# Length of Longest Fibonacci Subsequence

## Description

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`

## Solution

Both the time complexity and the space complexity are $$O(n^2)$$.

```cpp
class Solution {
public:
    int lenLongestFibSubseq(vector<int>& A) {
        int n = A.size();
        // dp[j][i]: length of the longest Fibonacci sequence ending with (A[j], A[i]).
        vector<vector<int>> dp(n, vector<int>(n));
        unordered_map<int, int> num2idx;
        for(int i = 0; i < n; ++i){
            num2idx[A[i]] = i;
        }
        int len = 0;
        for(int i = 1; i < A.size(); ++i){
            for(int j = 0; j < i; ++j){
                int a = A[i] - A[j];
                int b = A[j];
                int c = A[i];
                // check whether there is a k such that
                // k < j < i and (A[k], A[j], A[i]) is fibonacci-like
                if(a >= b){
                    // not possible to find A[k] because A[k] < A[j]
                    dp[j][i] = 2;
                }else{
                    auto it = num2idx.find(a);
                    if(it != num2idx.end()){
                        dp[j][i] = dp[it->second][j] + 1;
                        len = max(len, dp[j][i]);
                    }else{
                        dp[j][i] = 2;
                    }
                }
            }
        }
        return len;
    }
};
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://twchen.gitbook.io/leetcode/array/length-of-longest-fibonacci-subsequence.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.