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Make largest palindrome by changing at most K-digits
  • Difficulty Level : Medium
  • Last Updated : 22 Jan, 2021

Given a string containing all digits, we need to convert this string to a palindrome by changing at most K digits. If many solutions are possible then print lexicographically largest one.
Examples: 

Input   : str = “43435”    
          k = 3
Output  : "93939" 
Explanation:
Lexicographically largest palindrome 
after 3 changes is "93939" 

Input :  str = “43435”    
         k = 1
Output : “53435”
Explanation:
Lexicographically largest palindrome 
after 3 changes is “53435”

Input  : str = “12345”    
         k = 1
Output : "Not Possible"
Explanation:
It is not possible to make str palindrome
after 1 change.

Approach:

  1. Solve this problem using two pointers method. We start from left and right and if both digits are not equal then we replace the smaller value with larger value and decrease k by 1. S
  2. top when the left and right pointers cross each other, after they stop if value of k is negative, then it is not possible to make string palindrome using k changes. If k is positive, then we can further maximize the string by looping once again in the same manner from left and right and converting both the digits to 9 and decreasing k by 2. 
  3. If k value remains to 1 and string length is odd then we make the middle character as 9 to maximize whole value.
    Below is the implementation of above approach: 

C++

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// C++ program to get largest palindrome changing
// atmost K digits
#include <bits/stdc++.h>
using namespace std;
 
// Returns maximum possible
// palindrome using k changes
string maximumPalinUsingKChanges(string str, int k)
{
    string palin = str;
 
    // Iinitialize l and r by leftmost and
    // rightmost ends
    int l = 0;
    int r = str.length() - 1;
 
    //  first try to make string palindrome
    while (l < r) {
       
        // Replace left and right character by
        // maximum of both
        if (str[l] != str[r]) {
            palin[l] = palin[r] =
                  max(str[l], str[r]);
            k--;
        }
        l++;
        r--;
    }
 
    // If k is negative then we can't make
    // string palindrome
    if (k < 0)
        return "Not possible";
 
    l = 0;
    r = str.length() - 1;
 
    while (l <= r) {
       
        // At mid character, if K>0 then change
        // it to 9
        if (l == r) {
            if (k > 0)
                palin[l] = '9';
        }
 
        // If character at lth (same as rth) is
        // less than 9
        if (palin[l] < '9') {
            /* If none of them is changed in the
               previous loop then subtract 2 from K
               and convert both to 9 */
            if (k >= 2 && palin[l] == str[l]
                && palin[r] == str[r]) {
                k -= 2;
                palin[l] = palin[r] = '9';
            }
 
            /*  If one of them is changed
                in the previous
                loop then subtract 1 from K
                (1 more is
                subtracted already) and make them 9  */
            else if (k >= 1
                     && (palin[l] != str[l]
                         || palin[r] != str[r])) {
                k--;
                palin[l] = palin[r] = '9';
            }
        }
        l++;
        r--;
    }
 
    return palin;
}
 
//  Driver code to test above methods
int main()
{
    string str = "43435";
    int k = 3;
    cout << maximumPalinUsingKChanges(str, k);
    return 0;
}

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Java

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// Java program to get largest palindrome changing
// atmost K digits
 
import java.text.ParseException;
 
class GFG {
 
  // Returns maximum possible
  // palindrome using k changes
  static String maximumPalinUsingKChanges(String str,
                                          int k)
  {
    char palin[] = str.toCharArray();
    String ans = "";
 
    // Iinitialize l and r by leftmost and
    // rightmost ends
    int l = 0;
    int r = str.length() - 1;
 
    // First try to make String palindrome
    while (l < r) {
 
      // Replace left and right character by
      // maximum of both
      if (str.charAt(l) != str.charAt(r)) {
        palin[l] = palin[r] = (char)Math.max(
          str.charAt(l), str.charAt(r));
        k--;
      }
      l++;
      r--;
    }
 
    // If k is negative then we can't make
    // String palindrome
    if (k < 0) {
      return "Not possible";
    }
 
    l = 0;
    r = str.length() - 1;
 
    while (l <= r) {
 
      // At mid character, if K>0 then change
      // it to 9
      if (l == r) {
        if (k > 0) {
          palin[l] = '9';
        }
      }
 
      // If character at lth (same as rth) is
      // less than 9
      if (palin[l] < '9') {
 
        /* If none of them is changed in the
            previous loop then subtract 2 from K
            and convert both to 9 */
        if (k >= 2 && palin[l] == str.charAt(l)
            && palin[r] == str.charAt(r)) {
          k -= 2;
          palin[l] = palin[r] = '9';
        }
 
