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57 lines
3.2 KiB
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57 lines
3.2 KiB
HTML
<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>
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<ul>
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<li>A cell containing a thief if <code>grid[r][c] = 1</code></li>
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<li>An empty cell if <code>grid[r][c] = 0</code></li>
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</ul>
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<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>
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<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>
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<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>
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<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>
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<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>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2023/07/02/example1.png" style="width: 362px; height: 242px;" />
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<pre>
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<strong>Input:</strong> grid = [[1,0,0],[0,0,0],[0,0,1]]
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<strong>Output:</strong> 0
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<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).
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2023/07/02/example2.png" style="width: 362px; height: 242px;" />
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<pre>
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<strong>Input:</strong> grid = [[0,0,1],[0,0,0],[0,0,0]]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> The path depicted in the picture above has a safeness factor of 2 since:
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- 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.
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It can be shown that there are no other paths with a higher safeness factor.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2023/07/02/example3.png" style="width: 362px; height: 242px;" />
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<pre>
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<strong>Input:</strong> grid = [[0,0,0,1],[0,0,0,0],[0,0,0,0],[1,0,0,0]]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> The path depicted in the picture above has a safeness factor of 2 since:
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- 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.
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- 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.
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It can be shown that there are no other paths with a higher safeness factor.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= grid.length == n <= 400</code></li>
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<li><code>grid[i].length == n</code></li>
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<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
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<li>There is at least one thief in the <code>grid</code>.</li>
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</ul>
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