Describe an efficient algorithm that, given a set \{x_1, x_2, \ldots, x_n\}{x 1 ,x 2 ,…,x n} of points on the real line, determines the smallest set of unit-length closed intervals that contains all of the given points. argue that your algorithm is correct.

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.