# 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;
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```
```

## Inserting a Node Into a Sorted Doubly Linked List

Given a reference to the head of a doubly-linked list and an integer ,data , create a new DoublyLinkedListNode object having data value data and insert it at the proper location to maintain the sort. Example head refers to the list 1 <-> 2 <-> 4 - > NULL. data = 3 Return a reference to the new list: 1 <-> 2 <-> 4 - > NULL , Function Description Complete the sortedInsert function

## Reverse a doubly linked list

This challenge is part of a tutorial track by MyCodeSchool Given the pointer to the head node of a doubly linked list, reverse the order of the nodes in place. That is, change the next and prev pointers of the nodes so that the direction of the list is reversed. Return a reference to the head node of the reversed list. Note: The head node might be NULL to indicate that the list is empty.

## Tree: Preorder Traversal

Complete the preorder function in the editor below, which has 1 parameter: a pointer to the root of a binary tree. It must print the values in the tree's preorder traversal as a single line of space-separated values. Input Format Our test code passes the root node of a binary tree to the preOrder function. Constraints 1 <= Nodes in the tree <= 500 Output Format Print the tree's

## Tree: Postorder Traversal

Complete the postorder function in the editor below. It received 1 parameter: a pointer to the root of a binary tree. It must print the values in the tree's postorder traversal as a single line of space-separated values. Input Format Our test code passes the root node of a binary tree to the postorder function. Constraints 1 <= Nodes in the tree <= 500 Output Format Print the

## Tree: Inorder Traversal

In this challenge, you are required to implement inorder traversal of a tree. Complete the inorder function in your editor below, which has 1 parameter: a pointer to the root of a binary tree. It must print the values in the tree's inorder traversal as a single line of space-separated values. Input Format Our hidden tester code passes the root node of a binary tree to your \$inOrder* func

## Tree: Height of a Binary Tree

The height of a binary tree is the number of edges between the tree's root and its furthest leaf. For example, the following binary tree is of height : image Function Description Complete the getHeight or height function in the editor. It must return the height of a binary tree as an integer. getHeight or height has the following parameter(s): root: a reference to the root of a binary