cyclic permutations of a string

Write and algo to check if two strings are cyclic permutations of each other?
Ex : "abcde" and "deabc"

Answer:

1. Append the second the string with itself, we get, deabcdeabc O(n)
2. When we do step 2, notice that the first string occurs as a substring.
3. Search for the original string in the appended string. (O(2n) for space + O(n) time if suffix trees are used and this step depends on which sub string search algo we use)

|---||---|
deabcdeabc
  ^^^^^