Large DifferencesYou are given an array 𝐴A of length 𝑁N, and a positive integer 𝐾K.It is guaranteed that 1≤𝐴𝑖≤𝐾1≤A i​ ≤K for every index 𝑖i from 11 to 𝑁N.You can do the following at most once:Choose an index 𝑖i (1≤𝑖≤𝑁1≤i≤N) and a value 𝑥x (1≤𝑥≤𝐾1≤x≤K).Then, set 𝐴𝑖:=𝑥A i​ :=x.Find the maximum possible value of the sum of adjacent differences of 𝐴A after performing this operation at most once.That is, maximize the quantity∑𝑖=1𝑁−1∣𝐴𝑖−𝐴𝑖+1∣i=1∑N−1​ ∣A i​ −A i+1​ ∣Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝐾K — the length of the array and the maximum allowed integer 𝐾K, respectively.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ , the elements of array 𝐴A.Output FormatFor each test case, output on a new line the answer: the maximum possible sum of adjacent differences of 𝐴A after replacing exactly one element.Constraints1≤𝑇≤1001≤T≤1001≤𝑁≤10001≤N≤10001≤𝐾≤2⋅1061≤K≤2⋅10 6 1≤𝐴𝑖≤𝐾1≤A i​ ≤KThe sum of 𝑁N across all tests won't exceed 10001000.Sample 1:InputOutput32 51 53 87 2 75 2018 3 1 4 1941263Explanation:Test case 11: It's best to leave the array unchanged, giving us a difference of ∣1−5∣=4∣1−5∣=4.Test case 22: It's optimal to set 𝐴2:=1A 2​ :=1, giving us the array [7,1,7][7,1,7]. The sum of adjacent differences is 6+6=126+6=12.Test case 33: It's optimal to set 𝐴3:=20A 3​ :=20, to obtain [18,3,20,4,19][18,3,20,4,19]. The sum of adjacent differences is 6363.

You are given an array 𝐴A containing 𝑁N integers.Consider the following process:Let 𝑆=0S=0 initially.For each 𝑖i from 11 to 𝑁N in order, update 𝑆S to either (𝑆+𝐴𝑖)(S+A i​ ) or (𝑆×𝐴𝑖)(S×A i​ ).That is, either add 𝐴𝑖A i​ to 𝑆S or multiply 𝑆S by 𝐴𝑖A i​ .Before performing the process, you're allowed to freely rearrange the elements of 𝐴A as you like.If you choose the rearrangement of 𝐴A and the sequence of operations optimally, what's the maximum possible value of 𝑆S that you can obtain?This maximum value can be very large, so print it modulo 109+710 9 +7.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains a single integer 𝑁N — the number of elements in the array.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ - the elements of the array.Output FormatFor each test case, output on a new line the maximum possible value of 𝑆S, modulo 109+710 9 +7.Constraints1≤𝑇≤1031≤T≤10 3 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput244 2 5 231 2 1804Explanation:Test case 11: Choose the rearrangement 𝐴=[2,2,5,4]A=[2,2,5,4]. Then,Add 𝐴1=2A 1​ =2 to 𝑆S. Now, 𝑆=2S=2.Add 𝐴2=2A 2​ =2 to 𝑆S. Now, 𝑆=4S=4.Multiply 𝑆S by 𝐴3=5A 3​ =5. Now, 𝑆=20S=20.Multiply 𝑆S by 𝐴4=4A 4​ =4. Now, 𝑆=80S=80.This is the maximum value that can be obtained.Test case 22: Choose any rearrangement and sum up all the numbers to get 1+1+2=41+1+2=4.This is the maximum value that can be obtained.

Analyze the code for compile time errors. You are provided with the code skeleton having the full solution with compile time errors. Fix the compile time error in the code.Write a Java program to read an array of integer elements. The program should find the difference between the alternate numbers in the array and find the index position of the smallest element with the largest difference. If more than one pair has the same largest difference, consider the first occurrence.Note: When taking the difference, take the absolute value, i.e. neglecting the sign.Example: If it is 3 - 10= -7, consider it as 7.If the array size is less than 3, Display "Invalid array size".Note:In the Sample Input / Output provided, the highlighted text in bold corresponds to the input given by the user, and the rest of the text represents the output.Ensure to follow the object-oriented specifications provided in the question description.Ensure to provide the names for classes, attributes, and methods as specified in the question description.Adhere to the code template, if provided.Please do not use System.exit(0) to terminate the program.Sample Input/Output 1:Enter the size of the array6Enter the inputs43210861Explanation :Here alternate number difference means4-2, 3-10, 2-8, 10-6Neglect the sign So diff is 2,7,6,4Largest diff is 7 -------> 3-10, here the smallest number is 3 and its index is 1. Hence the output is 1.Sample Input/Output 2:Enter the size of the array7Enter the inputs76223182Sample Input/Output 3:-1Invalid array size

