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873. Length of Longest Fibonacci Subsequence

{leetcode}/problems/length-of-longest-fibonacci-subsequence/[LeetCode - 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++.)

link:{sourcedir}/_0873_LengthOfLongestFibonacciSubsequence.java[role=include]