Find Maximum number possible by doing at-most K swaps

Given two positive integers M and K, find the maximum integer possible by doing at-most K swap operations on its digits.

Examples:

Input: M = 254, K = 1
Output: 524
Explanation: Swap 5 with 2 so number becomes 524

Input: M = 254, K = 2
Output: 542
Explanation: Swap 5 with 2 so number becomes 524, Swap 4 with 2 so number becomes 542

Input: M = 68543, K = 1 
Output: 86543
Explanation: Swap 8 with 6 so number becomes 86543

Input: M = 7599, K = 2
Output: 9975
Explanation: Swap 9 with 5 so number becomes 7995, Swap 9 with 7 so number becomes 9975

Input: M = 76543, K = 1 
Output: 76543
Explanation: No swap is required.

Input: M = 129814999, K = 4
Output: 999984211
Explanation: Swap 9 with 1 so number becomes 929814991, Swap 9 with 2 so number becomes 999814291, Swap 9 with 8 so number becomes 999914281, Swap 1 with 8 so number becomes 999984211

Naive solution for the Largest number in K swaps:

The idea is to consider every digit and swap it with digits following it one at a time and see if it leads to the maximum number. The process is repeated K times. The code can be further optimized, if the current digit is swapped with a digit less than the following digit.

Follow the below steps to Implement the idea:

• Create a global variable that will store the maximum string or number.
• Define a recursive function that takes the string as a number and value of k
• Run a nested loop, the outer loop from 0 to the length of string -1, and the inner loop from i+1 to the end of the string.
• Swap the ith and jth characters and check if the string is now maximum and update the maximum string.
• Call the function recursively with parameters: string and k-1.
• Now again swap back the ith and jth character.

Below is the Implementation of the above approach:

C++

// C++ program to find maximum
// integer possible by doing
// at-most K swap operations
// on its digits.
#include <bits/stdc++.h>
using namespace std;

// Function to find maximum
// integer possible by
// doing at-most K swap
// operations on its digits
void findMaximumNum(
    string str, int k, string& max)
{
    // Return if no swaps left
    if (k == 0)
        return;

    int n = str.length();

    // Consider every digit
    for (int i = 0; i < n - 1; i++) {

        // Compare it with all digits after it
        for (int j = i + 1; j < n; j++) {
            // if digit at position i
            // is less than digit
            // at position j, swap it
            // and check for maximum
            // number so far and recurse
            // for remaining swaps
            if (str[i] < str[j]) {
                // swap str[i] with str[j]
                swap(str[i], str[j]);

                // If current num is more
                // than maximum so far
                if (str.compare(max) > 0)
                    max = str;

                // recurse of the other k - 1 swaps
                findMaximumNum(str, k - 1, max);

                // Backtrack
                swap(str[i], str[j]);
            }
        }
    }
}

// Driver code
int main()
{
    string str = "129814999";

    int k = 4;

    string max = str;
    findMaximumNum(str, k, max);

    cout << max << endl;

    return 0;
}

Java

// Java program to find maximum
// integer possible by doing
// at-most K swap operations
// on its digits.
import java.util.*;
class GFG{

static String max;
// Function to find maximum
// integer possible by
// doing at-most K swap
// operations on its digits
static void findMaximumNum(char[] str,
                           int k)
{
  // Return if no swaps left
  if (k == 0)
    return;

  int n = str.length;

  // Consider every digit
  for (int i = 0; i < n - 1; i++)
  {
    // Compare it with all digits
    // after it
    for (int j = i + 1; j < n; j++)
    {
      // if digit at position i
      // is less than digit
      // at position j, swap it
      // and check for maximum
      // number so far and recurse
      // for remaining swaps
      if (str[i] < str[j])
      {
        // swap str[i] with
        // str[j]
        char t = str[i];
        str[i] = str[j];
        str[j] = t;

        // If current num is more
        // than maximum so far
        if (String.valueOf(str).compareTo(max) > 0)
          max = String.valueOf(str);

        // recurse of the other
        // k - 1 swaps
        findMaximumNum(str, k - 1);

        // Backtrack
        char c = str[i];
        str[i] = str[j];
        str[j] = c;
      }
    }
  }
}

// Driver code
public static void main(String[] args)
{
  String str = "129814999";
  int k = 4;
  max = str;
  findMaximumNum(str.toCharArray(), k);
  System.out.print(max + "\n");
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to find maximum
# integer possible by doing at-most
# K swap operations on its digits.

