Minimize Total Assignment Distance
Company: Dark Alpha Capital
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Technical Screen
You are given the coordinates of `n` analysts and `m` field devices on a 2D grid, where `1 <= n <= 10` and `n <= m <= 15`. Each analyst must be assigned exactly one distinct device, and each device can be assigned to at most one analyst.
The cost of assigning analyst `i` at `(ax[i], ay[i])` to device `j` at `(dx[j], dy[j])` is the Manhattan distance:
`|ax[i] - dx[j]| + |ay[i] - dy[j]|`
Return the minimum possible total assignment cost after assigning a unique device to every analyst.
Design an algorithm efficient enough for the given constraints.
Quick Answer: This question evaluates competency in combinatorial optimization, assignment/matching problems, and reasoning about Manhattan distance cost metrics. Commonly asked to assess algorithmic reasoning about constrained assignments, search and complexity trade-offs, it belongs to the Coding & Algorithms domain and emphasizes practical application of algorithm design and implementation rather than purely conceptual theory.