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# Longest repeating and non-overlapping substring

Given a string str, find the longest repeating non-overlapping substring in it. In other words find 2 identical substrings of maximum length which do not overlap. If there exists more than one such substring return any of them.

Examples:

Input : str = "geeksforgeeks"
Output : geeks

Input : str = "aab"
Output : a

Input : str = "aabaabaaba"
Output : aaba

Input : str = "aaaaaaaaaaa"
Output : aaaaa

Input : str = "banana"
Output : an
or na

Naive Solution : The problem can be solved easily by taking all the possible substrings and for all the substrings check it for the remaining(non-overlapping) string if there exists an identical substring. There are O(n2) total substrings and checking them against the remaining string will take O(n) time. So overall time complexity of above solution is O(n3).

Dynamic Programming : This problem can be solved in O(n2) time using Dynamic Programming. The basic idea is to find the longest repeating suffix for all prefixes in the string str.

Length of longest non-repeating substring can be recursively
defined as below.

LCSRe(i, j) stores length of the matching and
non-overlapping substrings ending
with i'th and j'th characters.

If str[i-1] == str[j-1] && (j-i) > LCSRe(i-1, j-1)
LCSRe(i, j) = LCSRe(i-1, j-1) + 1,
Else
LCSRe(i, j) = 0

Where i varies from 1 to n and
j varies from i+1 to n

To avoid overlapping we have to ensure that the length of suffix is less than (j-i) at any instant.
The maximum value of LCSRe(i, j) provides the length of the longest repeating substring and the substring itself can be found using the length and the ending index of the common suffix.

Below is the implementation of the recurrence.

## C++

 // C++ program to find the longest repeated// non-overlapping substring#includeusing namespace std; // Returns the longest repeating non-overlapping// substring in strstring longestRepeatedSubstring(string str){    int n = str.length();    int LCSRe[n+1][n+1];     // Setting all to 0    memset(LCSRe, 0, sizeof(LCSRe));     string res; // To store result    int res_length  = 0; // To store length of result     // building table in bottom-up manner    int i, index = 0;    for (i=1; i<=n; i++)    {        for (int j=i+1; j<=n; j++)        {            // (j-i) > LCSRe[i-1][j-1] to remove            // overlapping            if (str[i-1] == str[j-1] &&                LCSRe[i-1][j-1] < (j - i))            {                LCSRe[i][j] = LCSRe[i-1][j-1] + 1;                 // updating maximum length of the                // substring and updating the finishing                // index of the suffix                if (LCSRe[i][j] > res_length)                {                    res_length = LCSRe[i][j];                    index = max(i, index);                }            }            else                LCSRe[i][j] = 0;        }    }     // If we have non-empty result, then insert all    // characters from first character to last    // character of string    if (res_length > 0)        for (i = index - res_length + 1; i <= index; i++)            res.push_back(str[i-1]);     return res;} // Driver program to test the above functionint main(){    string str = "geeksforgeeks";    cout << longestRepeatedSubstring(str);    return 0;}

## Java

 // Java program to find the longest repeated// non-overlapping substring class GFG { // Returns the longest repeating non-overlapping// substring in str    static String longestRepeatedSubstring(String str) {        int n = str.length();        int LCSRe[][] = new int[n + 1][n + 1];         String res = ""; // To store result        int res_length = 0; // To store length of result         // building table in bottom-up manner        int i, index = 0;        for (i = 1; i <= n; i++) {            for (int j = i + 1; j <= n; j++) {                // (j-i) > LCSRe[i-1][j-1] to remove                // overlapping                if (str.charAt(i - 1) == str.charAt(j - 1)                        && LCSRe[i - 1][j - 1] < (j - i)) {                    LCSRe[i][j] = LCSRe[i - 1][j - 1] + 1;                     // updating maximum length of the                    // substring and updating the finishing                    // index of the suffix                    if (LCSRe[i][j] > res_length) {                        res_length = LCSRe[i][j];                        index = Math.max(i, index);                    }                } else {                    LCSRe[i][j] = 0;                }            }        }         // If we have non-empty result, then insert all        // characters from first character to last        // character of String        if (res_length > 0) {            for (i = index - res_length + 1; i <= index; i++) {                res += str.charAt(i - 1);            }        }         return res;    } // Driver program to test the above function    public static void main(String[] args) {        String str = "geeksforgeeks";        System.out.println(longestRepeatedSubstring(str));    }}// This code is contributed by Rajput-JI

## Python 3

 # Python 3 program to find the longest repeated# non-overlapping substring # Returns the longest repeating non-overlapping# substring in strdef longestRepeatedSubstring(str):     n = len(str)    LCSRe = [[0 for x in range(n + 1)]                for y in range(n + 1)]     res = "" # To store result    res_length = 0 # To store length of result     # building table in bottom-up manner    index = 0    for i in range(1, n + 1):        for j in range(i + 1, n + 1):                         # (j-i) > LCSRe[i-1][j-1] to remove            # overlapping            if (str[i - 1] == str[j - 1] and                LCSRe[i - 1][j - 1] < (j - i)):                LCSRe[i][j] = LCSRe[i - 1][j - 1] + 1                 # updating maximum length of the                # substring and updating the finishing                # index of the suffix                if (LCSRe[i][j] > res_length):                    res_length = LCSRe[i][j]                    index = max(i, index)                             else:                LCSRe[i][j] = 0     # If we have non-empty result, then insert    # all characters from first character to    # last character of string    if (res_length > 0):        for i in range(index - res_length + 1,                                    index + 1):            res = res + str[i - 1]     return res # Driver Codeif __name__ == "__main__":         str = "geeksforgeeks"    print(longestRepeatedSubstring(str)) # This code is contributed by ita_c

## C#

 // C# program to find the longest repeated// non-overlapping substringusing System;  public class GFG {  // Returns the longest repeating non-overlapping// substring in str    static String longestRepeatedSubstring(String str) {        int n = str.Length;        int [,]LCSRe = new int[n + 1,n + 1];          String res = ""; // To store result        int res_length = 0; // To store length of result          // building table in bottom-up manner        int i, index = 0;        for (i = 1; i <= n; i++) {            for (int j = i + 1; j <= n; j++) {                // (j-i) > LCSRe[i-1][j-1] to remove                // overlapping                if (str[i - 1] == str[j - 1]                        && LCSRe[i - 1,j - 1] < (j - i)) {                    LCSRe[i,j] = LCSRe[i - 1,j - 1] + 1;                      // updating maximum length of the                    // substring and updating the finishing                    // index of the suffix                    if (LCSRe[i,j] > res_length) {                        res_length = LCSRe[i,j];                        index = Math.Max(i, index);                    }                } else {                    LCSRe[i,j] = 0;                }            }        }          // If we have non-empty result, then insert all        // characters from first character to last        // character of String        if (res_length > 0) {            for (i = index - res_length + 1; i <= index; i++) {                res += str[i - 1];            }        }          return res;    }  // Driver program to test the above function    public static void Main() {        String str = "geeksforgeeks";        Console.WriteLine(longestRepeatedSubstring(str));    }}// This code is contributed by Rajput-JI

## Javascript



Output

geeks

Time Complexity: O(n2
Auxiliary Space: O(n2)

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