Minimum steps to delete a string after repeated deletion of palindrome substrings in C++

Problem statement

Given a string containing characters as integers only. We need to delete all character of this string in a minimum number of steps where in one step we can delete the substring which is a palindrome. After deleting a substring remaining parts are concatenated.

Example

If input string is 3441213 then minimum 2 steps required

First remove 121 from string. Now remaining string is 3443
Remove remaining string as it’s palindrome

Algorithm

We can use dynamic programming to solve this problem

1. Let dp[i][j] denotes the number of steps it takes to delete the substring s[i, j]
2. Each character will be deleted alone or as part of some substring so in the first case we will delete the character itself and call subproblem (i+1, j)
3. In the second case we will iterate over all occurrence of the current character in right side, if K is the index of one such occurrence then the problem will reduce to two subproblems (i+1, K – 1) and (K+1, j)
4. We can reach to this subproblem (i+1, K-1) because we can just delete the same character and call for mid substring
5. We need to take care of a case when first two characters are same in that case we can directly reduce to the subproblem (i+2, j)

Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
int getMinRequiredSteps(string str) {
   int n = str.length();
   int dp[n + 1][n + 1];
   for (int i = 0; i <= n; i++) {
      for (int j = 0; j <= n; j++) {
         dp[i][j] = 0;
      }
   }
   for (int len = 1; len <= n; len++) {
      for (int i = 0, j = len - 1; j < n; i++, j++) {
         if (len == 1)
            dp[i][j] = 1;
         else {
            dp[i][j] = 1 + dp[i + 1][j];
            if (str[i] == str[i + 1]) {
               dp[i][j] = min(1 + dp[i+ 2][j], dp[i][j]);
            }
            for (int K = i + 2; K <= j; K++){
               if (str[i] == str[K]) {
                  dp[i][j] =
                  min(dp[i+1][K-1] + dp[K+1][j], dp[i][j]);
               }
            }
         }
      }
   }
   return dp[0][n - 1];
}
int main() {
   string str = "3441213";
   cout << "Minimum required steps: " <<
   getMinRequiredSteps(str) << endl;
   return 0;
}

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