delete-greatest-value-in-each-row

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Algorithms

You are given an <code>m x n</code> matrix <code>grid</code> consisting of positive integers.

Perform the following operation until <code>grid</code> becomes empty:

<ul>
	<li>Delete the element with the greatest value from each row. If multiple such elements exist, delete any of them.</li>
	<li>Add the maximum of deleted elements to the answer.</li>
</ul>

Note that the number of columns decreases by one after each operation.

Return the answer after performing the operations described above.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/19/q1ex1.jpg" style="width: 600px; height: 135px;" />
<pre>
Input: grid = [[1,2,4],[3,3,1]]
Output: 8
Explanation: The diagram above shows the removed values in each step.
- In the first operation, we remove 4 from the first row and 3 from the second row (notice that, there are two cells with value 3 and we can remove any of them). We add 4 to the answer.
- In the second operation, we remove 2 from the first row and 3 from the second row. We add 3 to the answer.
- In the third operation, we remove 1 from the first row and 1 from the second row. We add 1 to the answer.
The final answer = 4 + 3 + 1 = 8.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/19/q1ex2.jpg" style="width: 83px; height: 83px;" />
<pre>
Input: grid = [[10]]
Output: 10
Explanation: The diagram above shows the removed values in each step.
- In the first operation, we remove 10 from the first row. We add 10 to the answer.
The final answer = 10.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 100</code></li>
</ul>

deleteGreatestValue

Delete Greatest Value in Each Row

Equal Row and Column Pairs

equal-row-and-column-pairs

相等行列对

Array

Matrix

Sorting

Simulation

Heap (Priority Queue)

给你一个 <code>m x n</code> 大小的矩阵 <code>grid</code> ，由若干正整数组成。

执行下述操作，直到 <code>grid</code> 变为空矩阵：

<ul>
	<li>从每一行删除值最大的元素。如果存在多个这样的值，删除其中任何一个。</li>
	<li>将删除元素中的最大值与答案相加。</li>
</ul>

注意 每执行一次操作，矩阵中列的数据就会减 1 。

返回执行上述操作后的答案。

&nbsp;

示例 1：

<img alt="" src="https://assets.leetcode.com/uploads/2022/10/19/q1ex1.jpg" style="width: 600px; height: 135px;" />

<pre>
输入：grid = [[1,2,4],[3,3,1]]
输出：8
解释：上图展示在每一步中需要移除的值。
- 在第一步操作中，从第一行删除 4 ，从第二行删除 3（注意，有两个单元格中的值为 3 ，我们可以删除任一）。在答案上加 4 。
- 在第二步操作中，从第一行删除 2 ，从第二行删除 3 。在答案上加 3 。
- 在第三步操作中，从第一行删除 1 ，从第二行删除 1 。在答案上加 1 。
最终，答案 = 4 + 3 + 1 = 8 。
</pre>

示例 2：

<img alt="" src="https://assets.leetcode.com/uploads/2022/10/19/q1ex2.jpg" style="width: 83px; height: 83px;" />

<pre>
输入：grid = [[10]]
输出：10
解释：上图展示在每一步中需要移除的值。
- 在第一步操作中，从第一行删除 10 。在答案上加 10 。
最终，答案 = 10 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 100</code></li>
</ul>