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3945. Minimum Sensors To Cover Grid

3945. Minimum Sensors to Cover Grid

Medium

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

Solution

class Solution {
    public int minSensors(int n, int m, int k) {
        int temp = 2 * k + 1;
        return ((n + temp - 1) / temp) * ((m + temp - 1) / temp);
    }
}

Complexity Analysis

  • Time Complexity: O(?)
  • Space Complexity: O(?)

Explanation

[Add detailed explanation here]