Given a string of length n and a non-negative integer k. Find k distant string of given string.

Distance between two letters is difference between their positions in the alphabet. for example:

- dist(c, e) = dist(e, c) = 2.
- dist(a, z) = dist(z, a) = 25.

By using this concept, the distance between two strings is the sum of distances of corresponding letters. For example :

- dist(af, hf) = dist(a, h) + dist(f, f) = 7 + 0 = 7.

Given a string and a distance k. Task is to find a string such that distance of the result string is k from given string. If k distant string is not possible, then print “No”.

**Note: ** There may be exist multiple solutions. We meed to find one of them.

**Examples :**

Input : bear k = 26 Output : zcar Here, dist(bear, zcar) = dist(b, z) + dist(e, c) + + dist(a, a) + dist(r, r) = 24 + 2 + 0 + 0 = 26 Input : af k = 7 Output : hf Here, dist(af, hf) = dist(a, h) + dist(f, f) = 7 + 0 = 7 Input : hey k = 1000 Output : No Explaination : No such string exists.

There is no solution if the given required distance is too big. Think what is the maximum possible distance for the given string. Or the more useful thing — how to construct the lost string to maximize the distance? Treat each letter separately and replace it with the most distant letter. For example, we should replace ‘c’ with ‘z’, and we should replace ‘y’ with ‘a’. To be more precise, for first 13 letters of the alphabet the most distant letter is ‘z’, and for other letters it is ‘a’.

The approach is simple, iterate over letters of the given string and greedily change them. A word “greedily” means when changing a letter, don’t care about the next letters. Generally, there must be distant letters, because there may not be a solution otherwise. For each letter of the given string change it into the most distant letter, unless the total distance would be too big. As letters are changed, decrease the remaining required distance. So, for each letter of the given string consider only letters not exceeding the remaining distance, and among them choose the most distant one.

CPP and JAVA Implementation:

## CPP

// CPP program to find the k distant string #include <bits/stdc++.h> using namespace std; // function to find the // lost string string findKDistantString(string str, int k) { int n = str.length(); for (int i = 0; i < n; ++i) { char best_letter = str[i]; int best_distance = 0; for (char maybe = 'a'; maybe <= 'z'; ++maybe) { int distance = abs(maybe - str[i]); // check if "distance <= k", // so that, the total distance // will not exceed among // letters with "distance <= k" if (distance <= k && distance > best_distance) { best_distance = distance; best_letter = maybe; } } // decrease the remaining // distance k -= best_distance; str[i] = best_letter; } assert(k >= 0); // we found a correct // string only if "k == 0" if (k > 0) return "No"; else return str; } // driver function int main() { string str = "bear"; int k = 26; cout << findKDistantString(str, k) << endl; str = "af"; k = 7; cout << findKDistantString(str, k) << endl; return 0; }

## Java

// Java program to find k distant string import java.util.*; import java.lang.*; public class GfG { // function to find // the lost string public static String findKDistantString (String str1, int k) { int n = str1.length(); char[] str = str1.toCharArray(); for (int i = 0; i < n; ++i) { char best_letter = str[i]; int best_distance = 0; for (char maybe = 'a'; maybe <= 'z'; ++maybe) { int distance = Math.abs(maybe - str[i]); // Check if "distance <= k" // so that it should not // exceed the total distance // among letters with "distance // <= k" we choose the most // distant one if (distance <= k && distance > best_distance) { best_distance = distance; best_letter = maybe; } } // we decrease the remaining // distance k -= best_distance; str[i] = best_letter; } assert(k >= 0); // Correct string only // if "k == 0" if (k > 0) return "No"; else return (new String(str)); } public static void main(String argc[]) { String str = "bear"; int k = 26; System.out.println(findKDistantString(str, k)); str = "af"; k = 7; System.out.println(findKDistantString(str, k)); } }

## Python3

# Python implementation to check if # both halves of the string have # at least one different character MAX = 26 # Function which break string into two halves # Counts frequency of characters in each half # Compares the two counter array and returns # true if these counter arrays differ def function(st): global MAX l = len(st) # Declaration and initialization # of counter array counter1, counter2 = [0]*MAX, [0]*MAX for i in range(l//2): counter1[ord(st[i]) - ord('a')] += 1 for i in range(l//2, l): counter2[ord(st[i]) - ord('a')] += 1 for i in range(MAX): if (counter2[i] != counter1[i]): return True return False # Driver function st = "abcasdsabcae" if function(st): print("Yes, both halves differ by at least one character") else: print("No, both halves do not differ at all") # This code is contributed by Ansu Kumari

Output:

zcar hf

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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.