50. Length of Longest Fibonacci Subsequence

A sequence x1, x2, ..., xn is Fibonacci-like if:

• n >= 3

• xi + xi+1 == xi+2 for all i + 2 <= n

Given a strictly increasing array arr of positive integers forming a sequence, return the length of the longest Fibonacci-like subsequence of arr. If one does not exist, return 0.

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

Example 1:

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

Example 2:

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

Solution: (Brute force using set)

class Solution
{
public:
    int lenLongestFibSubseq(vector<int> &arr)
    {
        unordered_map<int, int> m;
        
        for (int i = 0; i < arr.size(); i++)
        {
            m.insert({arr[i], i});
        }

        int maxLen = 0;

        for (int i = 0; i < arr.size(); i++)
        {

            int j = i + 1;

            int len;

            while (j < arr.size())
            {
                int y = arr[j];
                int x = arr[i];
                len = 2;

                while (m.find(x + y) != m.end())
                {
                    len++;
                    int s = x + y;
                    x = y;
                    y = s;
                }

                maxLen = max(maxLen, len);

                j++;
            }
        }

        return (maxLen >= 3) ? maxLen : 0;
    }
};

Time Complexity: O(n ^2)