The greatest common divisor (GCD) of two integers a and b is defined as the largest integer that can divide both a and b without a remainder. For example, the GCD of 30 and 54 is 6, whereas the GCD of 7 and 5 is 1. The following procedure was developed by Euclid to compute the greatest common divisor of two positive integers a and b. In this exercise, we will prove the correctness of this algorithm. procedure Euclidean(a, b) 1 x ← a 2 y ← b 3 while x 6= y do 4 if x > y then 5 x ← x − y 6 else 7 y ← y − x 8 return x (a) State the loop invariant for the while loop in this procedure.
(b) Prove the loop invariant.
(c) Prove that procedure Euclidean always terminates provided that a and b are positive integers.
(d) Using the termination property of your loop invariant, prove that procedure Euclidean computes and returns the greatest common divisor of a and b.

Write a program that takes in 3 inputs [players (int type), expected game time (double type), team (char type)] and calculates actual game time (double) based on the following conditions: if the number of players or the expected game time is less than or equal to zero, it should output wrong input if the number of players is greater than 0 and less than or equal to 6 and if they are on the â€r’ or â€r’ team, their game time will be 10% faster. and if they are on the â€b’ or â€b’ team, their game time will be 15% faster. and if they are on the â€y’ or â€y’ team, their game time will be 20% faster. and if they are on any other team, they will play 0% faster. if the number of players is greater than 6 but less than or equal to 12 and if they are on the â€r’ or â€r’ team, their game time will be 20% faster. and if they are on the â€b’ or â€b’ team, their game time will be 25% faster. and if they are on the â€y’ or â€y’ team their game time will be 30% faster. and if they are on any other team, they will play 0% faster. if the number of players is greater than 12 but less than or equal to 18 and if they are on the â€r’ or â€r’ team, their game time will be 30% faster. and if they are on the â€b’ or â€b’ team, their game time will be 35% faster. and if they are on the â€y’ or â€y’ team, their game time will

Digital information is stored using a series of ones and zeros. computers are digital machines because they can only read information as on or off –1 or 0. this method of computation is known as the system

Which statistical function in a spreadsheet you to see how far each number varies, on average, from the average value of the list?