problem873

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Published: Mar 23, 2021 License: MIT

873. Length of Longest Fibonacci Subsequence (Medium)

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`

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