Minimum number of deletions to make a string palindrome in C++.

Problem statement

Given a string of size ‘n’. The task is to delete a minimum number of characters to make string palindrome.

If the given string is “abcda” then we can delete any 2 characters except first and last to make it a palindrome.

• If we delete character ‘b’ and ‘c’ then “ada” string is a palindrome

• If we delete character ‘c’ and ‘d’ then “aba” string is a palindrome

• If we delete character ‘b’ and ‘d’ then “aca” string is a palindrome

Algorithm

1. Find longest palindromic subsequence of given string. Let’s call it as “lpsSize”.
2. Minimum characters to be deleted = (length of string – lpsSize) Code.

Example

#include <iostream>
#include <algorithm>
using namespace std;
int lps(string s, int i, int j){
   if (i == j) {
      return 1;
   }
   if (s[i] == s[j] && i + 1 == j) {
      return 2;
   }
   if (s[i] == s[j]) {
      return lps(s, i + 1, j - 1) + 2;
   }
   return max(lps(s, i, j - 1), lps(s, i + 1, j));
}
int minDeletion(string s){
   int n = s.size();
   int lpsSize = lps(s, 0, n);
   return (n - lpsSize);
}
int main(){
   cout << "Minimum characters to be deleted = " <<
   minDeletion("abcda") << endl;
   return 0;
}

Output

When you compile and execute the above program. It generates the following output −

Minimum characters to be deleted = 2