## 题目描述：

LeetCode 873. 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++.)

## 解题思路：

`dp[y][x + y] = max(dp[y][x + y], dp[x][y] + 1)`

## Python代码：

``````class Solution(object):
def lenLongestFibSubseq(self, A):
"""
:type A: List[int]
:rtype: int
"""
vset = set(A)
dp = collections.defaultdict(lambda: collections.defaultdict(int))
size = len(A)
ans = 0
for i in range(size):
x = A[i]
for j in range(i + 1, size):
y = A[j]
if x + y not in vset: continue
dp[y][x + y] = max(dp[y][x + y], dp[x][y] + 1)
ans = max(dp[y][x + y], ans)
return ans and ans + 2 or 0
``````

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