Longest Arithmetic Sequence

• Lintcode : / Leetcode : 1027
• Level : Medium

Problem

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:

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

Concept & Algorithm

筆記

Time Complexity & Space Complexity

time : O(n ^ 2)
space: O(n ^ 3)

Answer

class Solution {
public:
    int longestArithSeqLength(vector<int>& A) {
        vector<map<int, int>> dp(A.size());
        int maxLen = 1;
        for (int i = 0; i < A.size(); i++) {
            for (int j = i + 1; j < A.size(); j++) {
                int d = A[j] - A[i];
                if (i == 0) {
                    dp[j][d] = 2;
                }else {
                    if (dp[i].find(d) != dp[i].end()) {
                        dp[j][d] = dp[i][d] + 1;
                    }else {
                        dp[j][d] = 2;
                    }
                }
                maxLen = max(maxLen, dp[j][d]);
            }
        }
        return maxLen;   
    }
};

tags: DP

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