# 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```
```

## 2D Array-DS

Given a 6*6 2D Array, arr: 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 An hourglass in A is a subset of values with indices falling in this pattern in arr's graphical representation: a b c d e f g There are 16 hourglasses in arr. An hourglass sum is the sum of an hourglass' values. Calculate the hourglass sum for every hourglass in arr, then print t

## Dynamic Array

Create a list, seqList, of n empty sequences, where each sequence is indexed from 0 to n-1. The elements within each of the n sequences also use 0-indexing. Create an integer, lastAnswer, and initialize it to 0. There are 2 types of queries that can be performed on the list of sequences: 1. Query: 1 x y a. Find the sequence, seq, at index ((x xor lastAnswer)%n) in seqList.

## Left Rotation

A left rotation operation on an array of size n shifts each of the array's elements 1 unit to the left. Given an integer, d, rotate the array that many steps left and return the result. Example: d=2 arr=[1,2,3,4,5] After 2 rotations, arr'=[3,4,5,1,2]. Function Description: Complete the rotateLeft function in the editor below. rotateLeft has the following parameters: 1. int d

## Sparse Arrays

There is a collection of input strings and a collection of query strings. For each query string, determine how many times it occurs in the list of input strings. Return an array of the results. Example: strings=['ab', 'ab', 'abc'] queries=['ab', 'abc', 'bc'] There are instances of 'ab', 1 of 'abc' and 0 of 'bc'. For each query, add an element to the return array, results=[2,1,0]. Fun

## Array Manipulation

Starting with a 1-indexed array of zeros and a list of operations, for each operation add a value to each of the array element between two given indices, inclusive. Once all operations have been performed, return the maximum value in the array. Example: n=10 queries=[[1,5,3], [4,8,7], [6,9,1]] Queries are interpreted as follows: a b k 1 5 3 4 8 7 6 9 1 Add the valu

## Print the Elements of a Linked List

This is an to practice traversing a linked list. Given a pointer to the head node of a linked list, print each node's data element, one per line. If the head pointer is null (indicating the list is empty), there is nothing to print. Function Description: Complete the printLinkedList function in the editor below. printLinkedList has the following parameter(s): 1.SinglyLinkedListNode