# utility function to swap two
# characters of a string
def swap(string, i, j):

    return (string[:i] + string[j] +
            string[i + 1:j] +
            string[i] + string[j + 1:])

# function to find maximum integer
# possible by doing at-most K swap
# operations on its digits
def findMaximumNum(string, k, maxm):

    # return if no swaps left
    if k == 0:
        return

    n = len(string)

    # consider every digit
    for i in range(n - 1):

        # and compare it with all digits after it
        for j in range(i + 1, n):

            # if digit at position i is less than
            # digit at position j, swap it and
            # check for maximum number so far and
            # recurse for remaining swaps
            if string[i] < string[j]:

                # swap string[i] with string[j]
                string = swap(string, i, j)

                # If current num is more than
                # maximum so far
                if string > maxm[0]:
                    maxm[0] = string

                # recurse of the other k - 1 swaps
                findMaximumNum(string, k - 1, maxm)

                # backtrack
                string = swap(string, i, j)

# Driver Code
if __name__ == "__main__":
    string = "129814999"
    k = 4
    maxm = [string]
    findMaximumNum(string, k, maxm)
    print(maxm[0])

# This code is contributed
# by vibhu4agarwal

C#

// C# program to find maximum
// integer possible by doing
// at-most K swap operations
// on its digits.
using System;
class GFG{

static String max;
// Function to find maximum
// integer possible by
// doing at-most K swap
// operations on its digits
static void findMaximumNum(char[] str,
                           int k)
{
  // Return if no swaps left
  if (k == 0)
    return;

  int n = str.Length;

  // Consider every digit
  for (int i = 0; i < n - 1; i++)
  {
    // Compare it with all digits
    // after it
    for (int j = i + 1; j < n; j++)
    {
      // if digit at position i
      // is less than digit
      // at position j, swap it
      // and check for maximum
      // number so far and recurse
      // for remaining swaps
      if (str[i] < str[j])
      {
        // swap str[i] with
        // str[j]
        char t = str[i];
        str[i] = str[j];
        str[j] = t;

        // If current num is more
        // than maximum so far
        if (String.Join("", str).CompareTo(max) > 0)
          max = String.Join("", str);

        // recurse of the other
        // k - 1 swaps
        findMaximumNum(str, k - 1);

        // Backtrack
        char c = str[i];
        str[i] = str[j];
        str[j] = c;
      }
    }
  }
}

// Driver code
public static void Main(String[] args)
{
  String str = "129814999";
  int k = 4;
  max = str;
  findMaximumNum(str.ToCharArray(), k);
  Console.Write(max + "\n");
}
}

// This code is contributed by gauravrajput1

Javascript

<script>
// Javascript program to find maximum
// integer possible by doing
// at-most K swap operations
// on its digits.

let max;

// Function to find maximum
// integer possible by
// doing at-most K swap
// operations on its digits
function findMaximumNum(str,k)
{

    // Return if no swaps left
  if (k == 0)
    return;

  let n = str.length;

  // Consider every digit
  for (let i = 0; i < n - 1; i++)
  {

    // Compare it with all digits
    // after it
    for (let j = i + 1; j < n; j++)
    {
      // if digit at position i
      // is less than digit
      // at position j, swap it
      // and check for maximum
      // number so far and recurse
      // for remaining swaps
      if (str[i] < str[j])
      {

        // swap str[i] with
        // str[j]
        let t = str[i];
        str[i] = str[j];
        str[j] = t;

        // If current num is more
        // than maximum so far
        if ((str).join("")>(max) )
          max = (str).join("");

        // recurse of the other
        // k - 1 swaps
        findMaximumNum(str, k - 1);

        // Backtrack
        let c = str[i];
        str[i] = str[j];
        str[j] = c;
      }
    }
  }
}

// Driver code
let str = "129814999";
let k = 4;
max = str;
findMaximumNum(str.split(""), k);
document.write(max + "<br>");

// This code is contributed by unknown2108
</script>

Output

999984211

Time Complexity: O((N²)^k). For every digit, N² recursive calls are generated until the value of k is 0 Thus O((N²)^k).
Auxiliary Space: O(N). This is the space required to store the output string.

Find the Maximum number possible by doing at-most K swaps by swapping with the maximum element on the right:

It can be observed that to make the maximum string, the maximum digit is shifted to the front. So, instead of trying all pairs, try only those pairs where one of the elements is the maximum digit that is not yet swapped to the front. 

