# Find minimum shift for longest common prefix

You are given two strings str1 and str2 of the same length. In a single shift, you can rotate one string (str2) by 1 element such that its 1st element becomes the last and the second one becomes the first like “abcd” will change to “bcda” after the one-shift operation. You have to find the minimum shift operation required to get the common prefix of maximum length from str1 and str2.

Examples:

```Input : str1[] = "geeks",
str2 = "dgeek"
Output : Shift = 1,
Prefix = geek

Input : str1[] = "practicegeeks",
str2 = "coderpractice"
Output : Shift = 5
Prefix = practice```
Recommended Practice

Naive Approach: Shift second string one by one and keep track of the length of the longest prefix for each shift, there is a total of n shifts and for each shift finding the length of the common prefix will take O(n) time. Hence, the overall time complexity for this approach is O(n^2).

Better Approach: If we will add a second string at the end of itself that is str2 = str2 + str2 then there is no need of finding a prefix for each shift separately. Now, after adding str2 to itself we have to only find the longest prefix of str1 present in str2 and the starting position of that prefix in str2 will give us the actual number of shifts required. For finding the longest prefix we can use KMP pattern search algorithm.

So, in this way, our time-complexity will reduce to O(n) only.

Implementation

## C++

 `// CPP program to find longest common prefix` `// after rotation of second string.` `#include ` `using` `namespace` `std;`   `// function for KMP search` `void` `KMP(``int` `m, ``int` `n, string str2, string str1)` `{` `    ``int` `pos = 0, len = 0;`   `    ``// preprocessing of longest proper prefix` `    ``int` `p[m + 1];` `    ``int` `k = 0;` `    ``p[1] = 0;`   `    ``for` `(``int` `i = 2; i <= n; i++) {` `        ``while` `(k > 0 && str1[k] != str1[i - 1])` `            ``k = p[k];` `        ``if` `(str1[k] == str1[i - 1])` `            ``++k;` `        ``p[i] = k;` `    ``}`   `    ``// find out the longest prefix and position` `    ``for` `(``int` `j = 0, i = 0; i < m; i++) {` `        ``while` `(j > 0 && str1[j] != str2[i])` `            ``j = p[j];` `        ``if` `(str1[j] == str2[i])` `            ``j++;`   `        ``// for new position with longer prefix in str2` `        ``// update pos and len` `        ``if` `(j > len) {` `            ``len = j;` `            ``pos = i - j + 1;` `        ``}` `    ``}`   `    ``// print result` `    ``cout << ``"Shift = "` `<< pos << endl;` `    ``cout << ``"Prefix = "` `<< str1.substr(0, len);` `}`   `// driver function` `int` `main()` `{` `    ``string str1 = ``"geeksforgeeks"``;` `    ``string str2 = ``"forgeeksgeeks"``;` `    ``int` `n = str1.size();` `    ``str2 = str2 + str2;` `    ``KMP(2 * n, n, str2, str1);` `    ``return` `0;` `}`

## Java

 `// Java program to find longest common prefix` `// after rotation of second string.`   `class` `GFG {`   `    ``// function for KMP search` `    ``static` `void` `KMP(``int` `m, ``int` `n, ` `                    ``String str2, String str1)` `    ``{` `        ``int` `pos = ``0``, len = ``0``;` `        ``int` `[]p = ``new` `int``[m + ``1``];` `        ``int` `k = ``0``;`   `        ``//p[1] = 0;` `        ``char` `[]ch1 = str1.toCharArray();` `        ``char` `[]ch2 = str2.toCharArray();`   `        ``for` `(``int` `i = ``2``; i <= n; i++)` `        ``{` `            ``while` `(k > ``0` `&& ch1[k] != ch1[i - ``1``])` `                ``k = p[k];` `            ``if` `(ch1[k] == ch1[i - ``1``])` `                ``++k;` `            ``p[i] = k;` `        ``}`   `        ``// find out the longest prefix and position` `        ``for` `(``int` `j = ``0``, i = ``0``; i < m; i++) ` `        ``{` `            ``while` `(j > ``0` `&& j < n && ch1[j] != ch2[i])` `                ``j = p[j];` `            ``if` `(j < n && ch1[j] == ch2[i])` `                ``j++;` `    `  `            ``// for new position with longer prefix in str2` `            ``// update pos and len` `            ``if` `(j > len)` `            ``{` `                ``len = j;` `                ``pos = i - j + ``1``;` `            ``}` `        ``}`   `            ``// print result` `            ``System.out.println(``"Shift = "` `+ pos);` `            ``System.out.println(``"Prefix = "` `+ ` `                                ``str1.substring(``0``,len));` `        ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args) ` `    ``{` `        ``String str1 = ``"geeksforgeeks"``;` `        ``String str2 = ``"forgeeksgeeks"``;` `        ``int` `n = str1.length();` `        ``str2 = str2 + str2;` `        ``KMP(``2` `* n, n, str2, str1);` `    ``}` `}`   `// This code is contributed by Ita_c.`

## Python3

 `# Python3 program to find longest common prefix` `# after rotation of second string.`   `# function for KMP search` `def` `KMP(m, n, str2, str1):`   `    ``pos ``=` `0` `    ``Len` `=` `0`   `    ``# preprocessing of longest proper prefix` `    ``p ``=` `[``0` `for` `i ``in` `range``(m ``+` `1``)]` `    ``k ``=` `0`   `    ``for` `i ``in` `range``(``2``, n ``+` `1``): ` `        ``while` `(k > ``0` `and` `str1[k] !``=` `str1[i ``-` `1``]):` `            ``k ``=` `p[k]` `        ``if` `(str1[k] ``=``=` `str1[i ``-` `1``]):` `            ``k ``+``=` `1` `        ``p[i] ``=` `k` `    `    `    ``# find out the longest prefix and position` `    ``j ``=` `0` `    ``for` `i ``in` `range``(m):` `        ``while` `(j > ``0` `and` `j < n ``and` `str1[j] !``=` `str2[i]):` `            ``j ``=` `p[j]` `        ``if` `(j < n ``and` `str1[j] ``=``=` `str2[i]):` `            ``j ``+``=` `1` ` `  `        ``# for new position with longer prefix ` `        ``# in str2 update pos and Len` `        ``if` `(j > ``Len``): ` `            ``Len` `=` `j` `            ``pos ``=` `i ``-` `j ``+` `1` `        `  `    ``# print result` `    ``print``(``"Shift = "``, pos)` `    ``print``(``"Prefix = "``, str1[:``Len``])`   `# Driver Code` `str1 ``=` `"geeksforgeeks"` `str2 ``=` `"forgeeksgeeks"` `n ``=` `len``(str1)` `str2 ``=` `str2 ``+` `str2` `KMP(``2` `*` `n, n, str2, str1)` `    `  `# This code is contributed by Mohit kumar 29`

## C#

 `// C# program to find longest common prefix` `// after rotation of second string.` `using` `System;` `    `  `class` `GFG {` ` `  `    ``// function for KMP search` `    ``static` `void` `KMP(``int` `m, ``int` `n, ` `                    ``String str2, String str1)` `    ``{` `        ``int` `pos = 0, len = 0;` `        ``int` `[]p = ``new` `int``[m + 1];` `        ``int` `k = 0;` ` `  `        ``//p[1] = 0;` `        ``char` `[]ch1 = str1.ToCharArray();` `        ``char` `[]ch2 = str2.ToCharArray();` ` `  `        ``for` `(``int` `i = 2; i <= n; i++)` `        ``{` `            ``while` `(k > 0 && ch1[k] != ch1[i - 1])` `                ``k = p[k];` `            ``if` `(ch1[k] == ch1[i - 1])` `                ``++k;` `            ``p[i] = k;` `        ``}` ` `  `        ``// find out the longest prefix and position` `        ``for` `(``int` `j = 0, i = 0; i < m; i++) ` `        ``{` `            ``while` `(j > 0 && j < n && ch1[j] != ch2[i])` `                ``j = p[j];` `            ``if` `(j < n && ch1[j] == ch2[i])` `                ``j++;` `     `  `            ``// for new position with longer prefix in str2` `            ``// update pos and len` `            ``if` `(j > len)` `            ``{` `                ``len = j;` `                ``pos = i - j + 1;` `            ``}` `        ``}` ` `  `            ``// print result` `            ``Console.WriteLine(``"Shift = "` `+ pos);` `            ``Console.WriteLine(``"Prefix = "` `+ ` `                                ``str1.Substring(0,len));` `        ``}` ` `  `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args) ` `    ``{` `        ``String str1 = ``"geeksforgeeks"``;` `        ``String str2 = ``"forgeeksgeeks"``;` `        ``int` `n = str1.Length;` `        ``str2 = str2 + str2;` `        ``KMP(2 * n, n, str2, str1);` `    ``}` `}`   `/* This code contributed by PrinciRaj1992 */`

## Javascript

 ``

Output:

```Shift = 8
Prefix = geeksforgeeks```

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