Minimum swaps required between two strings to make one string strictly greater than the other

Given two strings A and B of length M and N respectively, the task is to find the minimum swapping of two characters required to make string A lexicographically greater than the string B.

Examples:

Input: A = “1432”, B = “789”, M = 4, N = 3
Output: 1
Explanation:
One possible way is to swap characters at index 0 of both the strings. Therefore, A modifies to “7432” and B modifies to “189”.

Input: A = “3733”, B = “3333”, M = 4, N = 4
Output: 2
Explanation:
Step 1:Swap character at index 1 of string A with character at index 0 of string B. The strings A and B are modified to “3333” and “7333”.
Step 2: Swap the character at index 0 of string A with a character at index 0 of string B. The strings A and B are modified to “7333” and “3333”.

Approach: It can be observed that if M ? N and all the characters are the same, including both strings, then it is not possible to make string A strictly greater than string B. Otherwise, string A can be made strictly greater than string B by placing the two different characters at the 0^th index of both strings in a maximum of two moves.

Follow the steps below to solve the problem:

1. First, check if the first character of string A is greater than the first character of string B then print 0.
2. Otherwise, check if B[0] > A[0] then 1 swap is needed, so swap A[0] with B[0] and print 1.
3. Otherwise, check if all the characters are the same in both strings and M ? N then it is not possible, so print -1.
4. Otherwise, check if there lies any character in A which is smaller than A[0] or a character in B which is greater than B[0] then print 1.
5. Otherwise, check if there exists any character in A which is less than A[0] or any character in B which is greater than B[0] then print 2.
6. Otherwise, return 0 if none of the above conditions satisfies.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the minimum
// number of steps to make A > B
int minSteps(string A, string B, int M, int N)
{

    if (A[0] > B[0])
        return 0;

    if (B[0] > A[0]) {
        return 1;
    }

    // If all character are same and M <= N
    if (M <= N && A[0] == B[0]
        && count(A.begin(), A.end(), A[0]) == M
        && count(B.begin(), B.end(), B[0]) == N)
        return -1;

    // If there lies any character
    // in B which is greater than B[0]
    for (int i = 1; i < N; i++) {

        if (B[i] > B[0])
            return 1;
    }

    // If there lies any character
    // in A which is smaller than A[0]
    for (int i = 1; i < M; i++) {

        if (A[i] < A[0])
            return 1;
    }

    // If there lies a character which
    // is in A and greater than A[0]
    for (int i = 1; i < M; i++) {

        if (A[i] > A[0]) {

            swap(A[i], B[0]);
            swap(A[0], B[0]);
            return 2;
        }
    }

    // If there lies a character which
    // is in B and less than B[0]
    for (int i = 1; i < N; i++) {

        if (B[i] < B[0]) {

            swap(A[0], B[i]);
            swap(A[0], B[0]);
            return 2;
        }
    }

    // Otherwise
    return 0;
}

// Driver Code
int main()
{
    string A = "adsfd";
    string B = "dffff";

    int M = A.length();
    int N = B.length();

    cout << minSteps(A, B, M, N);

    return 0;
}

Java

// Java program for above approach
import java.util.*;
import java.lang.*;
class GFG
{

  // Function to find the minimum
  // number of steps to make A > B
  static int minSteps(StringBuilder A,
                      StringBuilder B,
                      int M, int N)
  {

    if (A.charAt(0) > B.charAt(0))
      return 0;

    if (B.charAt(0) > A.charAt(0))
    {
      return 1;
    }

    // If all character are same and M <= N
    if (M <= N && A.charAt(0) == B.charAt(0)
        && count(A, A.charAt(0)) == M
        && count(B, B.charAt(0)) == N)
      return -1;

    // If there lies any character
    // in B which is greater than B[0]
    for (int i = 1; i < N; i++)
    {

      if (B.charAt(i) > B.charAt(0))
        return 1;
    }

    // If there lies any character
    // in A which is smaller than A[0]
    for (int i = 1; i < M; i++)
    {

      if (A.charAt(i) < A.charAt(0))
        return 1;
    }

    // If there lies a character which
    // is in A and greater than A[0]
    for (int i = 1; i < M; i++)
    {
      if (A.charAt(i) > A.charAt(0))
      {
        swap(A, i, B, 0);
        swap(A, 0, B, 0);
        return 2;
      }
    }

    // If there lies a character which
    // is in B and less than B[0]
    for (int i = 1; i < N; i++)
    {
      if (B.charAt(i) < B.charAt(0))
      {
        swap(A, 0, B, i);
        swap(A, 0, B, 0);
        return 2;
      }
    }

    // Otherwise
    return 0;
  }

  static int count(StringBuilder a,
                   char c)
  {
    int count = 0;
    for(int i = 0; i < a.length(); i++)
      if(a.charAt(i) == c)
        count++;
    return count;
  }

  static void swap(StringBuilder s1,
                   int index1,
                   StringBuilder s2,
                   int index2)
  {
    char c = s1.charAt(index1);
    s1.setCharAt(index1,s2.charAt(index2));
    s2.setCharAt(index2,c);

  }
  // Driver function
  public static void main (String[] args)
  {
    StringBuilder A = new StringBuilder("adsfd");
    StringBuilder B = new StringBuilder("dffff");
    int M = A.length();
    int N = B.length();
    System.out.println(minSteps(A, B, M, N));
  }
}

// This code is contributed by offbeat.

