# Arithmetic Sequence Permutation - Amazon Top Interview Questions

### Problem Statement :

```Given a list of integers nums, return whether you can rearrange the order of nums such that the difference between every consecutive two numbers is the same.

Constraints

n ≤ 100,000 where n is the length of nums

Example 1

Input
nums = [7, 1, 5, 3]

Output
True

Explanation
If we rearrange nums to [1, 3, 5, 7], then the difference between every two consecutive numbers is 2.

Example 2

Input
nums = [1, 5, 1, 5, 1, 5]

Output
False

Explanation
The difference between every consecutive two numbers alternates between 4 and -4.```

### Solution :

```                        ```Solution in C++ :

bool solve(vector<int>& nums) {
// Finding Max and Min
int max = nums[0], min = nums[0], max_i = -1, min_i = -1;
for (int i = 1; i < nums.size(); i++) {
if (nums[i] > max) {
max = nums[i];
max_i = i;
}
if (nums[i] < min) {
min = nums[i];
min_i = i;
}
}
if (max - min == 0)  // All numbers same, diff=0
return true;
if ((max - min) % (nums.size() - 1) != 0)  // Case not possible
return false;
// Check for duplicates now
vector<int> freqArr(max + 1, 0);
for (int i = 0; i < nums.size(); i++) {
freqArr[nums[i]] += 1;
if (freqArr[nums[i]] > 1) return false;
}
int min_diff = (max - min) / (nums.size() - 1);
for (int i = 0; i < nums.size(); i++) {
if (i == min_i || i == max_i) continue;
int d2 = nums[i] - min;
if (d2 % min_diff != 0) {
return false;
}
}
return true;
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public boolean solve(int[] nums) {
Arrays.sort(nums);
for (int i = 2; i < nums.length; i++) {
if (nums[i] - nums[i - 1] != nums[i - 1] - nums[i - 2])
return false;
}
return true;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, nums):
minima = min(nums)
maxima = max(nums)

d = (maxima - minima) / (len(nums) - 1)
num = minima + d
nums_set = set(nums)
if d == 0:
return True
while num in nums_set:
num += d

if num > maxima:
return True
return False```
```

## Palindromic Subsets

Consider a lowercase English alphabetic letter character denoted by c. A shift operation on some c turns it into the next letter in the alphabet. For example, and ,shift(a) = b , shift(e) = f, shift(z) = a . Given a zero-indexed string, s, of n lowercase letters, perform q queries on s where each query takes one of the following two forms: 1 i j t: All letters in the inclusive range from i t

## Counting On a Tree

Taylor loves trees, and this new challenge has him stumped! Consider a tree, t, consisting of n nodes. Each node is numbered from 1 to n, and each node i has an integer, ci, attached to it. A query on tree t takes the form w x y z. To process a query, you must print the count of ordered pairs of integers ( i , j ) such that the following four conditions are all satisfied: the path from n

## Polynomial Division

Consider a sequence, c0, c1, . . . , cn-1 , and a polynomial of degree 1 defined as Q(x ) = a * x + b. You must perform q queries on the sequence, where each query is one of the following two types: 1 i x: Replace ci with x. 2 l r: Consider the polynomial and determine whether is divisible by over the field , where . In other words, check if there exists a polynomial with integer coefficie

## Costly Intervals

Given an array, your goal is to find, for each element, the largest subarray containing it whose cost is at least k. Specifically, let A = [A1, A2, . . . , An ] be an array of length n, and let be the subarray from index l to index r. Also, Let MAX( l, r ) be the largest number in Al. . . r. Let MIN( l, r ) be the smallest number in Al . . .r . Let OR( l , r ) be the bitwise OR of the

## The Strange Function

One of the most important skills a programmer needs to learn early on is the ability to pose a problem in an abstract way. This skill is important not just for researchers but also in applied fields like software engineering and web development. You are able to solve most of a problem, except for one last subproblem, which you have posed in an abstract way as follows: Given an array consisting

## Self-Driving Bus

Treeland is a country with n cities and n - 1 roads. There is exactly one path between any two cities. The ruler of Treeland wants to implement a self-driving bus system and asks tree-loving Alex to plan the bus routes. Alex decides that each route must contain a subset of connected cities; a subset of cities is connected if the following two conditions are true: There is a path between ever