<p>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>.</p>

<p>A <strong>subsequence</strong> 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.</p>

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

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

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

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

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

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

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= arr[i], difference &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int n, D;
    int t[100010];
    int longestSubsequence(vector<int>& arr, int d) {
        // n = arr.size();
        // D = d;
        // memset(t, -1, sizeof t);
        // int res = 0;
        // for(int i = 0; i < n; i++){
        //     res = max(res, 1 + solve(i, arr));
        // }
        // return res;
        n = arr.size();

        int res = 0;
        map<int, int>mp;
        for(int i = 0; i < n; i++){
            int prev = arr[i] - d;
            mp[arr[i]] = mp[prev] + 1;
            res = max(res, mp[arr[i]]);
        }
        return res;
    }

    int solve(int idx, vector<int>&arr){

        if(t[idx] != -1) return t[idx];
        int res = 0;
        int prev = arr[idx];

        for(int j = idx + 1; j < n; j++){
            int cur = arr[j];
            if(cur - prev == D) res = max(res, 1 + solve(j, arr));
        }
        return t[idx] = res;
    }
};
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