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2812-find-the-safest-path-in-a-grid/README.md

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+<h2><a href="https://leetcode.com/problems/find-the-safest-path-in-a-grid">2812. Find the Safest Path in a Grid</a></h2><h3>Medium</h3><hr><p>You are given a <strong>0-indexed</strong> 2D matrix <code>grid</code> of size <code>n x n</code>, where <code>(r, c)</code> represents:</p>
+
+<ul>
+	<li>A cell containing a thief if <code>grid[r][c] = 1</code></li>
+	<li>An empty cell if <code>grid[r][c] = 0</code></li>
+</ul>
+
+<p>You are initially positioned at cell <code>(0, 0)</code>. In one move, you can move to any adjacent cell in the grid, including cells containing thieves.</p>
+
+<p>The <strong>safeness factor</strong> of a path on the grid is defined as the <strong>minimum</strong> manhattan distance from any cell in the path to any thief in the grid.</p>
+
+<p>Return <em>the <strong>maximum safeness factor</strong> of all paths leading to cell </em><code>(n - 1, n - 1)</code><em>.</em></p>
+
+<p>An <strong>adjacent</strong> cell of cell <code>(r, c)</code>, is one of the cells <code>(r, c + 1)</code>, <code>(r, c - 1)</code>, <code>(r + 1, c)</code> and <code>(r - 1, c)</code> if it exists.</p>
+
+<p>The <strong>Manhattan distance</strong> between two cells <code>(a, b)</code> and <code>(x, y)</code> is equal to <code>|a - x| + |b - y|</code>, where <code>|val|</code> denotes the absolute value of val.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2023/07/02/example1.png" style="width: 362px; height: 242px;" />
+<pre>
+<strong>Input:</strong> grid = [[1,0,0],[0,0,0],[0,0,1]]
+<strong>Output:</strong> 0
+<strong>Explanation:</strong> All paths from (0, 0) to (n - 1, n - 1) go through the thieves in cells (0, 0) and (n - 1, n - 1).
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2023/07/02/example2.png" style="width: 362px; height: 242px;" />
+<pre>
+<strong>Input:</strong> grid = [[0,0,1],[0,0,0],[0,0,0]]
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> The path depicted in the picture above has a safeness factor of 2 since:
+- The closest cell of the path to the thief at cell (0, 2) is cell (0, 0). The distance between them is | 0 - 0 | + | 0 - 2 | = 2.
+It can be shown that there are no other paths with a higher safeness factor.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2023/07/02/example3.png" style="width: 362px; height: 242px;" />
+<pre>
+<strong>Input:</strong> grid = [[0,0,0,1],[0,0,0,0],[0,0,0,0],[1,0,0,0]]
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> The path depicted in the picture above has a safeness factor of 2 since:
+- The closest cell of the path to the thief at cell (0, 3) is cell (1, 2). The distance between them is | 0 - 1 | + | 3 - 2 | = 2.
+- The closest cell of the path to the thief at cell (3, 0) is cell (3, 2). The distance between them is | 3 - 3 | + | 0 - 2 | = 2.
+It can be shown that there are no other paths with a higher safeness factor.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= grid.length == n &lt;= 400</code></li>
+	<li><code>grid[i].length == n</code></li>
+	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
+	<li>There is at least one thief in the <code>grid</code>.</li>
+</ul>