sort-matrix-by-diagonals

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Algorithms

You are given an <code>n x n</code> square matrix of integers <code>grid</code>. Return the matrix such that:

<ul>
	<li>The diagonals in the bottom-left triangle (including the middle diagonal) are sorted in non-increasing order.</li>
	<li>The diagonals in the top-right triangle are sorted in non-decreasing order.</li>
</ul>

&nbsp;
Example 1:

<div class="example-block">
Input: grid = [[1,7,3],[9,8,2],[4,5,6]]

Output: [[8,2,3],[9,6,7],[4,5,1]]

Explanation:

<img alt="" src="https://assets.leetcode.com/uploads/2024/12/29/4052example1drawio.png" style="width: 461px; height: 181px;" />

The diagonals with a black arrow (bottom-left triangle) should be sorted in non-increasing order:

<ul>
	<li><code>[1, 8, 6]</code> becomes <code>[8, 6, 1]</code>.</li>
	<li><code>[9, 5]</code> and <code>[4]</code> remain unchanged.</li>
</ul>

The diagonals with a blue arrow (top-right triangle) should be sorted in non-decreasing order:

<ul>
	<li><code>[7, 2]</code> becomes <code>[2, 7]</code>.</li>
	<li><code>[3]</code> remains unchanged.</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: grid = [[0,1],[1,2]]

Output: [[2,1],[1,0]]

Explanation:

<img alt="" src="https://assets.leetcode.com/uploads/2024/12/29/4052example2adrawio.png" style="width: 383px; height: 141px;" />

The diagonals with a black arrow must be non-increasing, so <code>[0, 2]</code> is changed to <code>[2, 0]</code>. The other diagonals are already in the correct order.
</div>

Example 3:

<div class="example-block">
Input: grid = [[1]]

Output: [[1]]

Explanation:

Diagonals with exactly one element are already in order, so no changes are needed.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>grid.length == grid[i].length == n</code></li>
	<li><code>1 &lt;= n &lt;= 10</code></li>
	<li><code>-105 &lt;= grid[i][j] &lt;= 105</code></li>
</ul>

sortMatrix

Sort Matrix by Diagonals

Sort the Matrix Diagonally

sort-the-matrix-diagonally

将矩阵按对角线排序

Array

Matrix

Sorting

给你一个大小为&nbsp;<code>n x n</code> 的整数方阵 <code>grid</code>。返回一个经过如下调整的矩阵：

<ul>
	<li>左下角三角形（包括中间对角线）的对角线按&nbsp;非递增顺序&nbsp;排序。</li>
	<li>右上角三角形&nbsp;的对角线按&nbsp;非递减顺序&nbsp;排序。</li>
</ul>

&nbsp;

示例 1：

<div class="example-block">
输入： grid = [[1,7,3],[9,8,2],[4,5,6]]

输出： [[8,2,3],[9,6,7],[4,5,1]]

解释：

<img alt="" src="https://assets.leetcode.com/uploads/2024/12/29/4052example1drawio.png" style="width: 461px; height: 181px;" />

标有黑色箭头的对角线（左下角三角形）应按非递增顺序排序：

<ul>
	<li><code>[1, 8, 6]</code> 变为 <code>[8, 6, 1]</code>。</li>
	<li><code>[9, 5]</code> 和 <code>[4]</code> 保持不变。</li>
</ul>

标有蓝色箭头的对角线（右上角三角形）应按非递减顺序排序：

<ul>
	<li><code>[7, 2]</code> 变为 <code>[2, 7]</code>。</li>
	<li><code>[3]</code> 保持不变。</li>
</ul>
</div>

示例 2：

<div class="example-block">
输入： grid = [[0,1],[1,2]]

输出： [[2,1],[1,0]]

解释：

<img alt="" src="https://assets.leetcode.com/uploads/2024/12/29/4052example2adrawio.png" style="width: 383px; height: 141px;" />

标有黑色箭头的对角线必须按非递增顺序排序，因此 <code>[0, 2]</code> 变为 <code>[2, 0]</code>。其他对角线已经符合要求。
</div>

示例 3：

<div class="example-block">
输入： grid = [[1]]

输出： [[1]]

解释：

只有一个元素的对角线已经符合要求，因此无需修改。
</div>

&nbsp;

提示：

<ul>
	<li><code>grid.length == grid[i].length == n</code></li>
	<li><code>1 &lt;= n &lt;= 10</code></li>
	<li><code>-105 &lt;= grid[i][j] &lt;= 105</code></li>
</ul>