minimize-the-difference-between-target-and-chosen-elements

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Algorithms

You are given an <code>m x n</code> integer matrix <code>mat</code> and an integer <code>target</code>.

Choose one integer from each row in the matrix such that the absolute difference between <code>target</code> and the sum of the chosen elements is minimized.

Return the minimum absolute difference.

The absolute difference between two numbers <code>a</code> and <code>b</code> is the absolute value of <code>a - b</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1.png" style="width: 181px; height: 181px;" />
<pre>
Input: mat = [[1,2,3],[4,5,6],[7,8,9]], target = 13
Output: 0
Explanation: One possible choice is to:
- Choose 1 from the first row.
- Choose 5 from the second row.
- Choose 7 from the third row.
The sum of the chosen elements is 13, which equals the target, so the absolute difference is 0.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1-1.png" style="width: 61px; height: 181px;" />
<pre>
Input: mat = [[1],[2],[3]], target = 100
Output: 94
Explanation: The best possible choice is to:
- Choose 1 from the first row.
- Choose 2 from the second row.
- Choose 3 from the third row.
The sum of the chosen elements is 6, and the absolute difference is 94.
</pre>

Example 3:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1-3.png" style="width: 301px; height: 61px;" />
<pre>
Input: mat = [[1,2,9,8,7]], target = 6
Output: 1
Explanation: The best choice is to choose 7 from the first row.
The absolute difference is 1.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 70</code></li>
	<li><code>1 &lt;= mat[i][j] &lt;= 70</code></li>
	<li><code>1 &lt;= target &lt;= 800</code></li>
</ul>

minimizeTheDifference

Minimize the Difference Between Target and Chosen Elements

Partition Equal Subset Sum

partition-equal-subset-sum

分割等和子集

Closest Subsequence Sum

closest-subsequence-sum

最接近目标值的子序列和

Maximum Number of Points with Cost

maximum-number-of-points-with-cost

扣分后的最大得分

Array

Dynamic Programming

Matrix

给你一个大小为 <code>m x n</code> 的整数矩阵 <code>mat</code> 和一个整数 <code>target</code> 。

从矩阵的 每一行 中选择一个整数，你的目标是&nbsp;最小化&nbsp;所有选中元素之&nbsp;和&nbsp;与目标值 <code>target</code> 的 绝对差 。

返回 最小的绝对差 。

<code>a</code> 和 <code>b</code> 两数字的 绝对差 是 <code>a - b</code> 的绝对值。

&nbsp;

示例 1：

<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1.png" style="width: 181px; height: 181px;" />

<pre>
输入：mat = [[1,2,3],[4,5,6],[7,8,9]], target = 13
输出：0
解释：一种可能的最优选择方案是：
- 第一行选出 1
- 第二行选出 5
- 第三行选出 7
所选元素的和是 13 ，等于目标值，所以绝对差是 0 。
</pre>

示例 2：

<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1-1.png" style="width: 61px; height: 181px;" />

<pre>
输入：mat = [[1],[2],[3]], target = 100
输出：94
解释：唯一一种选择方案是：
- 第一行选出 1
- 第二行选出 2
- 第三行选出 3
所选元素的和是 6 ，绝对差是 94 。
</pre>

示例 3：

<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1-3.png" style="width: 301px; height: 61px;" />

<pre>
输入：mat = [[1,2,9,8,7]], target = 6
输出：1
解释：最优的选择方案是选出第一行的 7 。
绝对差是 1 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 70</code></li>
	<li><code>1 &lt;= mat[i][j] &lt;= 70</code></li>
	<li><code>1 &lt;= target &lt;= 800</code></li>
</ul>