Using Sentinels in Insert Sort

Although insert sort takes quadratic time in the worst case it has a very efficient inner loop. Its bestcase computing time is linear, which occurs when the data are already in sorted order. It is the method of choice for data stored in linked lists or small arrays. Algorithm 1 is typical, and is written in extended Pascal. Implementing the conditional 'cand' operation (to guard against the error of subscripting the array a when j–1=0) is problematic in Pascal. Though other languages (Ada, C, Algol, etc.) can overcome this problem of expression, the algorithm nevertheless performs two tests within the loop when only one is sufficient, as we shall see below. There are other optimizations, covered by Knuth,' which we shall not discuss here, for instance: (a) various minor transformations, such as initializing j to j–1, unwinding the inner loop and noticing that a[i]: =v is unnecessary when the inner loop is not executed