How do you solve Minimum Sensors to Cover Grid on LeetCode?

Minimum Sensors to Cover Grid (LeetCode #3648) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: Understanding Chebyshev distance helps visualize sensor coverage.

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

The optimal solution for Minimum Sensors to Cover Grid runs in O(1) time and uses O(1) space. Only a few arithmetic operations are performed, leading to constant time complexity.

What is the brute force solution for Minimum Sensors to Cover Grid?

The brute force approach for Minimum Sensors to Cover Grid is Brute Force, with O(n²) time complexity and O(1) space complexity. Place sensors one by one and check coverage for each cell. This method is straightforward but inefficient for larger grids. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Minimum Sensors to Cover Grid?

Minimum Sensors to Cover Grid uses the following concepts: Math. The recommended patterns to study are: Greedy, Mathematical Optimization.

What are the interview tips for Minimum Sensors to Cover Grid?

Clarify the problem requirements before coding. Discuss your thought process and approach with the interviewer. Practice similar grid problems to build intuition.

What are common mistakes when solving Minimum Sensors to Cover Grid?

Forgetting to account for edge cases where k is large. Misunderstanding the coverage area of a sensor.

#3648

Minimum Sensors to Cover Grid

Medium

MathGreedyMathematical Optimization

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(1)
Space	O(1)	O(1)

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Intuition

Time O(1)Space O(1)

Calculate the effective coverage area of each sensor and determine how many are needed based on grid dimensions.

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Algorithm

3 steps

1Step 1: Calculate the side length of coverage as s = 2 * k + 1.
2Step 2: Compute the number of sensors needed as ceil(n / s) * ceil(m / s).
3Step 3: Return the total number of sensors.

solution.py5 lines

1import math
2
3def min_sensors(n, m, k):
4    s = 2 * k + 1
5    return math.ceil(n / s) * math.ceil(m / s)

ℹ

Complexity note: Only a few arithmetic operations are performed, leading to constant time complexity.

1Understanding Chebyshev distance helps visualize sensor coverage.
2Grid dimensions directly influence the number of sensors needed.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.