        /* If one of them is changed in the
        previous loop then subtract
        1 from K (1 more
        is subtracted already) and make them 9 */
        else if (k >= 1
                 && (palin[l] != str.charAt(l)
                     || palin[r]
                     != str.charAt(r))) {
          k--;
          palin[l] = palin[r] = '9';
        }
      }
      l++;
      r--;
    }
    for (int i = 0; i < palin.length; i++)
      ans += palin[i];
    return ans;
  }
 
  // Driver code to test above methods
  public static void main(String[] args)
    throws ParseException
  {
    String str = "43435";
    int k = 3;
    System.out.println(
      maximumPalinUsingKChanges(str, k));
  }
}
// This code is contributed by 29ajaykumar

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C#

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// C# program to get largest palindrome changing
// atmost K digits
 
using System;
public class GFG {
 
  // Returns maximum possible
  // palindrome using k changes
  static String maximumPalinUsingKChanges(String str,
                                          int k)
  {
    char[] palin = str.ToCharArray();
    String ans = "";
     
    // Iinitialize l and r by leftmost and
    // rightmost ends
    int l = 0;
    int r = str.Length - 1;
 
    // First try to make String palindrome
    while (l < r) {
       
      // Replace left and right character by
      // maximum of both
      if (str[l] != str[r]) {
        palin[l] = palin[r]
          = (char)Math.Max(str[l], str[r]);
        k--;
      }
      l++;
      r--;
    }
 
    // If k is negative then we can't make
    // String palindrome
    if (k < 0) {
      return "Not possible";
    }
 
    l = 0;
    r = str.Length - 1;
 
    while (l <= r) {
       
      // At mid character, if K>0 then change
      // it to 9
      if (l == r) {
        if (k > 0) {
          palin[l] = '9';
        }
      }
 
      // If character at lth (same as rth) is
      // less than 9
      if (palin[l] < '9') {
         
        /* If none of them is changed in the
        previous loop then subtract 2 from K
        and convert both to 9 */
        if (k >= 2 && palin[l] == str[l]
            && palin[r] == str[r]) {
          k -= 2;
          palin[l] = palin[r] = '9';
        }
         
        /* If one of them is changed in the
        previous loop then subtract 1 from K (1 more
        is subtracted already) and make them 9 */
        else if (k >= 1
                 && (palin[l] != str[l]
                     || palin[r] != str[r])) {
          k--;
          palin[l] = palin[r] = '9';
        }
      }
      l++;
      r--;
    }
    for (int i = 0; i < palin.Length; i++)
      ans += palin[i];
    return ans;
  }
 
  // Driver code to test above methods
  public static void Main()
  {
    String str = "43435";
    int k = 3;
    Console.Write(maximumPalinUsingKChanges(str, k));
  }
}
// This code is contributed by Rajput-Ji

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Python

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# Python3 program to get largest palindrome changing
# atmost K digits
 
# Returns maximum possible
# palindrome using k changes
def maximumPalinUsingKChanges(strr, k):
    palin = strr[::]
 
    # Iinitialize l and r by leftmost and
    # rightmost ends
    l = 0
    r = len(strr) - 1
 
    # first try to make palindrome
    while (l <= r):
 
        # Replace left and right character by
        # maximum of both
        if (strr[l] != strr[r]):
            palin[l] = palin[r] =
                   max(strr[l], strr[r])
 
            # print(strr[l],strr[r])
            k -= 1
        l += 1
        r -= 1
 
    # If k is negative then we can't make
    # palindrome
    if (k < 0):
        return "Not possible"
 
    l = 0
    r = len(strr) - 1
 
    while (l <= r):
 
        # At mid character, if K>0 then change
        # it to 9
        if (l == r):
            if (k > 0):
                palin[l] = '9'
 
        # If character at lth (same as rth) is
        # less than 9
        if (palin[l] < '9'):
 
            # If none of them is changed in the
            # previous loop then subtract 2 from K
            # and convert both to 9
            if (k >= 2 and palin[l] == strr[l] and
                           palin[r] == strr[r]):
                k -= 2
                palin[l] = palin[r] = '9'
 
            # If one of them is changed in the previous
            # loop then subtract 1 from K (1 more is
            # subtracted already) and make them 9
            elif (k >= 1 and (palin[l] != strr[l] or
                              palin[r] != strr[r])):
                k -= 1
                palin[l] = palin[r] = '9'
 
        l += 1
        r -= 1
 
    return palin
 
 
# Driver code
st = "43435"
strr = [i for i in st]
k = 3
a = maximumPalinUsingKChanges(strr, k)
print("".join(a))
 
# This code is contributed by mohit kumar 29

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Output: 

93939

This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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