Largest even number that can be formed by any number of swaps

Given an integer N in the form of string, the task is to find the largest even number from the given number when you are allowed to do any number of swaps (swapping the digits of the number). If no even number can be formed then print -1.

Examples:

Input: N = 1324
Output: 4312

Input: N = 135
Output: -1
No even number can be formed using odd digits.



Approach: Sort the string in descending order then we will get the largest number possible with the given digit but it may or may not be an even number. In order to make it even (if it not already), an even digit from the number must be swapped with the last digit and in order to maximize the even number the even digit which is to be swapped must the smallest even digit from the number.
Note that the sorting can be done in linear time using frequency array for the digits of the number as the number of distinct elements that are need to be sorted can be at most 10 in the worst case.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
const int MAX = 10;
  
// Function to return the maximum
// even number that can be formed
// with any number of digit swaps
string getMaxEven(string str, int len)
{
  
    // To store the frequencies of
    // all the digits
    int freq[MAX] = { 0 };
  
    // To store the minimum even digit
    // and the minimum overall digit
    int i, minEvenDigit = MAX, minDigit = MAX;
    for (i = 0; i < len; i++) {
        int digit = str[i] - '0';
        freq[digit]++;
  
        // If digit is even then update
        // the minimum even digit
        if (digit % 2 == 0)
            minEvenDigit = min(digit, minEvenDigit);
  
        // Update the overall minimum digit
        minDigit = min(digit, minDigit);
    }
  
    // If there is no even digit then
    // it is not possible to generate
    // an even number with swaps
    if (minEvenDigit == MAX)
        return "-1";
  
    // Decrease the frequency of the
    // digits that need to be swapped
    freq[minEvenDigit]--;
    freq[minDigit]--;
  
    i = 0;
    // Take every digit starting from the maximum
    // in order to maximize the number
    for (int j = MAX - 1; j >= 0; j--) {
  
        // Take current digit number of times
        // it appeared in the original number
        for (int k = 0; k < freq[j]; k++)
            str[i++] = (char)(j + '0');
  
        // If current digit equals to the
        // minimum even digit then one instance of it
        // needs to be swapped with the minimum overall digit
        // i.e. append the minimum digit here
        if (j == minEvenDigit)
            str[i++] = (char)(minDigit + '0');
    }
  
    // Append once instance of the minimum
    // even digit in the end to make the number even
    str[i] = (char)(minEvenDigit + '0');
  
    return str;
}
  
// Driver code
int main()
{
    string str = "1023422";
    int len = str.length();
  
    cout << getMaxEven(str, len);
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG 
{
      
    static int MAX = 10;
      
    // Function to return the maximum
    // even number that can be formed
    // with any number of digit swaps
    static String getMaxEven(char[] str, int len)
    {
      
        // To store the frequencies of
        // all the digits
        int []freq = new int[MAX];
      
        // To store the minimum even digit
        // and the minimum overall digit
        int i, minEvenDigit = MAX, minDigit = MAX;
        for (i = 0; i < len; i++)
        {
            int digit = str[i] - '0';
            freq[digit]++;
      
            // If digit is even then update
            // the minimum even digit
            if (digit % 2 == 0)
                minEvenDigit = Math.min(digit, minEvenDigit);
      
            // Update the overall minimum digit
            minDigit = Math.min(digit, minDigit);
        }
      
        // If there is no even digit then
        // it is not possible to generate
        // an even number with swaps
        if (minEvenDigit == MAX)
            return "-1";
      
        // Decrease the frequency of the
        // digits that need to be swapped
        freq[minEvenDigit]--;
        freq[minDigit]--;
      
        i = 0;
          
        // Take every digit starting from the maximum
        // in order to maximize the number
        for (int j = MAX - 1; j >= 0; j--)
        {
      
            // Take current digit number of times
            // it appeared in the original number
            for (int k = 0; k < freq[j]; k++)
                str[i++] = (char)(j + '0');
      
            // If current digit equals to the
            // minimum even digit then one instance of it
            // needs to be swapped with the minimum overall digit
            // i.e. append the minimum digit here
            if (j == minEvenDigit)
                str[i++] = (char)(minDigit + '0');
        }
      
        // Append once instance of the minimum
        // even digit in the end to make the number even
        str[i-1] = (char)(minEvenDigit + '0');
      
        return String.valueOf(str);
    }
      
    // Driver code
    public static void main(String[] args) 
    {
        char[] str = "1023422".toCharArray();
        int len = str.length;
      
