Determining the values at the location marker by scanning

Look at the data obtained in Exercise 3.2. Notice that the values stored at the positions taken on by the location marker form a subsequence of the original data set; that is, the values of the subset are taken from the original set in the same relative order as in the original set. Explain in your own words how to scan the list from left to right and pick out the values that will be in this subsequence.

Smallest number of positions for the location marker

What would be the smallest number of positions that location marker could possibly point to during the execution of the algorithm? Describe the special conditions under which this would happen. Approximately how often would you expect this to occur?