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++.)
class Solution {
public int lenLongestFibSubseq(int[] A) {
int dp[][] = new int[A.length][A.length], max = 0;
// dp[i][j] is the length of longest fibnacci subsequence length
// which has A[i] as 2nd last and A[j] as last numbers in sequence
for (int i = 2; i < A.length; i++) {
// Given strictly increasing array
int start = 0, end = i - 1;
while (start < end) {
int sum = A[start] + A[end];
if (sum > A[i])
end--;
else if (sum < A[i])
start++;
else {
// If we are starting a new sequence then we need to add 2
// because dp[start][end] will be 0 at this point
dp[end][i] = 1 + (dp[start][end] == 0 ? 2 : dp[start][end]);
max = Math.max(max, dp[end][i]);
start++;
end--;
}
}
}
return max;
}
}