Minimum length of substring whose rotation generates a palindromic substring

Given a string str, the task is to find the minimum length of substring required to rotate that generates a palindromic substring from the given string.

Examples:

Input: str = “abcbd”
Output: 0
Explanation: No palindromic substring can be generated there is no repeating character in the string.

Input: str = “abcdeba”
Output: 3
Explanation: Rotate substring “deb” to convert the given string to abcbeda with a palindromic substring “bcb”.

Approach:



  • If no character repeats in the string, then no palindromic substring can be generated.
  • For every repeating character, check if the index of its previous occurrence is within one or two indices from the current index. If so, then a palindromic substring already exists.
  • Otherwise, calculate the length of (current index – index of previous occurrence – 1).
  • Return the minimum of all such lengths as the answer

Below is the implementation of the above approach:

C++

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// C++ Program to find the minimum
// length of substring whose rotation
// generates a palindromic substring
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the
// minimum lenth of substring
int count_min_length(string s)
{
  
    // Store the index of
    // previous occurrence
    // of the character
    int hash[26];
  
    // Variable to store
    // the maximum length
    // of substring
    int ans = INT_MAX;
  
    for (int i = 0; i < 26; i++)
        hash[i] = -1;
  
    for (int i = 0; i < s.size(); i++) {
        // If the current character
        // hasn't appeared yet
        if (hash[s[i] - 'a'] == -1)
            hash[s[i] - 'a'] = i;
        else {
            // If the character has occured
            // within one or two previous
            // index, a palindromic substring
            // already exists
            if (hash[s[i] - 'a'] == i - 1
                || hash[s[i] - 'a'] == i - 2)
                return 0;
  
            // Update the maximum
            ans = min(ans,
                      i - hash[s[i] - 'a'] - 1);
  
            // Replace the previous
            // index of the character by
            // the current index
            hash[s[i] - 'a'] = i;
        }
    }
  
    // If character appeared
    // at least twice
    if (ans == INT_MAX)
        return -1;
  
    return ans;
}
// Driver Code
int main()
{
    string str = "abcdeba";
    cout << count_min_length(str);
}

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Java

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// Java Program to find the minimum
// length of substring whose rotation
// generates a palindromic substring
import java.util.*;
import java.lang.*;
class GFG{
  
// Function to return the
// minimum lenth of substring
static int count_min_length(String s)
{
  
    // Store the index of
    // previous occurrence
    // of the character
    int[] hash = new int[26];
  
    // Variable to store
    // the maximum length
    // of substring
    int ans = Integer.MAX_VALUE;
  
    for (int i = 0; i < 26; i++)
        hash[i] = -1;
  
    for (int i = 0; i < s.length(); i++) 
    {
        // If the current character
        // hasn't appeared yet
        if (hash[s.charAt(i) - 'a'] == -1)
            hash[s.charAt(i) - 'a'] = i;
        else 
        {
            // If the character has occured
            // within one or two previous
            // index, a palindromic substring
            // already exists
            if (hash[s.charAt(i) - 'a'] == i - 1 || 
                hash[s.charAt(i) - 'a'] == i - 2)
                return 0;
  
            // Update the maximum
            ans = Math.min(ans, 
                       i - hash[s.charAt(i) - 'a'] - 1);
  
            // Replace the previous
            // index of the character by
            // the current index
            hash[s.charAt(i) - 'a'] = i;
        }
    }
  
    // If character appeared
    // at least twice
    if (ans == Integer.MAX_VALUE)
        return -1;
  
    return ans;
}
  
// Driver code
public static void main(String[] args)
{
    String str = "abcdeba";
  
    System.out.println(count_min_length(str));
}
}
  
// This code is contributed by offbeat

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Python3

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# Python3 program to find the minimum 
# length of substring whose rotation 
# generates a palindromic substring 
import sys
  
INT_MAX = sys.maxsize;
  
# Function to return the 
# minimum lenth of substring 
def count_min_length(s): 
  
    # Store the index of 
    # previous occurrence 
    # of the character 
    hash = [0] * 26
  
    # Variable to store 
    # the maximum length 
    # of substring 
    ans = sys.maxsize; 
  
    for i in range(26):
        hash[i] = -1
  
    for i in range(len(s)):
          
        # If the current character 
        # hasn't appeared yet 
        if (hash[ord(s[i]) - ord('a')] == -1):
            hash[ord(s[i]) - ord('a')] = i; 
        else :
              
            # If the character has occured 
            # within one or two previous 
            # index, a palindromic substring 
            # already exists 
            if (hash[ord(s[i]) - ord('a')] == i - 1 or 
                hash[ord(s[i]) - ord('a')] == i - 2) :
                return 0
  
            # Update the maximum 
            ans = min(ans, i - hash[ord(s[i]) - 
                                    ord('a')] - 1); 
  
            # Replace the previous 
            # index of the character by 
            # the current index 
            hash[ord(s[i]) - ord('a')] = i; 
  
    # If character appeared 
    # at least twice 
    if (ans == INT_MAX):
        return -1
  
    return ans; 
  
# Driver Code 
if __name__ == "__main__"
  
    string = "abcdeba"
      
    print(count_min_length(string)); 
  
# This code is contributed by AnkitRai01

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C#

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// C# Program to find the minimum
// length of substring whose rotation
// generates a palindromic substring
using System;
class GFG{
  
// Function to return the
// minimum lenth of substring
static int count_min_length(string s)
{
  
    // Store the index of
    // previous occurrence
    // of the character
    int[] hash = new int[26];
  
    // Variable to store
    // the maximum length
    // of substring
    int ans = int.MaxValue;
  
    for (int i = 0; i < 26; i++)
        hash[i] = -1;
  
    for (int i = 0; i < s.Length; i++) 
    {
        // If the current character
        // hasn't appeared yet
        if (hash[s[i] - 'a'] == -1)
            hash[s[i] - 'a'] = i;
        else
        {
            // If the character has occured
            // within one or two previous
            // index, a palindromic substring
            // already exists
            if (hash[s[i] - 'a'] == i - 1 || 
                hash[s[i] - 'a'] == i - 2)
                return 0;
  
            // Update the maximum
            ans = Math.Min(ans, 
                      i - hash[s[i] - 'a'] - 1);
  
            // Replace the previous
            // index of the character by
            // the current index
            hash[s[i] - 'a'] = i;
        }
    }
  
    // If character appeared
    // at least twice
    if (ans == int.MaxValue)
        return -1;
  
    return ans;
}
  
// Driver code
public static void Main(string[] args)
{
    string str = "abcdeba";
  
    Console.WriteLine(count_min_length(str));
}
}
  
// This code is contributed by AnkitRai01

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Output:

3

Time Complexity: O(N)

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Improved By : offbeat, AnkitRai01, nidhi_biet