Describe an efficient algorithm that, given a

set $\{$x$1,$ x$2,...,$ xn$\}$ of points on the real line, determines the smallest set of unitlength closed intervals that contains all of the given points. Give a correct greedy

algorithm for this problem $(15$ marks$),$ prove that it finds the optimal solution $(20$

marks$),$ and give an efficient implementation $(15$ marks$).$