Formatted question description: https://leetcode.ca/all/1027.html

1027. Longest Arithmetic Sequence (Medium)

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

Related Topics:
Dynamic Programming

Solution 1. DP

// OJ: https://leetcode.com/problems/longest-arithmetic-sequence/

// Time: O(N^2)
// Space: O(N^2)
class Solution {
public:
    int longestArithSeqLength(vector<int>& A) {
        unordered_map<int, unordered_map<int, int>> m;
        int ans = 0;
        for (int n : A) {
            m[n] = {};
            for (auto &p : m) {
                int d = n - p.first;
                ans = max(ans, m[n][d] = p.second.count(d) ? p.second[d] + 1 : 2);
            }
        }
        return ans;
    }
};

Java

class Solution {
    public int longestArithSeqLength(int[] A) {
        if (A == null)
            return 0;
        int length = A.length;
        if (length <= 2)
            return length;
        int maxLength = 2;
        Map<Integer, TreeSet<Integer>> numIndicesMap = new HashMap<Integer, TreeSet<Integer>>();
        for (int i = 0; i < length; i++) {
            int num = A[i];
            TreeSet<Integer> indices = numIndicesMap.getOrDefault(num, new TreeSet<Integer>());
            indices.add(i);
            numIndicesMap.put(num, indices);
            if (indices.size() > maxLength)
                maxLength = indices.size();
        }
        for (int i = 0; i < length; i++) {
            int num1 = A[i];
            for (int j = i + 1; j < length; j++) {
                int num2 = A[j];
                int difference = num2 - num1;
                if (difference == 0)
                    continue;
                int curLength = 2;
                int prevIndex = j;
                int prevNum = num2;
                while (true) {
                    int curNum = prevNum + difference;
                    TreeSet<Integer> indices = numIndicesMap.getOrDefault(curNum, new TreeSet<Integer>());
                    Integer curIndex = indices.ceiling(prevIndex);
                    if (curIndex == null)
                        break;
                    curLength++;
                    prevIndex = curIndex;
                    prevNum = curNum;
                }
                maxLength = Math.max(maxLength, curLength);
            }
        }
        return maxLength;
    }
}

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