<p>Given an integer array <code>nums</code>, return <em>the number of all the <strong>arithmetic subsequences</strong> of</em> <code>nums</code>.</p>

<p>A sequence of numbers is called arithmetic if it consists of <strong>at least three elements</strong> and if the difference between any two consecutive elements is the same.</p>

<ul>
	<li>For example, <code>[1, 3, 5, 7, 9]</code>, <code>[7, 7, 7, 7]</code>, and <code>[3, -1, -5, -9]</code> are arithmetic sequences.</li>
	<li>For example, <code>[1, 1, 2, 5, 7]</code> is not an arithmetic sequence.</li>
</ul>

<p>A <strong>subsequence</strong> of an array is a sequence that can be formed by removing some elements (possibly none) of the array.</p>

<ul>
	<li>For example, <code>[2,5,10]</code> is a subsequence of <code>[1,2,1,<strong><u>2</u></strong>,4,1,<u><strong>5</strong></u>,<u><strong>10</strong></u>]</code>.</li>
</ul>

<p>The test cases are generated so that the answer fits in <strong>32-bit</strong> integer.</p>

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

<pre>
<strong>Input:</strong> nums = [2,4,6,8,10]
<strong>Output:</strong> 7
<strong>Explanation:</strong> All arithmetic subsequence slices are:
[2,4,6]
[4,6,8]
[6,8,10]
[2,4,6,8]
[4,6,8,10]
[2,4,6,8,10]
[2,6,10]
</pre>

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

<pre>
<strong>Input:</strong> nums = [7,7,7,7,7]
<strong>Output:</strong> 16
<strong>Explanation:</strong> Any subsequence of this array is arithmetic.
</pre>

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

<ul>
	<li><code>1&nbsp; &lt;= nums.length &lt;= 1000</code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

#include <vector>
#include <map>
#include <algorithm>

using namespace std;

class Solution {
public:
    int numberOfArithmeticSlices(vector<int>& a) {
        int n = a.size(); 
        // sort(a.begin(), a.end()); 
        vector<vector<vector<long long>>> dp(n, vector<vector<long long>>(n, vector<long long>(2, 0))); 

        for(long long i = 0; i < n; i++){
            for(long long j = i + 1; j < n; j++){
                dp[i][j][0] = 1; 
            }
        }

        map<long long, vector<long long>> mp; // Stores the value and the index 
        mp[a[n-1]].push_back(n-1); 

        for(long long i = n-2; i >= 0; i--){
            for(long long j = i + 1; j < n; j++){
                long long diff = a[j]*1ll - a[i]*1ll; 
                long long nxt = a[j]*1ll + diff*1ll;
                if(mp.find(nxt) != mp.end()){
                    for(auto indx : mp[nxt]){
                        dp[i][j][1] = (dp[i][j][1] + dp[j][indx][0]); 
                        dp[i][j][0] = (dp[i][j][0] + dp[j][indx][0]);
                    }
                }
            }
            mp[a[i]].push_back(i); 
        }

        long long res = 0; 
        for(long long i = 0; i < n; i++){
            for(long long j = i + 1; j < n; j++){
                res += dp[i][j][1]; 
            }
        }
        return static_cast<int>(res); // Cast back to int if necessary
    }
};

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