if it is possible, please send the text solution instead of handwriting. if handwriting, please make it clear as possible as you can.

Problem 6 (3 points). Let Ln be a directed line on the vertices 11,2 n with directed edges (i, i 1) for every i E 11,2 ...,n 1). A 2-spanner for Ln is a graph S obtained by adding directed edges (from the smaller to the larger indices, so that the directions of the paths are preserved) to Ln such that for every pair i,j E {1,2 with i j there is a path of length at most 2 in S. Show an algorithm that builds a 2-spanner for La with O(n logn) edges. Prove that your algorithm indeed produces a 2-spanner