length-of-longest-fibonacci-subsequence.py

# Time:  O(n^2)
# Space: O(n)

# 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(object):
    def lenLongestFibSubseq(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        lookup = set(A)
        result = 2
        for i in xrange(len(A)):
            for j in xrange(i+1, len(A)):
                x, y, l = A[i], A[j], 2
                while x+y in lookup:
                    x, y, l = y, x+y, l+1
                result = max(result, l)
        return result if result > 2 else 0