Dynamic Programming

February 27, 2025

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].

Constraints:

• 3 <= arr.length <= 1000
• 1 <= arr[i] < arr[i + 1] <= 109