There is a popular task at software developer job interviews: having a singly linked list, write a piece of code which tells if the list has a cycle.
In a linked list, each element is a structure which contains the value of an element and the link to the next element. The next-link of the last element has a special value which marks the end (usually, null). If a list has a cycle, the last element points to some element inside the list.
There are some algorithms of exact substring searching (e.g. Knuth-Morris-Pratt, Boyer-Moore etc.) I want to explain one of them which is called Z algorithm in some sources.
Let’s consider the concept of Z-box. Take the string S = “abcxxxabyyy”. We have an internal part “ab” in the string which repeats its prefix. The internal “ab” is a Z-box. It has the beginning at the position with index 6 and the end in 7 (0-based). Z-boxes are substrings which match string prefixes with the same length. For the Z-box, let’s call the corresponding prefix the prototype (it’s my term but I think it’s OK to use it.)
