Form lexicographically smallest string with minimum replacements having equal number of 0s, 1s and 2s

Given a string str of length n (n is a multiple of 3) containing characters only from the set {0, 1, 2}. The task is to update the string such that each character has the same frequency with minimum number of operations. In a single operation, any character of the string can be replaced with any other character (also from the same set). If there are multiple strings possible then print the lexicographically smallest one.

Examples:

Input: str = “000000”
Output: 001122
Replace 3rd and 4th ‘0’ with ‘1’ and 5th and 6th ‘0’ with ‘2’ such that given condition is satisfied and it forms lexicographically smallest string



Input: str = “211200”
Output: 211200
The string already has equal number of 0s, 1s and 2s, hence there is no need to perform any operation.

Approach: This problem can be solved using greedy approach. We need only n / 3 number of characters of each type where n is the size of the string. Iterate over the string and count the number of characters of each type. Again, iterate over the string and now check if the current character’s count is equal to n / 3 then there is no need to perform any operation on the current character.
However, if count(currentChar) != n / 3 then we may need to perform replacement operation depending on the value of the character in such a way that it maintains smallest lexicographical order as follows:

  • If the current character is zero(0) and we have already processed required number of zeroes, then this character needs to be replaced with either one(1) if count[1] < (n / 3) or with two(1) if count[2] < (n / 3).
  • If the current character is one(1), then we can either replace it with zero(0) if count[0] < (n / 3) or with two(2) if count[2] < (n / 3) and we have already processed required number of ones to maintain lowest lexicographical order
  • If the current character is two(2), then we can either replace it with zero(0) if count[0] < (n / 3) or with two(2) if count[2] < (n / 3).

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;
  
// Function that returns the modified lexicographically
// smallest string after performing minimum number
// of given operations
string formStringMinOperations(string s)
{
    // Stores the initial frequencies of characters
    // 0s, 1s and 2s
    int count[3] = { 0 };
    for (auto& c : s)
        count++;
  
    // Stores number of processed characters upto that
    // point of each type
    int processed[3] = { 0 };
  
    // Required number of characters of each type
    int reqd = (int)s.size() / 3;
    for (int i = 0; i < s.size(); i++) {
  
        // If the current type has already reqd
        // number of characters, no need to perform
        // any operation
        if (count[s[i] - '0'] == reqd)
            continue;
  
        // Process all 3 cases
        if (s[i] == '0' && count[0] > reqd &&
                     processed[0] >= reqd) {
  
            // Check for 1 first
            if (count[1] < reqd) {
                s[i] = '1';
                count[1]++;
                count[0]--;
            }
  
            // Else 2
            else if (count[2] < reqd) {
                s[i] = '2';
                count[2]++;
                count[0]--;
            }
        }
  
        // Here we need to check processed[1] only
        // for 2 since 0 is less than 1 and we can
        // replace it anytime
        if (s[i] == '1' && count[1] > reqd) {
            if (count[0] < reqd) {
                s[i] = '0';
                count[0]++;
                count[1]--;
            }
            else if (count[2] < reqd &&
                    processed[1] >= reqd) {
                s[i] = '2';
                count[2]++;
                count[1]--;
            }
        }
  
        // Here we can replace 2 with 0 and 1 anytime
        if (s[i] == '2' && count[2] > reqd) {
            if (count[0] < reqd) {
                s[i] = '0';
                count[0]++;
                count[2]--;
            }
            else if (count[1] < reqd) {
                s[i] = '1';
                count[1]++;
                count[2]--;
            }
        }
  
        // keep count of processed characters of each
        // type
        processed[s[i] - '0']++;
    }
    return s;
}
  
// Driver Code
int main()
{
    string s = "011200";
    cout << formStringMinOperations(s);
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG 
{
  
    // Function that returns the 
    // modified lexicographically
    // smallest String after 
    // performing minimum number
    // of given operations
    static String formStringMinOperations(char[] s) 
    {
          
        // Stores the initial frequencies 
        // of characters 0s, 1s and 2s
        int count[] = new int[3];
        for (char c : s) 
        {
            count[(int)c - 48] += 1;
        }
  
        // Stores number of processed characters 
        // upto that point of each type
        int processed[] = new int[3];
  
        // Required number of characters of each type
        int reqd = (int) s.length / 3;
        for (int i = 0; i < s.length; i++) 
        {
  
