Length of Longest Fibonacci Subsequence

A sequence X_1, X_2, ..., X_n is fibonacci-like if:

• n >= 3

• X_i + X_{i+1} = X_{i+2} for all i + 2 <= n

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

(Recall that a subsequence is derived from another sequence A by deleting any number of elements (including none) from A, 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: [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: [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].

Note:

• 3 <= A.length <= 1000

• 1 <= A[0] < A[1] < ... < A[A.length - 1] <= 10^9

• (The time limit has been reduced by 50% for submissions in Java, C, and C++.)

class Solution {
    public int lenLongestFibSubseq(int[] A) {
        int dp[][] = new int[A.length][A.length], max = 0;
        // dp[i][j] is the length of longest fibnacci subsequence length
        // which has A[i] as 2nd last and A[j] as last numbers in sequence
        for (int i = 2; i < A.length; i++) {
            // Given strictly increasing array
            int start = 0, end = i - 1;
            while (start < end) {
                int sum = A[start] + A[end];
                if (sum > A[i])
                    end--;
                else if (sum < A[i])
                    start++;
                else {
                    // If we are starting a new sequence then we need to add 2
                    // because dp[start][end] will be 0 at this point
                    dp[end][i] = 1 + (dp[start][end] == 0 ? 2 : dp[start][end]);
                    max = Math.max(max, dp[end][i]);
                    start++;
                    end--;
                }
            }
        }
        return max;
    }
}