Follow the below steps to Implement the idea:: 

1. Create a global variable that will store the maximum string or number.
2. Define a recursive function that takes the string as a number, the value of k, and the current index.
3. Find the index of the maximum element in the range current index to end.
4. if the index of the maximum element is not equal to the current index then decrement the value of k.
5. Run a loop from the current index to the end of the array
6. If the ith digit is equal to the maximum element
7. Swap the ith and element at the current index and check if the string is now maximum and update the maximum string.
8. Call the function recursively with parameters: string and k.
9. Now again swap back the ith and element at the current index.

Below is the Implementation of the above approach:

C++

// C++ program to find maximum
// integer possible by doing
// at-most K swap operations on
// its digits.
#include <bits/stdc++.h>
using namespace std;

// Function to find maximum
// integer possible by
// doing at-most K swap operations
// on its digits
void findMaximumNum(
    string str, int k,
    string& max, int ctr)
{
    // return if no swaps left
    if (k == 0)
        return;

    int n = str.length();

    // Consider every digit after
    // the cur position
    char maxm = str[ctr];
    for (int j = ctr + 1; j < n; j++) {
        // Find maximum digit greater
        // than at ctr among rest
        if (maxm < str[j])
            maxm = str[j];
    }

    // If maxm is not equal to str[ctr],
    // decrement k
    if (maxm != str[ctr])
        --k;

    // search this maximum among the rest from behind
    //first swap the last maximum digit if it occurs more than 1 time
   //example str= 1293498 and k=1 then max string is 9293418 instead of 9213498
    for (int j = n-1; j >=ctr; j--) {
        // If digit equals maxm swap
        // the digit with current
        // digit and recurse for the rest
        if (str[j] == maxm) {
            // swap str[ctr] with str[j]
            swap(str[ctr], str[j]);

            // If current num is more than
            // maximum so far
            if (str.compare(max) > 0)
                max = str;

            // recurse other swaps after cur
            findMaximumNum(str, k, max, ctr + 1);

            // Backtrack
            swap(str[ctr], str[j]);
        }
    }
}

// Driver code
int main()
{
    string str = "129814999";
    int k = 4;

    string max = str;
    findMaximumNum(str, k, max, 0);

    cout << max << endl;

    return 0;
}

Java

// Java program to find maximum
// integer possible by doing
// at-most K swap operations on
// its digits.

import java.io.*;
class Res {
    static String max = "";
}

class Solution {
    // Function to set highest possible digits at given
    // index.
    public static void findMaximumNum(char ar[], int k,
                                      Res r)
    {
        if (k == 0)
            return;
        int n = ar.length;
        for (int i = 0; i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                // if digit at position i is less than digit
                // at position j, we swap them and check for
                // maximum number so far.
                if (ar[j] > ar[i]) {
                    char temp = ar[i];
                    ar[i] = ar[j];
                    ar[j] = temp;

                    String st = new String(ar);

                    // if current number is more than
                    // maximum so far
                    if (r.max.compareTo(st) < 0) {
                        r.max = st;
                    }
                    // calling recursive function to set the
                    // next digit.
                    findMaximumNum(ar, k - 1, r);

                    // backtracking
                    temp = ar[i];
                    ar[i] = ar[j];
                    ar[j] = temp;
                }
            }
        }
    }

    // Function to find the largest number after k swaps.
    public static void main(String[] args)
    {
        String str = "129814999";
        int k = 4;
        Res r = new Res();
        r.max = str;
        findMaximumNum(str.toCharArray(), k, r);
        //Print the answer stored in res class
        System.out.println(r.max);
    }
}

Python3

# Python3 program to find maximum
# integer possible by doing at-most
# K swap operations on its digits.

# function to find maximum integer
# possible by doing at-most K swap
# operations on its digits
def findMaximumNum(string, k, maxm, ctr):

    # return if no swaps left
    if k == 0:
        return

    n = len(string)
    # Consider every digit after
    # the cur position
    mx = string[ctr]

    for i in range(ctr+1,n):
        # Find maximum digit greater
        # than at ctr among rest
        if int(string[i]) > int(mx):
            mx=string[i]