        System.out.println(getMaxEven(str, len));
    }
}
  
/* This code contributed by PrinciRaj1992 */

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Python3

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# Python3 implementation of the approach 
  
MAX = 10
  
# Function to return the maximum 
# even number that can be formed 
# with any number of digit swaps 
def getMaxEven(string, length) :
      
    string = list(string)
      
    # To store the frequencies of 
    # all the digits
    freq = [0]*MAX
      
    # To store the minimum even digit
    # and the minimum overall digit 
    minEvenDigit = MAX;
    minDigit = MAX
    for i in range(length) :
        digit = ord(string[i]) - ord('0');
        freq[digit] += 1;
          
        # If digit is even then update 
        # the minimum even digit
        if (digit % 2 == 0) :
            minEvenDigit = min(digit, minEvenDigit);
          
        # Update the overall minimum digit 
        minDigit = min(digit, minDigit);
          
    # If there is no even digit then 
    # it is not possible to generate 
    # an even number with swaps 
    if (minEvenDigit == MAX) :
        return "-1"
          
    # Decrease the frequency of the 
    # digits that need to be swapped 
    freq[minEvenDigit] -= 1;
    freq[minDigit] -= 1;
      
    i = 0;
      
    # Take every digit starting from the maximum
    # in order to maximize the number 
    for j in range(MAX - 1, -1, -1) :
          
        # Take current digit number of times
        # it appeared in the original number
        for k in range(freq[j]) :
            string[i] = chr(j + ord('0'));
            i += 1
          
        # If current digit equals to the 
        # minimum even digit then one instance of it 
        # needs to be swapped with the minimum overall digit 
        # i.e. append the minimum digit here
        if (j == minEvenDigit) :
            string[i] = chr(minDigit + ord('0'));
            i += 1
      
    # Append once instance of the minimum
    # even digit in the end to make the number even
    #string.append(chr(minEvenDigit + ord('0'))); 
      
    return "".join(string); 
  
  
# Driver code 
if __name__ == "__main__"
    string = "1023422"
    length = len(string); 
  
    print(getMaxEven(string, length)); 
  
# This code is contributed by AnkitRai01

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C#

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// C# implementation of the approach
using System;
      
class GFG 
{
       
    static int MAX = 10;
       
    // Function to return the maximum
    // even number that can be formed
    // with any number of digit swaps
    static String getMaxEven(char[] str, int len)
    {
       
        // To store the frequencies of
        // all the digits
        int []freq = new int[MAX];
       
        // To store the minimum even digit
        // and the minimum overall digit
        int i, minEvenDigit = MAX, minDigit = MAX;
        for (i = 0; i < len; i++)
        {
            int digit = str[i] - '0';
            freq[digit]++;
       
            // If digit is even then update
            // the minimum even digit
            if (digit % 2 == 0)
                minEvenDigit = Math.Min(digit, minEvenDigit);
       
            // Update the overall minimum digit
            minDigit = Math.Min(digit, minDigit);
        }
       
        // If there is no even digit then
        // it is not possible to generate
        // an even number with swaps
        if (minEvenDigit == MAX)
            return "-1";
       
        // Decrease the frequency of the
        // digits that need to be swapped
        freq[minEvenDigit]--;
        freq[minDigit]--;
       
        i = 0;
           
        // Take every digit starting from the maximum
        // in order to maximize the number
        for (int j = MAX - 1; j >= 0; j--)
        {
       
            // Take current digit number of times
            // it appeared in the original number
            for (int k = 0; k < freq[j]; k++)
                str[i++] = (char)(j + '0');
       
            // If current digit equals to the
            // minimum even digit then one instance of it
            // needs to be swapped with the minimum overall digit
            // i.e. append the minimum digit here
            if (j == minEvenDigit)
                str[i++] = (char)(minDigit + '0');
        }
       
        // Append once instance of the minimum
        // even digit in the end to make the number even
        str[i-1] = (char)(minEvenDigit + '0');
       
        return String.Join("",str);
    }
       
    // Driver code
    public static void Main(String[] args) 
    {
        char[] str = "1023422".ToCharArray();
        int len = str.Length;
       
        Console.WriteLine(getMaxEven(str, len));
    }
}
  
// This code has been contributed by 29AjayKumar

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Output:

4322210

Time Complexity: O(n)



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