A sample of DNA is exposed to a restriction enzyme for only a limited time. This prevents the DNA sample from being cut at all restriction sites, but does generate the set of all possible restriction fragments between every two cuts (not necessarily consecutive). The following fragment sizes are obtained: { 4, 4, 7, 11, 11, 15, 15, 19, 22, 26 }.
(i) What is the total length of the DNA sequence ?
(ii) Determine the positions of the restriction sites in the DNA sequence.