Minimum number of swaps between two strings such that one string is strictly greater than the other

In this article, we will discuss an interesting string manipulation problem - "The minimum number of exchanges required between two strings such that one string is strictly larger than the other string". We'll look at the problem, detail strategies for solving it, implement it in C, and clarify concepts with a relevant example.

Understanding the problem statement

Given two strings of equal length, our goal is to determine the minimum number of character swaps required to make one string strictly larger than the other. Characters are swapped between the two strings, with each swap involving a character from both strings. Strings are compared lexicographically, where 'a'

method

The idea is to use a greedy algorithm. We start from the beginning of the string, and for each position, if the character in the first string is smaller than the corresponding character in the second string, we swap them. If they are equal, we look for the larger character in the second string to swap. If no such character is found, we continue to the next position. We repeat this process until all characters in the string have been processed.

Example

Let's implement this method in C -

#include<bits/stdc++.h>
using namespace std;

int minSwaps(string &s1, string &s2) {
   int swaps = 0;
   int n = s1.size();
   for(int i=0; i<n; i++) {
      if(s1[i] < s2[i]) {
         swap(s1[i], s2[i]);
         swaps++;
      }
      else if(s1[i] == s2[i]) {
         for(int j=i+1; j<n; j++) {
               if(s2[j] > s1[i]) {
                  swap(s1[i], s2[j]);
                  swaps++;
                  break;
               }
         }
      }
   }
   return (s1 > s2) ? swaps : -1;
}

int main() {
   string s1 = "bbca";
   string s2 = "abbc";
   int swaps = minSwaps(s1, s2);
   if(swaps != -1)
      cout << "Minimum swaps: " << swaps << "\n";
   else
      cout << "Cannot make string 1 greater\n";
   return 0;
}

Output

Minimum swaps: 2

Test Case

Let us consider the strings "bbca" and "abbc". The following exchange will occur −

• Exchange 'b' in the first string with 'a' in the second string. The strings are now "bbac" and "abbc".

• Exchange "c" in the first string with "b" in the second string. The strings now are "bbcb" and "abac".

"bbcb" is lexicographically greater than "abac". Therefore, the minimum number of swaps required is 2, and the output of the program will be "Minimum number of swaps: 2".

in conclusion

In this article, we explore the problem of determining the minimum number of swaps required between two strings so that one string is lexicographically larger than the other. We discuss strategies for solving the problem, implement it in C, and explain the concept with examples. String manipulation questions like this are common in interviews and competitive programming, and understanding these concepts is very beneficial.

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