# 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 sequenceA 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++.)

class Solution {
public:
int lenLongestFibSubseq(vector<int>& A) {
int res = 0, n = A.size();
unordered_set<int> st(A.begin(), A.end());
for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
int a = A[i], b = A[j], cnt = 2;
while (st.count(a + b)) {
b = a + b;
a = b - a;
++cnt;
}
res = max(res, cnt);
}
}
return (res > 2) ? res : 0;
}
};

class Solution {
public:
int lenLongestFibSubseq(vector<int>& A) {
int res = 0, n = A.size();
unordered_map<int, int> m;
vector<vector<int>> dp(n, vector<int>(n));
for (int i = 0; i < n; ++i) {
m[A[i]] = i;
for (int j = 0; j < i; ++j) {
int k = m.count(A[i] - A[j]) ? m[A[i] - A[j]] : -1;
dp[j][i] = (A[i] - A[j] < A[j] && k >= 0) ? (dp[k][j] + 1) : 2;
res = max(res, dp[j][i]);
}
}
return (res > 2) ? res : 0;
}
};

Github 同步地址:

https://github.com/grandyang/leetcode/issues/873

Split Array into Fibonacci Sequence

Fibonacci Number

Coin Change

https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/

https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/discuss/152343/C%2B%2BJavaPython-Check-Pair

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