficulty of the i-th module. Your objective is to assign all n modules to exactly three servers, S1, S2, and S3, subject to the following rules:
- Each server must receive at least one module.
- Every module must be assigned to exactly one server.
After an assignment (partition) of modules into three non-empty groups S1, S2, and S3 is fixed, you must choose one module from each server to minimize a specific value. Let d1 = difficulty[i1] where i1 ∈ S1, d2 = difficulty[i2] where i2 ∈ S2, and d3 = difficulty[i3] where i3 ∈ S3. The value for this assignment is defined as:
F(S1, S2, S3) = min_{i1 ∈ S1, i2 ∈ S2, i3 ∈ S3} (|d1 - d2| + |d2 - d3|)
Your overall goal is to choose an assignment of modules to the three servers that maximizes this minimal value F. In other words, you need to compute max_{(S1, S2, S3)} F(S1, S2, S3) over all valid partitions (S1, S2, S3) of the modules into three non-empty, disjoint sets whose union is all modules.
Input:
n: The number of software modules (n ≥ 3).difficulty: An integer array of lengthnrepresenting module difficulties.
Output:
- A single integer: The maximum possible value of
F(S1, S2, S3)over all valid assignments.
Efficiency Requirement:
Design an algorithm that is significantly more efficient than enumerating all possible assignments (which is exponential in n) and can handle large n (e.g., up to 2 × 10^5).
AI interview prep
Core dilemma
Balancing efficient pattern detection in sequential data (Problem 1) with optimizing a complex min-max objective function over partitions of a large dataset (Problem 2), both under strict time complexity constraints.
2 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Count segments and optimize 3-server assignment
Interview Question: Transaction Segments & Server Assignment
This interview consists of two independent programming tasks.
Problem 1: Transaction Segments
You are tasked with analyzing a series of financial transactions. Given an array transactionValues of length n, where transactionValues[i] represents the transaction amount at time i, and an integer k (where 1 ≤ k ≤ n), your goal is to count the number of contiguous subarrays of length exactly k that are strictly increasing.
A contiguous segment transactionValues[l..r] is considered strictly increasing if, for every i such that l ≤ i < r, transactionValues[i] < transactionValues[i + 1] holds true.
Formally, you need to count the number of starting indices s such that 0 ≤ s ≤ n - k and the subarray transactionValues[s], transactionValues[s + 1], ..., transactionValues[s + k - 1] is strictly increasing.
Input:
n: The length of thetransactionValuesarray.k: The required length of the strictly increasing segments.transactionValues: An integer array of lengthnrepresenting transaction amounts.
Output:
- A single integer: The total count of strictly increasing contiguous subarrays of length exactly
k.
Efficiency Requirement:
Design an algorithm that runs efficiently for large n (e.g., up to 2 × 10^5).
Problem 2: Efficient Tasks Across 3 Servers
You are given n software modules, each with an associated difficulty value. The difficulty array has length n, where difficulty[i] is the difficulty of the i-th module. Your objective is to assign all n modules to exactly three servers, S1, S2, and S3, subject to the following rules:
- Each server must receive at least one module.
- Every module must be assigned to exactly one server.
After an assignment (partition) of modules into three non-empty groups S1, S2, and S3 is fixed, you must choose one module from each server to minimize a specific value. Let d1 = difficulty[i1] where i1 ∈ S1, d2 = difficulty[i2] where i2 ∈ S2, and d3 = difficulty[i3] where i3 ∈ S3. The value for this assignment is defined as:
F(S1, S2, S3) = min_{i1 ∈ S1, i2 ∈ S2, i3 ∈ S3} (|d1 - d2| + |d2 - d3|)
Your overall goal is to choose an assignment of modules to the three servers that maximizes this minimal value F. In other words, you need to compute max_{(S1, S2, S3)} F(S1, S2, S3) over all valid partitions (S1, S2, S3) of the modules into three non-empty, disjoint sets whose union is all modules.
Input:
n: The number of software modules (n ≥ 3).difficulty: An integer array of lengthnrepresenting module difficulties.
Output:
- A single integer: The maximum possible value of
F(S1, S2, S3)over all valid assignments.
Efficiency Requirement:
Design an algorithm that is significantly more efficient than enumerating all possible assignments (which is exponential in n) and can handle large n (e.g., up to 2 × 10^5).