Tuesday, May 7, 2019

LeetCode [1027] Longest Arithmetic Sequence

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
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class Solution {
public:
    int longestArithSeqLength(vector<int>& A) {
        unordered_map<int, unordered_map<int, int>> dp;//dp[diff][index] is the subsequence lenght with "diff" at "index" 
        int n = A.size(), ret = 0;
        for(int i=0; i<n; ++i)
        {
            for(int j=i+1; j<n; ++j)
            {
                int diff = A[j]-A[i];
                dp[diff][j] = dp[diff].count(i) ? dp[diff][i]+1 : 2;
                ret = max(ret, dp[diff][j]);
            }
        }
        return ret;
    }
};

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