Python3

# Python3 program for the above approach

# Function to find the minimum
# number of steps to make A > B
def minSteps(A, B, M, N):

    if (A[0] > B[0]):
        return 0

    if (B[0] > A[0]):
        return 1

    # If all character are same and M <= N
    if (M <= N and A[0] == B[0] and
           A.count(A[0]) == M and
           B.count(B[0]) == N):
        return -1

    # If there lies any character
    # in B which is greater than B[0]
    for i in range(1, N):
        if (B[i] > B[0]):
            return 1

    # If there lies any character
    # in A which is smaller than A[0]
    for i in range(1, M):
        if (A[i] < A[0]):
            return 1

    # If there lies a character which
    # is in A and greater than A[0]
    for i in range(1, M):
        if (A[i] > A[0]):
            A[0], B[i] = B[i], A[0]
            A[0], B[0] = B[0], A[0]
            return 2

    # If there lies a character which
    # is in B and less than B[0]
    for i in range(1, N):
        if (B[i] < B[0]):
            A[0], B[i] = B[i], A[0]
            A[0], B[0] = B[0], A[0]
            return 2

    # Otherwise
    return 0

# Driver Code
if __name__ == '__main__':

    A = "adsfd"
    B = "dffff"

    M = len(A)
    N = len(B)

    print(minSteps(A, B, M, N))

# This code is contributed by mohit kumar 29

C#

// C# program for above approach
using System;
using System.Text;

public class GFG
{

  // Function to find the minimum
  // number of steps to make A > B
  static int minSteps(StringBuilder A, StringBuilder B,  int M, int N)
  {
    if (A[0] > B[0])
      return 0;

    if (B[0] > A[0])
    {
      return 1;
    }

    // If all character are same and M <= N
    if (M <= N && A[0] == B[0]
        && count(A, A[0]) == M
        && count(B, B[0]) == N)
      return -1;

    // If there lies any character
    // in B which is greater than B[0]
    for (int i = 1; i < N; i++)
    {

      if (B[i] > B[0])
        return 1;
    }

    // If there lies any character
    // in A which is smaller than A[0]
    for (int i = 1; i < M; i++)
    {

      if (A[i] < A[0])
        return 1;
    }

    // If there lies a character which
    // is in A and greater than A[0]
    for (int i = 1; i < M; i++)
    {
      if (A[i] > A[0])
      {
        swap(A, i, B, 0);
        swap(A, 0, B, 0);
        return 2;
      }
    }

    // If there lies a character which
    // is in B and less than B[0]
    for (int i = 1; i < N; i++)
    {
      if (B[i] < B[0])
      {
        swap(A, 0, B, i);
        swap(A, 0, B, 0);
        return 2;
      }
    }

    // Otherwise
    return 0;

  }

  static int count(StringBuilder a,
                   char c)
  {
    int count = 0;
    for(int i = 0; i < a.Length; i++)
      if(a[i] == c)
        count++;
    return count;
  }

  static void swap(StringBuilder s1,
                   int index1,
                   StringBuilder s2,
                   int index2)
  {

    char c = s1[index1];
    s1[index1] = s2[index2];
    s2[index2] = c;
  }

  // Driver function
  static public void Main ()
  {
    StringBuilder A = new StringBuilder("adsfd");
    StringBuilder B = new StringBuilder("dffff");
    int M=A.Length;
    int N=B.Length;
    Console.WriteLine(minSteps(A, B, M, N));
  }
}

// This code is contributed by avanitrachhadiya2155

Javascript

<script>
//Javascript  program to implement
// the above approach

// Function to find the minimum
// number of steps to make A > B
function minSteps( A, B,M, N)
{

    if (A[0] > B[0])
    return 0;

    if (B[0] > A[0])
    {
        return 1;
    }

    // If all character are same and M <= N
    if (M <= N && A[0] == B[0] && count(A, A[0]) == M
        && count(B, B[0]) == N)
        return -1;

    // If there lies any character
    // in B which is greater than B[0]
    for (var i = 1; i < N; i++)
    {

        if (B[i] > B[0])
            return 1;
    }

    // If there lies any character
    // in A which is smaller than A[0]
    for (var i = 1; i < M; i++)
    {

        if (A[i] < A[0])
            return 1;
    }

    // If there lies a character which
    // is in A and greater than A[0]
    for (var i = 1; i < M; i++)
    {
        if (A[i] > A[0])
          {
            swap(A, i, B, 0);
            swap(A, 0, B, 0);
            return 2;
          }
    }

    // If there lies a character which
    // is in B and less than B[0]
    for (var i = 1; i < N; i++)
    {
        if (B[i] < B[0])
          {
            swap(A, 0, B, i);
            swap(A, 0, B, 0);
            return 2;
          }
    }

    // Otherwise
    return 0;
}

function count(a, c)
{
    count = 0;
    for(var i = 0; i < a.length; i++)
          if(a[i] == c)
            count++;
    return count;
}

function swap(s1, index1, s2, index2)
{
      var c = s1[index1];
    s1[index1] = s2[index2];
    s2[index2] = c;
}

var A = "adsfd";
var B = "dffff";
var M = A.length;
var N = B.length;

document.write(minSteps(A, B, M, N));

// This code is contributed by SoumikMondal
</script>

Output:

1

Time Complexity: O(N)
Auxiliary Space: O(1)