Find the Minimum Shift for the Longest Common Prefix in Java

Problem Statement

Finding the smallest number of shifts required for a string to share the longest common prefix with another string.

Input:

Output:

 
2   

Explanation: Shifting str1 twice to the left gives "cdeab", which matches str2.

Method 1: Brute Force Approach

The most straightforward approach is to brute-force the solution by rotating one of the strings repeatedly and checking the LCP with the other string. It involves shifting the string str1 by one character at a time and comparing it with str2 to find the maximum LCP.

File Name: MinShiftLCP.java

Output:

 
Minimum shift required: 2   

Explanation

This technique uses a loop to create a new string that begins at character two and finishes with character one by shifting str1 one character to the left each time. The loop keeps track of the number of shifts and the maximum LCP that was discovered. Although the brute force method is simple, it is inefficient for longer strings due to its O(n^2) time complexity.

Method 2: Optimized Approach Using String Concatenation

Instead of shifting the string manually, we can leverage the property of string concatenation. By concatenating str1 with itself, all possible shifts are covered within the string. It allows us to find the LCP between the concatenated string and str2 without explicit shifts.

File Name: MinShiftLCP.java

Output:

 
Minimum shift required: 2   

Explanation

In this method, instead of explicitly shifting str1 multiple times, we concatenate str1 with itself, creating a string that contains all possible shifts of str1 within a single string.

The program then iterates over this concatenated string and checks the LCP between each possible shift and str2. By slicing the concatenated string, the program efficiently checks each possible shift, and for each one, it calculates the LCP with str2.

The method reduces the need for explicit string shifts, but it still has a time complexity of O(n^2) due to the substring operations and LCP calculations.

Method 3: Optimized Approach Using Z-Algorithm

The Z- The Z-array, which is effectively computed by the strong string matching algorithm technique, Z[i] denotes the length of the longest substring beginning at the i-th position in the string and serving as a prefix of the string.

File Name: MinShiftLCP.java

Output:

 
Minimum shift required: 2   

Explanation

In this method, instead of explicitly shifting str1 multiple times, we concatenate str1 with itself, creating a string that contains all possible shifts of str1 within a single string.

The program then iterates over this concatenated string and checks the LCP between each possible shift and str2. By slicing the concatenated string, the program efficiently checks each possible shift, and for each one, it calculates the LCP with str2.

The method reduces the need for explicit string shifts, but it still has a time complexity of O(n^2) due to the substring operations and LCP calculations.

Conclusion

One of the most exciting string processing problems is determining the minimal shift for the longest common prefix between two strings. We have discussed the two approaches: one that used brute force and the other that used the Z-algorithm to be even more optimized. The fastest solution is offered by the Z-Algorithm, which has an O(n) time complexity.