Which function grows faster: n log n or n1+ε/ log n, ε > 0?

Ahorse is how much percent more powerful than a pony

Write a program called assignment3 (saved in a file assignment3.java) that computes the greatest common divisor of two given integers. one of the oldest numerical algorithms was described by the greek mathematician, euclid, in 300 b. c. it is a simple but very e↵ective algorithm that computes the greatest common divisor of two given integers. for instance, given integers 24 and 18, the greatest common divisor is 6, because 6 is the largest integer that divides evenly into both 24 and 18. we will denote the greatest common divisor of x and y as gcd(x, y). the algorithm is based on the clever idea that the gcd(x, y) = gcd(x ! y, y) if x > = y and gcd(x, y) = gcd(x, y ! x) if x < y. the algorithm consists of a series of steps (loop iterations) where the “larger” integer is replaced by the di↵erence of the larger and smaller integer. this continues until the two values are equal. that is then the gcd.

Kirk found a local community college with a two-year program and he is comparing the cost with that of an out-of-state two-year school. what is the expected total cost for one year at the local community college if kirk lives at home? what is the expected total cost for one year at the out-of-state school if kirk lives on campus?