<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 trav(vector<int>& arr, int diff,int i,int n,int pre,vector<vector<int>> &dp)
    {
        if(i==n)
        {
            return 0;

        }
        else if(dp[i][pre+1]!=-1)
        {
            return dp[i][pre+1];
        }

        int ans1=0;
        int ans2=0;
        if(pre==-1||(arr[i]-arr[pre]==diff))
        {
            ans1=trav(arr,diff,i+1,n,i,dp)+1;
        }

        ans2=trav(arr,diff,i+1,n,pre,dp);

        dp[i][pre+1]=max(ans1,ans2);
        return dp[i][pre+1];

    }

    int tabtrav(vector<int>& arr, int diff,int n)
    {
        vector<vector<int>> dp(n+1,vector<int>(n+2,0));

        for(int i=n-1;i>=0;i--)
        {
            for(int pre=-1;pre<i;pre++)
            {
                int ans1=0;
                int ans2=0;
                if(pre==-1||(arr[i]-arr[pre]==diff))
                {
                    ans1=dp[i+1][i+1]+1;
                }

               
                    ans2=dp[i+1][pre+1];
                
               

                dp[i][pre+1]=max(ans1,ans2);
                    }
        }
        return dp[0][0];

    }

    int optimize(vector<int>& arr, int diff,int n)
    {
        unordered_map<int,int> map;
        int ans=0;
        for(int i=0;i<n;i++)
        {
            int temp=arr[i]-diff;
            int count=0;
            if(map[temp]>0)
            {
                count=map[temp];
            }

            map[arr[i]]=count+1;
            ans=max(ans,map[arr[i]]);
        }
        return ans;
    }


    int longestSubsequence(vector<int>& arr, int difference) {
        
        int n=arr.size();
        // vector<vector<int>> dp(n+1,vector<int>(n+2,-1));
        // return trav(arr,difference,0,n,-1,dp);

        // return tabtrav(arr,difference,n);
        return optimize(arr,difference,n);
    }
};
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