Answer multi-round grid and data-structure questions
Problem Description
You are given an m x n 2D grid where each cell is either a house (1) or empty (0). Your task is to place exactly one turret on any cell within this grid.
A turret protects a house if the Manhattan distance between the turret's cell (r_t, c_t) and the house's cell (r_h, c_h) is less than or equal to a given integer k. The Manhattan distance is defined as |r_t - r_h| + |c_t - c_h|.
The objective is to determine the maximum number of houses that can be protected by placing a single turret optimally.
Constraints
1 <= m, n <= 20000 <= k <= 2000- Values
mandnmight require discussion of scalable approaches if they exceed typical limits.
AI interview prep
Core dilemma
The central engineering conflict is efficiently calculating the number of protected houses for every possible turret placement in an `M x N` grid, given a Manhattan distance constraint `k`. The challenge lies in optimizing the range query for diamond-shaped regions without resorting to an `O((MN)^2)` or `O(MNK^2)` brute-force approach, especially for large grid dimensions and `k`.
2 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Answer multi-round grid and data-structure questions
Problem Description
You are given an m x n 2D grid where each cell is either a house (1) or empty (0). Your task is to place exactly one turret on any cell within this grid.
A turret protects a house if the Manhattan distance between the turret's cell (r_t, c_t) and the house's cell (r_h, c_h) is less than or equal to a given integer k. The Manhattan distance is defined as |r_t - r_h| + |c_t - c_h|.
The objective is to determine the maximum number of houses that can be protected by placing a single turret optimally.
Constraints
1 <= m, n <= 20000 <= k <= 2000- Values
mandnmight require discussion of scalable approaches if they exceed typical limits.