<p>A sequence <code>x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub></code> is <em>Fibonacci-like</em> if:</p>

<ul>
	<li><code>n &gt;= 3</code></li>
	<li><code>x<sub>i</sub> + x<sub>i+1</sub> == x<sub>i+2</sub></code> for all <code>i + 2 &lt;= n</code></li>
</ul>

<p>Given a <b>strictly increasing</b> array <code>arr</code> of positive integers forming a sequence, return <em>the <strong>length</strong> of the longest Fibonacci-like subsequence of</em> <code>arr</code>. If one does not exist, return <code>0</code>.</p>

<p>A <strong>subsequence</strong> is derived from another sequence <code>arr</code> by deleting any number of elements (including none) from <code>arr</code>, without changing the order of the remaining elements. For example, <code>[3, 5, 8]</code> is a subsequence of <code>[3, 4, 5, 6, 7, 8]</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [1,2,3,4,5,6,7,8]
<strong>Output:</strong> 5
<strong>Explanation:</strong> The longest subsequence that is fibonacci-like: [1,2,3,5,8].</pre>

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

<pre>
<strong>Input:</strong> arr = [1,3,7,11,12,14,18]
<strong>Output:</strong> 3
<strong>Explanation</strong>:<strong> </strong>The longest subsequence that is fibonacci-like: [1,11,12], [3,11,14] or [7,11,18].</pre>

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

<ul>
	<li><code>3 &lt;= arr.length &lt;= 1000</code></li>
	<li><code>1 &lt;= arr[i] &lt; arr[i + 1] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    int solve(vector<int>& arr, vector<vector<int>>& dp, int i, int j)
    {
        if (j >= arr.size() || i > j)
        {
            return 0;
        }

        if (dp[i][j] != -1)
        {
            return dp[i][j];
        }

        int x = 0; 
        int l = j + 1, r = arr.size() - 1;

        while (l <= r)
        {
            int mid = (l + r) / 2;
            if (arr[mid] == arr[j] + arr[i])
            {
                x = 1 + solve(arr, dp, j, mid);
                break;
            }
            else if (arr[mid] > arr[j] + arr[i])
            {
                r = mid - 1;
            }
            else
            {
                l = mid + 1;
            }

        }

        return dp[i][j] = x;
    }
    int lenLongestFibSubseq(vector<int>& arr) 
    {
        int n = arr.size();
        vector<vector<int>> dp(n, vector<int>(n, -1));

        int result = 0;
        map<int, int> mp;

        for (int i = 0; i < arr.size(); i++)
        {
            mp[arr[i]] = i;
        }

        for (int i = 0; i < n; i++)
        {
            for (int j = i + 1; j < n; j++)
            {
                if (mp.find(arr[i] + arr[j]) != mp.end())
                {
                    result = max(result, 2 + solve(arr, dp, i, j));
                }
            }
        }

        return result >= 3? result : 0;
        
    }
};
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