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>());
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;
}
}