            // If the current type has already 
            // reqd number of characters, no 
            // need to perform any operation
            if (count[s[i] - '0'] == reqd) 
            {
                continue;
            }
  
            // Process all 3 cases
            if (s[i] == '0' && count[0] > reqd
                    && processed[0] >= reqd) 
            {
  
                // Check for 1 first
                if (count[1] < reqd) 
                {
                    s[i] = '1';
                    count[1]++;
                    count[0]--;
                
                  
                // Else 2
                else if (count[2] < reqd) 
                {
                    s[i] = '2';
                    count[2]++;
                    count[0]--;
                }
            }
  
            // Here we need to check processed[1] only
            // for 2 since 0 is less than 1 and we can
            // replace it anytime
            if (s[i] == '1' && count[1] > reqd) 
            {
                if (count[0] < reqd) 
                {
                    s[i] = '0';
                    count[0]++;
                    count[1]--;
                
                else if (count[2] < reqd
                        && processed[1] >= reqd) 
                {
                    s[i] = '2';
                    count[2]++;
                    count[1]--;
                }
            }
  
            // Here we can replace 2 with 0 and 1 anytime
            if (s[i] == '2' && count[2] > reqd) 
            {
                if (count[0] < reqd)
                {
                    s[i] = '0';
                    count[0]++;
                    count[2]--;
                
                else if (count[1] < reqd) 
                {
                    s[i] = '1';
                    count[1]++;
                    count[2]--;
                }
            }
  
            // keep count of processed 
            // characters of each type
            processed[s[i] - '0']++;
        }
        return String.valueOf(s);
    }
  
    // Driver Code
    public static void main(String[] args) 
    {
        String s = "011200";
        System.out.println(formStringMinOperations(s.toCharArray()));
    }
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 implementation of the approach 
import math
  
# Function that returns the modified 
# lexicographically smallest string after 
# performing minimum number of given operations 
def formStringMinOperations(ss):
      
    # Stores the initial frequencies of 
    # characters 0s, 1s and 2s 
    count = [0] * 3;
    s = list(ss);
    for i in range(len(s)): 
        count[ord(s[i]) - ord('0')] += 1
  
    # Stores number of processed characters 
    # upto that point of each type 
    processed = [0] * 3
  
    # Required number of characters of each type 
    reqd = math.floor(len(s) / 3); 
    for i in range(len(s)): 
  
        # If the current type has already reqd 
        # number of characters, no need to 
        # perform any operation 
        if (count[ord(s[i]) - ord('0')] == reqd): 
            continue
  
        # Process all 3 cases 
        if (s[i] == '0' and count[0] > reqd and
                            processed[0] >= reqd):
  
            # Check for 1 first 
            if (count[1] < reqd):
                s[i] = '1'
                count[1] += 1
                count[0] -= 1
  
            # Else 2 
            elif (count[2] < reqd): 
                s[i] = '2'
                count[2] += 1
                count[0] -= 1
  
        # Here we need to check processed[1] only 
        # for 2 since 0 is less than 1 and we can 
        # replace it anytime 
        if (s[i] == '1' and count[1] > reqd):
            if (count[0] < reqd):
                s[i] = '0'
                count[0] += 1
                count[1] -= 1
            elif (count[2] < reqd and 
                  processed[1] >= reqd):
                s[i] = '2'
                count[2] += 1
                count[1] -= 1
  
        # Here we can replace 2 with 0 and 1 anytime 
        if (s[i] == '2' and count[2] > reqd):
            if (count[0] < reqd):
                s[i] = '0'
                count[0] += 1
                count[2] -= 1
            elif (count[1] < reqd):
                s[i] = '1'
                count[1] += 1
                count[2] -= 1
  
        # keep count of processed characters 
        # of each type 
        processed[ord(s[i]) - ord('0')] += 1
    return ''.join(s); 
  
# Driver Code 
s = "011200"
print(formStringMinOperations(s)); 
  
# This code is contributed by mits

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C#

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// C# implementation of the approach
using System;
  
class GFG 
{
  
    // Function that returns the 
    // modified lexicographically
    // smallest String after 
    // performing minimum number
    // of given operations
    static String formStringMinOperations(char[] s) 
    {
          
        // Stores the initial frequencies 
        // of characters 0s, 1s and 2s
        int []count = new int[3];
        foreach (char c in s) 
        {
            count[(int)c - 48] += 1;
        }
  
        // Stores number of processed characters 
        // upto that point of each type
        int []processed = new int[3];
  
