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.
\n\n\n
Example 1:
\n\nInput: n = 5, m = 5, k = 1
\n\nOutput: 4
\n\nExplanation:
\n\nPlacing 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:
\n\nInput: n = 2, m = 2, k = 2
\n\nOutput: 1
\n\nExplanation:
\n\nWith k = 2, a single sensor can cover the entire 2 * 2 grid regardless of its position. Thus, the answer is 1.
\n
Constraints:
\n\n1 <= n <= 1031 <= m <= 1030 <= k <= 103给你一个 n × m 的网格和一个整数 k。
一个放置在单元格 (r, c) 的传感器可以覆盖所有与 (r, c) 的 切比雪夫距离不超过 k 的单元格。
两个单元格 (r1, c1) 和 (r2, c2) 之间的 切比雪夫距离 为 max(|r1 − r2|,|c1 − c2|)。
你的任务是返回覆盖整个网格所需传感器的 最少 数量。
\n\n\n\n
示例 1:
\n\n输入: n = 5, m = 5, k = 1
\n\n输出: 4
\n\n解释:
\n\n在位置 (0, 3)、(1, 0)、(3, 3) 和 (4, 1) 放置传感器可以确保网格中的每个单元格都被覆盖。因此，答案是 4。
示例 2:
\n\n输入: n = 2, m = 2, k = 2
\n\n输出: 1
\n\n解释:
\n\n当 k = 2 时，无论传感器放在哪个位置，单个传感器都可以覆盖整个 2 * 2 的网格。因此，答案是 1。
\n\n
提示:
\n\n1 <= n <= 1031 <= m <= 1030 <= k <= 103s = 2*k + 1, the side length each sensor covers.",
"The minimum number is ceil(n / s) * ceil(m / s)."
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