Algorithms (12 points + 3 bonus points) In general we express algorithms in pseudocode, i.e., in a sequence of statements that resemblesomeprogramminglanguage. Pseudocodecomprisesstep-by-stepinstructions that execute a solution. Using your own pseudocode write algorithms for the following problems. Your pseudocode could be any syntactically-relaxed programming language that you like or just plain pseudocode as weve used in class. (a) (3 points) Write an algorithm to compute the sum u(n) = n X i=1 (1)2i = (1)2 + (1)4 + (1)6 ... (b) (3 points) Consider the following algorithm. Assuming that you are paying $ 1 for each numerical operation, what is the cost to run this algorithm in terms of n and m? Why? input : Variables n and m output: u(n) =Pn i=1Pm j=1(i2 + j2) sum 0; for i 1 to n do for j 1 to m do sumsum+ i2 + j2;endend (c) (3 points) Given the algorithm in the previous problem, is there a way to reduce the cost of running it? By how much? Why? (d) (3 points) Write an algorithm that will convert military-style time to ante meridiem or post meridiem time. For example, 1800 76 : 00 PM.(e) (3 bonus points) Write an algorithm that will take as input the number n such that 1 6 n 6 366 and will return the day and month in a year, assuming that n = 1 7January 1, n = 2 7January 2, ..., n = 31 7January 31, n = 32 7February 1, etc.

1. Algorithms (12 points 3 bonus points) In general we express algorithms in pseudocode, i.e., in a sequence of statements that resemble some programming language. Pseudocode comprises step-by-step instructions that cxccute a solution. Using your own pseudocode write algorithms for the following problems. Your pseu- docode could be any syntactically-relaxed programming language that you like or just plain pseudocode as we've used in class. (a) (3 points) Write an algorithm to compute the sunm ! (b) (3 points) Consider the following algorithm. Assuming that you are paying S 1 for each numerica operation, what is the cost to run this algorithm in tes of n and m? Why? input : Variables n and m output: u(n)- n-1 ml(i2 + j2) sum for i 1 to n do forj1 to m do sumsum2 end end (c) (3 points) Given the algorithm in the previous problem, is there a way to reduce (d) (3 points) Write an algorithm that will convert military-style time to ante meri (e) (3 bonus points) Write an algorithm that wll take as input the number n such n = 1-January 1, the cost of running it? By how h? Why? diem or post meridiem time. For example, 1800 >6:00 PM that I 366 and will return the day and month in a year, assuming that n = 2-January 2, n-31 n-32 February 1, etc. January 31