Maximize count of unique array elements by incrementing array elements by K

Last Updated : 17 May, 2021
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Given an array arr[] consisting of N integers and an integer K, the task is to find the maximum number of unique elements possible by increasing any array element by K only once.

Examples: 

Input: arr[] = {0, 2, 4, 3, 4}, K = 1
Output: 5
Explanation:
Increase arr[2] ( = 4) by K ( = 1). Therefore, new array is {0, 2, 4, 3, 5} which has 5 unique elements.

Input: arr[] = {2, 3, 2, 4, 5, 5, 7, 4}, K = 2
Output: 7
Explanation: 
Increase 4 by 2 = 6. 
Increase element 7 by 2 = 9
Increase 5 by 2 = 7. 
The new array is {2, 3, 2, 4, 5, 7, 9, 6} which contains 7 unique elements.

Approach: The idea to solve this problem is to store the frequency of elements of the array in a Map and change the array elements accordingly to get unique elements in the array after incrementing any values by K. Follow the steps below to solve the problem:

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 maximum unique
// elements in array after incrementing
// any element by K
void maxDifferent(int arr[], int N, int K)
{
    // Stores the count of element
    // in array
    map<int, int> M;

    // Traverse the array
    for (int i = 0; i < N; i++) {

        // Increase the counter of
        // the array element by 1
        M[arr[i]]++;
    }

    // Traverse the map
    for (auto it = M.begin();
         it != M.end(); it++) {

        // Extract the current element
        int current_element = it->first;

        // Number of times the current
        // element is present in array
        int count = it->second;

        // If element is present only
        // once, then do not change it
        if (count == 1)
            continue;

        // If the count > 1 then change
        // one of the same current
        // elements to (current_element + K)
        // and increase its count by 1
        M[current_element + K]++;
    }

    // The size of the map is the
    // required answer
    cout << M.size();
}

// Driver Code
int main()
{
    int arr[] = { 2, 3, 2, 4, 5, 5, 7, 4 };
    int K = 2;
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function Call
    maxDifferent(arr, N, K);

    return 0;
}
Java 
// Java program for the above approach
import java.io.*;
import java.util.*;

class GFG{

// Function to find the maximum unique
// elements in array after incrementing
// any element by K
static void maxDifferent(int arr[], int N, int K)
{
    
    // Stores the count of element
    // in array
    HashMap<Integer, 
            Integer> M = new HashMap<Integer, 
                                     Integer>();

    // Traverse the array
    for(int i = 0; i < N; i++) 
    {
        
        // Increase the counter of
        // the array element by 1
        Integer count = M.get(arr[i]);
        
        if (count == null)
        {
            M.put(arr[i], 1);
        }
        else 
        {
            M.put(arr[i], count + 1);
        }
    }

    // Iterator itr = M.entrySet().iterator();
    Iterator<Map.Entry<Integer, 
                       Integer>> itr = M.entrySet().iterator();

    int[] ar1 = new int[N];

    // Traverse the map
    while (itr.hasNext()) 
    {
        Map.Entry<Integer, Integer> Element = itr.next();

        // Extract the current element
        int current_element = (int)Element.getKey();

        // Number of times the current
        // element is present in array
        int count = (int)Element.getValue();

        // If element is present only
        // once, then do not change it
        if (count == 1)
            continue;

        // If the count > 1 then change
        // one of the same current
        // elements to (current_element + K)
        // and increase its count by 1
        ar1[current_element + K]++;
    }

    for(int i = 0; i < N; i++) 
    {
        if (ar1[i] >= 0)
        {
            Integer count = M.get(ar1[i]);
            
              if (count == null)
              {
                  M.put(ar1[i], 1);
            }
            else
            {
                M.put(ar1[i], count + 1);
            }
        }
    }

    // The size of the map is the
    // required answer
    System.out.println(M.size());
}

// Driver Code
public static void main(String[] args)
{
    int arr[] = { 2, 3, 2, 4, 5, 5, 7, 4 };
    int K = 2;
    int N = arr.length;
    
    // Function Call
    maxDifferent(arr, N, K);
}
}

// This code is contributed by Dharanendra L V
Python3 
# Python3 program for the above approach

# Function to find the maximum unique
# elements in array after incrementing
# any element by K
def maxDifferent(arr, N, K):
    
