Analysis of Computer AlgorithmsTo get into your local grocery store you must wait in line. Outside the front door there are n spaces in a single long row. Each space is either empty or has a single person. Due to social distancing guidelines, people cannot stand in adjacent spaces (i. e. there must be at least one empty space between them). Let S(n) denote the total number of states this line could be in (based on which spaces are occupied or not). For example, S(3) = 5 since the possibilities are {eee, pee, epe, eep, pep}, where 'e' denotes that the space is empty and 'p' denotes that it has a person. Write a recurrence for S(n). Explain why this recurrence is correct. You do not need to solve your recurrence. You should assume S(0) = 1.

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

Write a program which asks you to enter a name in the form of first middle initial last. so you might enter for example samuel p. clemens. use getline to read in the string because it contains spaces. also, apparently the shift key on your keyboard doesn’t work, because you enter it all lower case. pass the string to a function which uses .find to locate the letters which need to be upper case and use toupper to convert those characters to uppercase. the revised string should then be returned to main in the form last, first mi where it will be displayed.

How to print: number is equal to: 1 and it is odd number number is equal to: 2 and it is even number number is equal to: 3 and it is odd number number is equal to: 4 and it is even number in the console using java using 1 if statement, 1 while loop, 1 else loop also using % to check odds and evens