        // Required number of characters of each type
        int reqd = (int) s.Length / 3;
        for (int i = 0; i < s.Length; i++) 
        {
  
            // If the current type has already 
            // reqd number of characters, no 
            // need to perform any operation
            if (count[s[i] - '0'] == reqd) 
            {
                continue;
            }
  
            // Process all 3 cases
            if (s[i] == '0' && count[0] > reqd
                    && processed[0] >= reqd) 
            {
  
                // Check for 1 first
                if (count[1] < reqd) 
                {
                    s[i] = '1';
                    count[1]++;
                    count[0]--;
                
                  
                // Else 2
                else if (count[2] < reqd) 
                {
                    s[i] = '2';
                    count[2]++;
                    count[0]--;
                }
            }
  
            // Here we need to check processed[1] only
            // for 2 since 0 is less than 1 and we can
            // replace it anytime
            if (s[i] == '1' && count[1] > reqd) 
            {
                if (count[0] < reqd) 
                {
                    s[i] = '0';
                    count[0]++;
                    count[1]--;
                
                else if (count[2] < reqd
                        && processed[1] >= reqd) 
                {
                    s[i] = '2';
                    count[2]++;
                    count[1]--;
                }
            }
  
            // Here we can replace 2 with 0 and 1 anytime
            if (s[i] == '2' && count[2] > reqd) 
            {
                if (count[0] < reqd)
                {
                    s[i] = '0';
                    count[0]++;
                    count[2]--;
                
                else if (count[1] < reqd) 
                {
                    s[i] = '1';
                    count[1]++;
                    count[2]--;
                }
            }
  
            // keep count of processed 
            // characters of each type
            processed[s[i] - '0']++;
        }
        return String.Join("",s);
    }
  
    // Driver Code
    public static void Main(String[] args) 
    {
        String s = "011200";
        Console.WriteLine(formStringMinOperations(s.ToCharArray()));
    }
}
  
// This code is contributed by Rajput-Ji

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PHP

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<?php
// PHP implementation of the approach 
  
// Function that returns the modified lexicographically 
// smallest string after performing minimum number 
// of given operations 
function formStringMinOperations($s
    // Stores the initial frequencies of 
    // characters 0s, 1s and 2s 
    $count = array_fill(0, 3, 0);
      
    for ($i = 0; $i < strlen($s) ; $i++) 
        $count[$s[$i] - '0']++; 
  
    // Stores number of processed characters 
    // upto that point of each type 
    $processed = array_fill(0, 3, 0); 
  
    // Required number of characters of each type 
    $reqd = floor(strlen($s) / 3); 
    for ($i = 0; $i < strlen($s); $i++) 
    
  
        // If the current type has already reqd 
        // number of characters, no need to 
        // perform any operation 
        if ($count[$s[$i] - '0'] == $reqd
            continue
  
        // Process all 3 cases 
        if ($s[$i] == '0' && $count[0] > $reqd && 
                             $processed[0] >= $reqd)
        
  
            // Check for 1 first 
            if ($count[1] < $reqd)
            
                $s[$i] = '1'
                $count[1]++; 
                $count[0]--; 
            
  
            // Else 2 
            else if ($count[2] < $reqd
            
                $s[$i] = '2'
                $count[2]++; 
                $count[0]--; 
            
        
  
        // Here we need to check processed[1] only 
        // for 2 since 0 is less than 1 and we can 
        // replace it anytime 
        if ($s[$i] == '1' && $count[1] > $reqd
        
            if ($count[0] < $reqd
            
                $s[$i] = '0'
                $count[0]++; 
                $count[1]--; 
            
            else if (count[2] < $reqd && 
                                $processed[1] >= $reqd
            
                $s[$i] = '2'
                $count[2]++; 
                $count[1]--; 
            
        
  
        // Here we can replace 2 with 0 and 1 anytime 
        if ($s[$i] == '2' && $count[2] > $reqd)
        
            if ($count[0] < $reqd)
            
                $s[$i] = '0'
                $count[0]++; 
                $count[2]--; 
            
            else if ($count[1] < $reqd
            
                $s[$i] = '1'
                $count[1]++; 
                $count[2]--; 
            
        
  
        // keep count of processed characters 
        // of each type 
        $processed[$s[$i] - '0']++; 
    
    return $s
  
// Driver Code 
$s = "011200"
echo formStringMinOperations($s); 
  
// This code is contributed by Ryuga
?>

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Output:

011202


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