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Length of Longest Fibonacci Subsequence

A sequence x1, x2, ..., xn is Fibonacci-like if: Given a strictly increasing array arr of positive integers forming a sequence, return the length of the longest Fibonacci-like...

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

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].

Length of Longest Fibonacci Subsequence diagram

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] <= 10^9

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