Array-DifferenceMark has an array of 𝑁 elements of positive integers. He is interested in finding out the maximum absolute difference between any 2 elements in the array. But he wants to minimize this maximum absolute difference.             He can perform the following two types of operation on the array elements any number of times.              If the element 𝐸 is even then he can replace it by 𝐸/2.             If the element 𝐸 is odd then he can replace it by 2𝐸.              Can you help him minimize this maximum absolute difference? Input Format:The first line consists of a single integer 𝑇, the number of test cases.Each test case consists of 2 lines, 1st line has an integer 𝑁, the number of elements in the array.Next lines have 𝑁 space separated integers, denoting array elements.Output Format:For each test case, output in a separate line, the answer to the given question.Constraints:1≤𝑇≤5002≤𝑁≤500001≤𝐴[𝑖]≤106 for each valid 𝑖It is guaranteed that summation of 𝑁 over all test cases doesn't exceed 250000.Sample input121 2Sample output0ExplanationHe can make 1 as 1*2 = 2So array becomes { 2 , 2}Min(max absolute diff) he can get is (2-2) = 0

Write a program for the maximum possible difference between two subsets of an array.Given an array of n integers. The array may contain repetitive elements, but the highest frequency of any element must not exceed two. Make two subsets such that the difference of the sum of their elements is maximum and both of them jointly contain all elements of the given array along with the most important condition, no subset should contain repetitive elements. ExampleInput:45 8 -1 4Output:Maximum Difference = 18Explanation:Suppose arr[ ] = {5, 8, -1, 4}Let Subset A = {5, 8, 4} & Subset B = {-1}Sum of elements of subset A = 17, of subset B = -1Difference of Sum of Both subsets = 17 - (-1) = 18Input format :The first input line consists of the size of an array, n.The second input consists of the array elements, separated by space.Output format :The output displays the maximum possible difference between two subsets of an array.Refer to the sample output for the formatting specifications.Code constraints :2 ≤ n ≤ 100Sample test cases :Input 1 :74 2 -3 3 -2 -2 8Output 1 :Maximum Difference = 20Input 2 :45 8 -1 4Output 2 :Maximum Difference = 18

You are given an array 𝐴A of length 𝑁N, and an integer 𝐾K.You can perform the following operation:Choose any index 𝑖i (1≤𝑖≤𝑁1≤i≤N), and increase 𝐴𝑖A i​ by 𝐾K.Find the minimum possible value of max⁡(𝐴)−min⁡(𝐴)max(A)−min(A) attainable, if you can perform this operation as many times as you like (possibly, zero times).Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝐾K — the length of the array and the parameter 𝐾K.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ — the initial values of the array elements.Output FormatFor each test case, output on a new line the answer: the minimum possible value of max⁡(𝐴)−min⁡(𝐴)max(A)−min(A) if you can perform the given operation any number of times.Constraints1≤𝑇≤1051≤T≤10 5 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐾≤1091≤K≤10 9 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput43 41 5 43 212 8 44 11 43 62 8256 121 2 4 128 130 1311008Explanation:Test case 11: Increase the first element by 𝐾=4K=4 to obtain the array [5,5,4][5,5,4].Here, max⁡−min⁡=5−4=1max−min=5−4=1, which is the best possible.Test case 22: The second and third elements can be increased by 22 till they reach 1212, at which point all the elements of the array are equal, so max⁡(𝐴)−min⁡(𝐴)=0max(A)−min(A)=0.Test case 33: Since 𝐾=1K=1, again it's possible to make all the elements equal.Test case 44: Do the following:Increase 𝐴1A 1​ by 1212 repeatedly to make it 133133.Increase 𝐴2A 2​ by 1212 repeatedly to make it 134134.Increase 𝐴3A 3​ by 1212 repeatedly to make it 136136.The array is now [133,134,136,128,130,131][133,134,136,128,130,131].For this array, max⁡(𝐴)−min⁡(𝐴)=136−128=8max(A)−min(A)=136−128=8.It can be shown that this is optimal.