<p>Given an array <code>nums</code> of integers, return <em>the length of the longest arithmetic subsequence in</em> <code>nums</code>.</p>

<p><strong>Note</strong> that:</p>

<ul>
	<li>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</li>
	<li>A sequence <code>seq</code> is arithmetic if <code>seq[i + 1] - seq[i]</code> are all the same value (for <code>0 &lt;= i &lt; seq.length - 1</code>).</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,6,9,12]
<strong>Output:</strong> 4
<strong>Explanation: </strong> The whole array is an arithmetic sequence with steps of length = 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [9,4,7,2,10]
<strong>Output:</strong> 3
<strong>Explanation: </strong> The longest arithmetic subsequence is [4,7,10].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [20,1,15,3,10,5,8]
<strong>Output:</strong> 4
<strong>Explanation: </strong> The longest arithmetic subsequence is [20,15,10,5].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 500</code></li>
</ul>

from functools import cache
from collections import defaultdict

class Solution:
    def longestArithSeqLength(self, nums: List[int]) -> int:
        ans = [defaultdict(lambda:1) for i in range(len(nums))]

        for i in range(len(nums)):
            for j in range(i-1,-1,-1):
                diff = nums[i] - nums[j]
                if ans[i][diff] == 1:
                    ans[i][diff] += ans[j][diff]
        
        # print(ans[2].values())

        ans2 = 1
        for i in range(len(nums)):
            for vals in ans[i].values():
                ans2 = max(ans2, vals)
        return ans2
            

        # @cache
        # def dp(i, diff):
        #     # return the length of the longest subsequence ending at i with diff as difference
        #     if i==0 or diff not in dict1[i]:
        #         return 1

        #     ans = 1
        #     for k in range(i):
        #         if nums[i] - nums[k] == diff:
        #             ans = max(ans, dp(k, diff) + 1)
        #     return ans
        
        # dict1 = defaultdict(list)
        
        # ans = 1
        # for j in range(len(nums)):
        #     arr = []
        #     for l in range(j+1):
        #         arr.append(nums[j] - nums[l])
        #     arr = list(set(arr))
        #     dict1[j] = arr
        #     # print(len(arr))
        #     for k in arr:
        #         # print(f"({j},{k}) : {dp(j, k)}")
        #         ans = max(ans, dp(j, k))
        # return ans
39351