The smallest substring that needs to be removed to make the given string a palindrome

A palindrome is a sequence of characters that reads the same in both forward and reverse directions. In computer science and programming, palindromes are a common theme in string manipulation problems. In this article, we will explore how to find the minimum size substring that must be removed from a given string to make it a palindrome. We will provide a well-structured C solution and include an example to illustrate the test case.

Problem Statement

Given a string 's' of length 'n', we need to find the minimum size of the substring that should be removed so that the remaining string becomes a palindrome.

algorithm

• Create a function called isPalindrome that takes the string 's' as a parameter and returns true if it is a palindrome, otherwise it returns false.

• Create a function called minSizeSubstringToRemove that takes the string 's' as a parameter.

• Initialize the variable 'minSize' to the length of the string.

• Iterate over the string using a loop, incrementing an index 'i' from 0 to 'n'.

• In each iteration, perform the following steps −

• Create two substrings from the beginning of the string to index 'i' and one from index 'i' to the end of the string.

• Check whether any of the substrings is a palindrome.

• If any substring is a palindrome, update 'minSize' to the minimum value between the length of the non-palindrome substring and 'minSize'.

• Return 'minSize' as the result.

Example

#include <iostream>
#include <string>
#include <algorithm>

// Function to check if a string is a palindrome
bool isPalindrome(const std::string &s) {
   int left = 0;
   int right = s.length() - 1;
   
   while (left < right) {
      if (s[left] != s[right]) {
         return false;
      }
      ++left;
      --right;
   }
   
   return true;
}

// Function to find the minimum size substring to be removed
int minSizeSubstringToRemove(std::string s) {
   int n = s.length();
   int minSize = n;
   
   for (int i = 0; i <= n; ++i) {
      std::string leftSubstring = s.substr(0, i);
      std::string rightSubstring = s.substr(i, n - i);
   
      if (isPalindrome(leftSubstring)) {
         minSize = std::min(minSize, static_cast<int>(rightSubstring.length()));
      }
      if (isPalindrome(rightSubstring)) {
         minSize = std::min(minSize, static_cast<int>(leftSubstring.length()));
      }
   }
   
   return minSize;
}

int main() {
   std::string s = "abccbaab";
   int result = minSizeSubstringToRemove(s);
   std::cout << "Minimum size substring to be removed: " << result << std::endl;
   
   return 0;
}

Output

Minimum size substring to be removed: 2

Test case example

Consider the following string: "abccbaab". Possible substrings and their corresponding palindromic states are as follows:

• Left substring = "", right substring = "abccbaab", palindrome = false

• Left substring = "a", right substring = "bccbaab", palindrome = false

• Left substring = "ab", right substring = "ccbaab", palindrome = false

• Left substring = "abc", right substring = "cbaab", palindrome = false

• Left substring = "abcc", right substring = "baab", palindrome = false

• Left substring = "abccb", right substring = "aab", palindrome = true (left substring)

• Left substring = "abccba", right substring = "ab", palindrome = true (left substring)

• Left substring = "abccbaa", right substring = "b", palindrome = false

• Left substring = "abccbaab", right substring = "", palindrome = false

From the above iteration, we can see that the minimum size of substring to delete is 2, which occurs when the left substring is "abccba" and the right substring is "ab". In this case, deleting the right substring "ab" will make the remaining string "abccba" a palindrome.

in conclusion

In this article, we explore the problem of finding the smallest size substring that must be removed to make a given string a palindrome. We provide a clear and efficient C implementation that utilizes a simple loop to iterate over a string, create substrings and check their palindrome status to find the minimum size of the substring that must be deleted.

By understanding this algorithm, you can apply similar concepts to solving other string manipulation and palindrome problems in computer science and programming.

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