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57 lines
3.3 KiB
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57 lines
3.3 KiB
HTML
<p>You are given a <strong>positive</strong> integer <code>k</code>. You are also given:</p>
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<ul>
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<li>a 2D integer array <code>rowConditions</code> of size <code>n</code> where <code>rowConditions[i] = [above<sub>i</sub>, below<sub>i</sub>]</code>, and</li>
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<li>a 2D integer array <code>colConditions</code> of size <code>m</code> where <code>colConditions[i] = [left<sub>i</sub>, right<sub>i</sub>]</code>.</li>
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</ul>
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<p>The two arrays contain integers from <code>1</code> to <code>k</code>.</p>
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<p>You have to build a <code>k x k</code> matrix that contains each of the numbers from <code>1</code> to <code>k</code> <strong>exactly once</strong>. The remaining cells should have the value <code>0</code>.</p>
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<p>The matrix should also satisfy the following conditions:</p>
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<ul>
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<li>The number <code>above<sub>i</sub></code> should appear in a <strong>row</strong> that is strictly <strong>above</strong> the row at which the number <code>below<sub>i</sub></code> appears for all <code>i</code> from <code>0</code> to <code>n - 1</code>.</li>
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<li>The number <code>left<sub>i</sub></code> should appear in a <strong>column</strong> that is strictly <strong>left</strong> of the column at which the number <code>right<sub>i</sub></code> appears for all <code>i</code> from <code>0</code> to <code>m - 1</code>.</li>
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</ul>
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<p>Return <em><strong>any</strong> matrix that satisfies the conditions</em>. If no answer exists, return an empty matrix.</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/2022/07/06/gridosdrawio.png" style="width: 211px; height: 211px;" />
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<pre>
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<strong>Input:</strong> k = 3, rowConditions = [[1,2],[3,2]], colConditions = [[2,1],[3,2]]
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<strong>Output:</strong> [[3,0,0],[0,0,1],[0,2,0]]
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<strong>Explanation:</strong> The diagram above shows a valid example of a matrix that satisfies all the conditions.
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The row conditions are the following:
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- Number 1 is in row <u>1</u>, and number 2 is in row <u>2</u>, so 1 is above 2 in the matrix.
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- Number 3 is in row <u>0</u>, and number 2 is in row <u>2</u>, so 3 is above 2 in the matrix.
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The column conditions are the following:
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- Number 2 is in column <u>1</u>, and number 1 is in column <u>2</u>, so 2 is left of 1 in the matrix.
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- Number 3 is in column <u>0</u>, and number 2 is in column <u>1</u>, so 3 is left of 2 in the matrix.
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Note that there may be multiple correct answers.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]]
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<strong>Output:</strong> []
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<strong>Explanation:</strong> From the first two conditions, 3 has to be below 1 but the third conditions needs 3 to be above 1 to be satisfied.
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No matrix can satisfy all the conditions, so we return the empty matrix.
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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>2 <= k <= 400</code></li>
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<li><code>1 <= rowConditions.length, colConditions.length <= 10<sup>4</sup></code></li>
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<li><code>rowConditions[i].length == colConditions[i].length == 2</code></li>
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<li><code>1 <= above<sub>i</sub>, below<sub>i</sub>, left<sub>i</sub>, right<sub>i</sub> <= k</code></li>
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<li><code>above<sub>i</sub> != below<sub>i</sub></code></li>
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<li><code>left<sub>i</sub> != right<sub>i</sub></code></li>
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</ul>
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