**Longest Arithmetic Subsequence - Amazon Top Interview Questions**

### Problem Statement :

Given a list of integers nums, return the length of the longest arithmetic subsequence. A sequence B[i] is defined as an arithmetic sequence if B[i+1] - B[i] have the same value for every 0 ≤ i < len(B) - 1. For example, [1, 5, 9, 13, 17] is the longest arithmetic subsequence of [-30, 1, 10, 5, 9, -20, 13, 17]. Constraints n ≤ 1,000 where n is the length of nums Example 1 Input nums = [1, 3, 5, 7, 9] Output 5 Explanation The whole array is arithmetic since the difference between each consecutive element is 2. Example 2 Input nums = [1, 3, 6, 7, 5, 8, 9] Output 4 Explanation [6, 7, 8, 9] is the longest arithmetic subsequence.

### Solution :

` ````
Solution in C++ :
unordered_map<int, int> dp[1005];
int solve(vector<int>& nums) {
int n = nums.size();
int ret = min(1, n);
for (int i = 0; i < n; i++) {
dp[i].clear();
for (int j = 0; j < i; j++) {
int diff = nums[i] - nums[j];
if (dp[j].count(diff)) {
dp[i][diff] = max(dp[i][diff], dp[j][diff] + 1);
} else {
dp[i][diff] = 2;
}
ret = max(ret, dp[i][diff]);
}
}
return ret;
}
```

` ````
Solution in Java :
import java.util.*;
class Solution {
public int solve(int[] nums) {
if (nums.length == 0)
return 0;
HashMap<Integer, Integer>[] maps = new HashMap[nums.length];
int res = 1;
for (int j = 0; j != nums.length; j++) {
final HashMap<Integer, Integer> map = maps[j] = new HashMap<>();
for (int i = 0; i != j; i++) {
int length = maps[i].getOrDefault(nums[j] - nums[i], 1) + 1;
map.put(nums[j] - nums[i], length);
res = Math.max(res, length);
}
}
return res;
}
}
```

` ````
Solution in Python :
class Solution:
def solve(self, arr):
n = len(arr)
if n <= 1:
return n
res = 0
dp = defaultdict(lambda: 1)
for i in range(1, n):
for j in range(i):
diff = arr[i] - arr[j]
dp[i, diff] = dp[j, diff] + 1
res = max(res, dp[i, diff])
return res
```

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