Unit-Length Closed Intervals

Question

I am working on a program that has somewhat focus on the below:

unit-length closed interval on the real line is an interval [x, 1+x]. For given input set

X={x1,x2,..., Xn}, x1 < x2 <...xn, how can i determine the smallest set of unit-lenght closed intervals that contains all of the given points and how i calculate time complexity.

I dont need code but an algorithm to set up my program correctly will just do fine

Thanks

Answer 1

Since its an instance of a set-cover problem, a polynomial time algorithm is unlikely to beat a greedy solution by much. So you could try placing unit intervals that cover the most number of yet uncovered points. For the position of the intervals you dont lose by aligning it with some data point in X.