LeetCode 873. Length of Longest Fibonacci Subsequence

原题链接在这里：https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/

题目：

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].

题解：

Take a = A[i] and b = A[j] as first 2 elements, j>i.

Check if A contains A[i]+A[j]. If yes, then a = b, b = a+b, and fibonacci sequence length ++.

Until A doesn't contian (A[i] + A[j]), update the global longest length.

Time Complexity: O(n^2 * logM). n = A.length. M is the largest number in A, since in while loop it grows exponentially, while takes logM.

Space: O(n).

AC Java:

 class Solution {
     public int lenLongestFibSubseq(int[] A) {
         if(A == null || A.length < 3){
             return 0;
         }

         HashSet<Integer> hs = new HashSet<>();
         for(int a : A){
             hs.add(a);
         }

         int res = 0;

         int n = A.length;
         for(int i = 0; i<n-2; i++){
             for(int j = i+1; j<n-1; j++){
                 int a = A[i];
                 int b = A[j];
                 int l = 2;
                 while(hs.contains(a+b)){
                     int temp = a;
                     a = b;
                     b = temp+b;
                     l++;
                 }

                 res = Math.max(res, l);
             }
         }

         return res > 2 ? res : 0;
     }
 }

类似Fibonacci Number.