    # Stores the count of element
    # in array
    M = {}

    # Traverse the array
    for i in range(N):

        # Increase the counter of
        # the array element by 1
        M[arr[i]] = M.get(arr[i], 0) + 1

    # Traverse the map
    for it in list(M.keys()):

        # Extract the current element
        current_element = it

        # Number of times the current
        # element is present in array
        count = M[it]

        # If element is present only
        # once, then do not change it
        if (count == 1):
            continue

        # If the count > 1 then change
        # one of the same current
        # elements to (current_element + K)
        # and increase its count by 1
        M[current_element + K] = M.get(current_element, 0) + 1

    # The size of the map is the
    # required answer
    print(len(M))

# Driver Code
if __name__ == '__main__':
    arr=[2, 3, 2, 4, 5, 5, 7, 4]
    K = 2
    N = len(arr)

    # Function Call
    maxDifferent(arr, N, K)

    # This code is contributed by mohit kumar 29
C# 
// C# program for the above approach
using System;
using System.Collections.Generic;

public class GFG
{

// Function to find the maximum unique
// elements in array after incrementing
// any element by K
static void maxDifferent(int []arr, int N, int K)
{
    
    // Stores the count of element
    // in array
    Dictionary<int, 
            int> M = new Dictionary<int, 
                                     int>();

    // Traverse the array
    for(int i = 0; i < N; i++) 
    {
        
        // Increase the counter of
        // the array element by 1
        int count = M.ContainsKey(arr[i]) ? M[arr[i]] : 0;
        
        if (count == 0)
        {
            M.Add(arr[i], 1);
        }
        else 
        {
            M[arr[i]] = count + 1;
        }
    }

    int[] ar1 = new int[N];

    // Traverse the map
    foreach(KeyValuePair<int, int> Element in M) 
    {

        // Extract the current element
        int current_element = (int)Element.Key;

        // Number of times the current
        // element is present in array
        int count = (int)Element.Value;

        // If element is present only
        // once, then do not change it
        if (count == 1)
            continue;

        // If the count > 1 then change
        // one of the same current
        // elements to (current_element + K)
        // and increase its count by 1
        ar1[current_element + K]++;
    }

    for(int i = 0; i < N; i++) 
    {
        if (ar1[i] >= 0)
        {
            int count = M.ContainsKey(ar1[i]) ? M[ar1[i]] : 0;            
              if (count == 0)
              {
                  M.Add(ar1[i], 1);
            }
            else
            {
                M[ar1[i]] = count + 1;
            }
        }
    }

    // The size of the map is the
    // required answer
    Console.WriteLine(M.Count);
}

// Driver Code
public static void Main(String[] args)
{
    int []arr = { 2, 3, 2, 4, 5, 5, 7, 4 };
    int K = 2;
    int N = arr.Length;
    
    // Function Call
    maxDifferent(arr, N, K);
}
}

// This code contributed by shikhasingrajput
JavaScript 
<script>

// JavaScript program for the above approach

// Function to find the maximum unique
// elements in array after incrementing
// any element by K
function maxDifferent(arr, N, K)
{
    // Stores the count of element
    // in array
    var M = new Map();

    // Traverse the array
    for (var i = 0; i < N; i++) {

        // Increase the counter of
        // the array element by 1
        if(M.has(arr[i]))
        {
            M.set(arr[i], M.get(arr[i])+1);
        }
        else
        {
            M.set(arr[i],1);
        }
    }

    M.forEach((value, key) => {

        // Extract the current element
        var current_element = key;

        // Number of times the current
        // element is present in array
        var count = value;

        // If element is present only
        // once, then do not change it
        if (count != 1)
        {

        // If the count > 1 then change
        // one of the same current
        // elements to (current_element + K)
        // and increase its count by 1
        if(M.has(current_element+K))
        {
            M.set(current_element+K, 
            M.get(current_element+K)+1)
        }
        else
        {
            M.set(current_element+K,1);
        }
        
        }
    });

    // The size of the map is the
    // required answer
    document.write( M.size);
}

// Driver Code
var arr = [2, 3, 2, 4, 5, 5, 7, 4];
var K = 2;
var N = arr.length;

// Function Call
maxDifferent(arr, N, K);

</script>

Output: 
7

 

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


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