Is Minimum Sensors to Cover Grid easy or hard?

The problem is typically classified as Medium because the key step is recognizing the tiling pattern. Once you identify that each sensor covers a fixed 3 x 3 region, the implementation becomes a simple constant-time formula.

Minimum Sensors to Cover Grid Python/Java solution

In Python or Java, compute the result using ceiling division: (m + 2) // 3 and (n + 2) // 3, then multiply the results. This avoids floating-point operations and directly produces the minimum number of sensors.

How to solve Minimum Sensors to Cover Grid in O(1)?

Recognize that a single sensor covers a 3 x 3 block. Instead of iterating through the grid, compute how many such blocks are required to cover the rows and columns. The answer is ceil(m / 3) * ceil(n / 3), which can be calculated directly in constant time.

What is the best approach for Minimum Sensors to Cover Grid?

The optimal approach uses a mathematical tiling observation. Each sensor covers a 3 x 3 region of the grid, so the grid can be partitioned into coverage blocks. The minimum sensors required is ceil(m / 3) * ceil(n / 3). This runs in O(1) time and constant space.

Is Minimum Sensors to Cover Grid asked at Google/Amazon/Meta?

Grid coverage and tiling problems appear frequently in interviews at companies like Google, Amazon, and Meta. While the exact problem may vary, the pattern of converting grid coverage into a mathematical formula is commonly tested.

What data structure is used in Minimum Sensors to Cover Grid?

The optimal solution does not require any special data structures. It relies purely on mathematical reasoning and integer arithmetic. A simulation-based approach may use simple grid traversal with loops.

What is the time complexity of Minimum Sensors to Cover Grid?

The optimal solution runs in O(1) time because it only performs a few arithmetic operations using ceiling division. A naive simulation that scans the entire grid would take O(m * n) time.

Description Hints 2 Video 17:45

3648. Minimum Sensors to Cover Grid

Medium67.6% acceptance4 companies

You are given n × m grid and an integer k.

A sensor placed on cell (r, c) covers all cells whose Chebyshev distance from (r, c) is at most k.

The Chebyshev distance between two cells (r₁, c₁) and (r₂, c₂) is max(|r₁ − r₂|,|c₁ − c₂|).

Your task is to return the minimum number of sensors required to cover every cell of the grid.

Example 1:

Input: n = 5, m = 5, k = 1

Output: 4

Explanation:

Placing sensors at positions (0, 3), (1, 0), (3, 3), and (4, 1) ensures every cell in the grid is covered. Thus, the answer is 4.

Example 2:

Input: n = 2, m = 2, k = 2

Output: 1

Explanation:

With k = 2, a single sensor can cover the entire 2 * 2 grid regardless of its position. Thus, the answer is 1.

Constraints:

1 <= n <= 10³
1 <= m <= 10³
0 <= k <= 10³

Asked at 4 companies

Cisco Amazon Microsoft

Google

Topics

Math

Hints open one at a time

Hint 1

Let s = 2*k + 1, the side length each sensor covers.

Hint 2

The minimum number is ceil(n / s) * ceil(m / s).

LanguageLoading editor…

1class Solution:
2    def minSensors(self, n: int, m: int, k: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

5
5
1

Input

2
2
2

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