longest-arithmetic-subsequence-of-given-difference

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Algorithms

Given an integer array <code>arr</code> and an integer <code>difference</code>, return the length of the longest subsequence in <code>arr</code> which is an arithmetic sequence such that the difference between adjacent elements in the subsequence equals <code>difference</code>.

A subsequence is a sequence that can be derived from <code>arr</code> by deleting some or no elements without changing the order of the remaining elements.

&nbsp;
Example 1:

<pre>
Input: arr = [1,2,3,4], difference = 1
Output: 4
Explanation: The longest arithmetic subsequence is [1,2,3,4].</pre>

Example 2:

<pre>
Input: arr = [1,3,5,7], difference = 1
Output: 1
Explanation: The longest arithmetic subsequence is any single element.
</pre>

Example 3:

<pre>
Input: arr = [1,5,7,8,5,3,4,2,1], difference = -2
Output: 4
Explanation: The longest arithmetic subsequence is [7,5,3,1].
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= arr.length &lt;= 105</code></li>
	<li><code>-104 &lt;= arr[i], difference &lt;= 104</code></li>
</ul>

longestSubsequence

Longest Arithmetic Subsequence of Given Difference

Destroy Sequential Targets

destroy-sequential-targets

摧毁一系列目标

Array

Hash Table

Dynamic Programming

给你一个整数数组 <code>arr</code> 和一个整数 <code>difference</code>，请你找出并返回 <code>arr</code> 中最长等差子序列的长度，该子序列中相邻元素之间的差等于 <code>difference</code> 。

子序列 是指在不改变其余元素顺序的情况下，通过删除一些元素或不删除任何元素而从 <code>arr</code> 派生出来的序列。

 

示例 1：

<pre>
输入：arr = [1,2,3,4], difference = 1
输出：4
解释：最长的等差子序列是 [1,2,3,4]。</pre>

示例 2：

<pre>
输入：arr = [1,3,5,7], difference = 1
输出：1
解释：最长的等差子序列是任意单个元素。
</pre>

示例 3：

<pre>
输入：arr = [1,5,7,8,5,3,4,2,1], difference = -2
输出：4
解释：最长的等差子序列是 [7,5,3,1]。
</pre>

 

提示：

<ul>
	<li><code>1 <= arr.length <= 105</code></li>
	<li><code>-104 <= arr[i], difference <= 104</code></li>
</ul>