An improved insert sort algorithm

Many algorithms involve a search, and they typically require two types of test: one test checks for the element being searched for, and another test is required to check the search remains within the bounds of the data structure being searched. Both of these tests can be combined into one by using a so-called sentinel. In particular, sentinels can be used in insert sort algorithms to make them more efficient, effectively halving the number of tests in a loop. An insert sort suggested by Thimbleby, 1 which has the advantage of neither requiring extra memory nor a special value (such as MAX VALUE) that cannot be sorted, however repeatedly re-computes a sentinel value, an operation which itself incurs a time penalty. Since the sentinel value for insert sort is an extremal element, one can be found and placed in position in linear time, and this need only be done once. Using this idea, this paper gives Java code to sort a given array a into increasing order. Algorithms are presented for both stable and (the more efficient) unstable sorts.