1027. Longest Arithmetic Sequence

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Given an array A of integers, return the length of the longest arithmetic subsequence in A.

Recall that a subsequence of A is a list A[i_1], A[i_2], ..., A[i_k] with 0 <= i_1 < i_2 < ... < i_k <= A.length - 1, and that a sequence B is arithmetic if B[i+1] - B[i] are all the same value (for 0 <= i < B.length - 1).

Example 1:

Input: [3,6,9,12]
Output: 4
Explanation: 
The whole array is an arithmetic sequence with steps of length = 3.

Example 2:

Input: [9,4,7,2,10]
Output: 3
Explanation: 
The longest arithmetic subsequence is [4,7,10].

Example 3:

Input: [20,1,15,3,10,5,8]
Output: 4
Explanation: 
The longest arithmetic subsequence is [20,15,10,5].

Note:

1. 2 <= A.length <= 2000
2. 0 <= A[i] <= 10000

思路：以前好像出现过这个题目，DP，dp[i]维护一个dict，dp[i][k]表示以A[i]结束，公差为d的最长长度

class Solution(object):
    def longestArithSeqLength(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        dp=[{} for _ in range(len(A))]
        dp[1] = {A[1]-A[0]:2}
        res=2
        for i in range(2,len(A)):
            for j in range(i):
                d = A[i]-A[j]
                dp[i][d] = max(dp[i].get(d,0), dp[j].get(d,1)+1)
                res=max(res,dp[i][d])
        return res