[CTCI] String Rotation

Posted 2020-09-23

Assume you have a method isSubstring which checks if one word is a substring of another.

Given two strings, s1 and s2, write code to check if s2 is a rotation of s1 using only one call to isSubstring.

For example, "waterbottle" is a rotation of "erbottlewat".

 

An obvious solution is to get all s1.length() rotations of s1 in O(n^2); then check if each rotation is the same with s2 in O(n) time.

The runtime is O(n^3), which is very inefficient.

 

The BCR of this problem is O(n). Can you achieve this run time? 

Observation: for a string that is rotated,  there is a "split line". If s1 = x + y, then all rotations of s1 have the form of y + x; 

yx is a substring of xyxy, which is s1s1. 

 

Based on the above observation, we can develop a smart O(n) algorithm. Just call isSubstring(s1 + s1, s2).