<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 f (int j ,int i , int d ,vector<int>& arr,vector<vector<int>> &dp){
//         int n = arr.size();
//         if (i>=n) {
//             return 0;
//         }
//         if (dp[j+1][i]!=-1) return dp[j+1][i];
//         int nottake = f(j,i+1,d,arr,dp);
//         int take = 0 ;
//         if(j==-1 || arr[i] == d + arr[j]) take = 1 + f(i,i+1,d,arr,dp);

//         dp[j+1][i] = max(take,nottake);
//         return dp[j+1][i];
//     }
//     int longestSubsequence(vector<int>& arr, int d) {
    
//        int n = arr.size();
//         vector<vector<int>> dp(n+1, vector<int>(n, 0));
//         for (int i=0;i)
//         return f (-1,0,d,arr,dp);
        
//     }
// };

class Solution {
public:
    int longestSubsequence(vector<int>& arr, int difference) {
        unordered_map<int, int> dp;
        int ans = 1;

        for(int a: arr) {
            int prev = dp.count(a - difference) ? dp[a-difference] : 0;
            dp[a] = prev + 1;
            ans = max(ans, dp[a]);
        }

        return ans;
    }
};
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