873

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

Companies:
Amazon, Bloomberg, Baidu

Related Topics:
Array, Hash Table, Dynamic Programming

Similar Questions:

• Fibonacci Number (Easy)

Solution 1. Hash Table

Because of the exponential growth of these terms, there are at most 43 terms in any Fibonacci-like subsequence that has maximum value <= 1e9.

// OJ: https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/
// Author: github.com/lzl124631x
// Time: O(N^2 * logM) where N is the length of `A` and `M` is the maximum value of `A`
// Space: O(N)
class Solution {
public:
    int lenLongestFibSubseq(vector<int>& A) {
        unordered_set<int> s(begin(A), end(A));
        int ans = 0, N = A.size();
        for (int i = 0; i < N; ++i) {
            for (int j = i + 1; j < N; ++j) {
                int a = A[i], b = A[j], len = 2, next = a + b;
                while (s.count(next)) {
                    a = b;
                    b = next;
                    next = a + b;
                    ++len;
                }
                if (len > 2) ans = max(ans, len);
            }
        }
        return ans;
    }
};