Describe an efficient algorithm that, given a set {x1, } of points on the real line, determines the smallest set of unit-length closed intervals that contains all of the given points. (a unit length interval just means any closed interval with length 1. i. e., an interval [a, b] where b − a = 1.)
a. briefly describe a greedy algorithm for the unit length interval problem.
b. state and prove a "swapping lemma" for your greedy algorithm.
c. write a proof that uses your swapping lemma to show that your greedy algorithm does indeed produce a set of intervals that contain all of the points {x1, } with the fewest number of intervals.

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

How would you categorize the software that runs on mobile devices? break down these apps into at least three basic categories and give an example of each.

Which phrase is the best definition of a pivottable a a table containing data that is organized horizontally b a table used to calculate financial pivot values c a tool used to summarize data d a table containing specific formatting