    # If maxm is not equal to str[ctr],
    # decrement k
    if(mx!=string[ctr]):
        k=k-1

    # search this maximum among the rest from behind
    # first swap the last maximum digit if it occurs more than 1 time
    # example str= 1293498 and k=1 then max string is 9293418 instead of 9213498
    for i in range(ctr,n):
        # If digit equals maxm swap
        # the digit with current
        # digit and recurse for the rest
        if(string[i]==mx):
            # swap str[ctr] with str[j]
            string[ctr], string[i] = string[i], string[ctr]
            new_str = "".join(string)
            # If current num is more than
            # maximum so far
            if int(new_str) > int(maxm[0]):
                  maxm[0] = new_str

            # recurse of the other k - 1 swaps
            findMaximumNum(string, k , maxm, ctr+1)

            # backtrack
            string[ctr], string[i] = string[i], string[ctr]

# Driver Code
if __name__ == "__main__":
    string = "129814999"
    k = 4
    maxm = [string]
    string = [char for char in string]
    findMaximumNum(string, k, maxm, 0)
    print(maxm[0])

# This code is contributed Aarti_Rathi

C#

// C# program to find maximum
// integer possible by doing
// at-most K swap operations on
// its digits.
using System;

class Res {
  public String max = "";
}

public class Solution {
  // Function to set highest possible digits at given
  // index.
  static void findMaximumNum(char []ar, int k,
                             Res r)
  {
    if (k == 0)
      return;
    int n = ar.Length;
    for (int i = 0; i < n - 1; i++)
    {
      for (int j = i + 1; j < n; j++)
      {
        // if digit at position i is less than digit
        // at position j, we swap them and check for
        // maximum number so far.
        if (ar[j] > ar[i]) {
          char temp = ar[i];
          ar[i] = ar[j];
          ar[j] = temp;

          String st = new String(ar);

          // if current number is more than
          // maximum so far
          if (r.max.CompareTo(st) < 0) {
            r.max = st;
          }

          // calling recursive function to set the
          // next digit.
          findMaximumNum(ar, k - 1, r);

          // backtracking
          temp = ar[i];
          ar[i] = ar[j];
          ar[j] = temp;
        }
      }
    }
  }

  // Function to find the largest number after k swaps.
  public static void Main(String[] args)
  {
    String str = "129814999";
    int k = 4;
    Res r = new Res();
    r.max = str;
    findMaximumNum(str.ToCharArray(), k, r);

    // Print the answer stored in res class
    Console.WriteLine(r.max);
  }
}

// This code is contributed by shikhasingrajput

Javascript

function findMaximumNum(string, k, maxm, ctr) {
  // return if no swaps left
  if (k == 0) {
    return;
  }

  const n = string.length;
  // Consider every digit after
  // the cur position
  let mx = string[ctr];

  for (let i = ctr + 1; i < n; i++) {
    // Find maximum digit greater
    // than at ctr among rest
    if (parseInt(string[i]) > parseInt(mx)) {
      mx = string[i];
    }
  }

  // If maxm is not equal to str[ctr],
  // decrement k
  if (mx != string[ctr]) {
    k = k - 1;
  }

  // search this maximum among the rest from behind
  // first swap the last maximum digit if it occurs more than 1 time
  // example str= 1293498 and k=1 then max string is 9293418 instead of 9213498
  for (let i = ctr; i < n; i++) {
    // If digit equals maxm swap
    // the digit with current
    // digit and recurse for the rest
    if (string[i] == mx) {
      // swap str[ctr] with str[j]
      [string[ctr], string[i]] = [string[i], string[ctr]];
      const new_str = string.join("");
      // If current num is more than
      // maximum so far
      if (parseInt(new_str) > parseInt(maxm[0])) {
        maxm[0] = new_str;
      }
      // recurse of the other k - 1 swaps
      findMaximumNum(string, k, maxm, ctr + 1);

      // backtrack
      [string[ctr], string[i]] = [string[i], string[ctr]];
    }
  }
}

// Driver Code
const string = "129814999";
const k = 4;
const maxm = [string];
const strArr = string.split("");
findMaximumNum(strArr, k, maxm, 0);
console.log(maxm[0]);

Output

999984211

Time Complexity: O(N^k), For every recursive call N recursive calls are generated until the value of k is 0, Thus O((N^k).
Auxiliary Space: O(N). The space required to store the output string.

Exercise:

• Find the minimum integer possible by doing at least K swap operations on its digits.
• Find the maximum/minimum integer possible by doing exactly K swap operations on its digits.

This article is contributed by Aarti Rathi and Aditya Goel.If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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