Let x1, . . , xn be an array x of n distinct numbers. we say two numbers xi and xj form an inversion if i < j but xi > xj . (a) what are the maximum and minimum possible numbers of inversions for an array of size n? provide examples of arrays attaining these two numbers. (b) prove that array x is sorted in increasing order if and only if the total number of inversions in x is zero. (c) design an o(n 2 )-time brute-force algorithm to count the total number of inversions in x. (d) consider the following divide-and-conquer approach for counting the number of inversions in x: partition x into xl = {x1, . . , xn/2} and xr = {xn/2+ }. all we need to do is to add nl (total number inversions in xl), nr (total number inversions in xr), and the number of inversions occur between xl and xr. complete the design and analysis this algorithm. (e) design another efficient algorithm that counts the number of inversions using binary search trees.

Matlab question: use switch and anythe lottery game matches three different integer numbers between 1 and 10. winning depends on how many matching numbers are provided by a player. the player provides three different integers between 1 and 10.if there is a match of all 3 numbers, the winning $ 1000.if there is a match with 2 numbers, the winning $ 10.if there is a match of all with 1 numbers, the winning $ 1.with no match, the winning is $0.write a function lottery3 that checks three numbers provided by a player and determine the winning amount. if the user mistakenly enters same number twice/thrice and if that number matches one of the winning numbers, the code should count that number only once and display correct result. the player doesn’t have to guess the order of numbers.the input to the function lottery3 can have up to two input arguments. the first input argument is a row array numbers with 3 numbers. if the second argument input testcode is present, and is a row vector of 3 values, the function lottery3 uses the code in testcode as the three winning numbers (the test must be three different integer numbers between 1 and 10), else three different numbers will be automatically generated by testcode.the ouput should return the variable winnings and the three winning numbers in the row array winnumbers.hint: make use of the internal function any.restriction: the function must use switch-case statements to determine the winning.example #1: winning = lottery3( [1,2,1],[1,2,3])produceswinning =10example #2: [winning,winnumbers] = lottery3( [1,2,3])produceswinning =3winnumbers =8 5 3

Nathan wants to create multiple worksheet containing common formatting styles for his team members. which file extension him to save these worksheets? nathan to create multiple worksheets with common styles. he needs to save them with the extension.

Whats three fourths of 15(this is supposed to be in math but i clicked too fast)