Partition an array into two subsets with equal count of unique elements

Given an array arr[] consisting of N integers, the task is to partition the array into two subsets such that the count of unique elements in both the subsets is the same and for each element, print 1 if that element belongs to the first subset. Otherwise, print 2. If it is not possible to do such a partition, then print “-1”.

Examples:

Input: arr[] = {1, 1, 2, 3, 4, 4}
Output: 1 1 1 2 1 1
Explanation: Consider the first and the second subset of the partition of the array as {1, 1, 2, 4 4} and {3}. Now, the above partition of subsets has equal count of distinct elements..

Input: arr[] = {1, 1, 2, 2, 3}
Output: -1

Naive Approach: The given problem can be solved by generating all possible partition of the array elements into two subsets and if there exists any such partition whose count of distinct elements are the same, then print 1 and 2 according to the respective set array elements belongs to. Otherwise, print “-1” as there doesn’t exist any such possible partition of the array.

Time Complexity: O(N*2^N)
Auxiliary Space: O(N)

Efficient Approach: The above approach can also be optimized by finding the frequency of unique array elements if the frequency is odd, then there no such possible partition. Otherwise, print the partition of the subset accordingly. Follow the steps below to solve the problem:

• Initialize a Map, say M to store the frequency of all array elements.
• Initialize the array, say ans[] that stores the subset number where each array element belongs to.
• Find the count of the unique elements in the array by count the element having frequency 1 in the map M. Let this count be C.
• If the value of C is even, then move half of these elements into the first subset by marking those elements as 1 and rest all elements as 2 in the array ans[].
• Otherwise, check if there exist any element having a frequency greater than 2, then shift one instance of that element to the second subset. Otherwise, print “-1”.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to partition the array into
// two subsets such that count of unique
// elements in both subsets is the same
void arrayPartition(int a[], int n)
{
    // Stores the subset number for
    // each array elements
    int ans[n];

    // Stores the count of unique
    // array elements
    int cnt = 0;
    int ind, flag = 0;

    // Stores the frequency of elements
    map<int, int> mp;

    // Traverse the array
    for (int i = 0; i < n; i++) {
        mp[a[i]]++;
    }

    // Count of elements having a
    // frequency of 1
    for (int i = 0; i < n; i++) {

        if (mp[a[i]] == 1)
            cnt++;

        // Check if there exists any
        // element with frequency > 2
        if (mp[a[i]] > 2 && flag == 0) {
            flag = 1;
            ind = i;
        }
    }

    // Count of elements needed to
    // have frequency exactly 1 in
    // each subset
    int p = (cnt + 1) / 2;
    int ans1 = 0;

    // Initialize all values in the
    /// array ans[] as 1
    for (int i = 0; i < n; i++)
        ans[i] = 1;

    // Traverse the array ans[]
    for (int i = 0; i < n; i++) {

        // This array element is a
        // part of first subset
        if (mp[a[i]] == 1 && ans1 < p) {
            ans[i] = 1;
            ans1++;
        }

        // Half array elements with
        // frequency 1 are part of
        // the second subset
        else if (mp[a[i]] == 1) {
            ans[i] = 2;
        }
    }

    // If count of elements is exactly
    // 1 are odd and has no element
    // with frequency > 2
    if (cnt % 2 == 1 && flag == 0) {
        cout << -1 << endl;
        return;
    }

    // If count of elements that occurs
    // exactly once are even
    if (cnt % 2 == 0) {

        // Print the result
        for (int i = 0; i < n; i++) {
            cout << ans[i] << " ";
        }
    }

    // If the count of elements has
    // exactly 1 frequency are odd
    // and there is an element with
    // frequency greater than 2
    else {

        // Print the result
        for (int i = 0; i < n; i++) {
            if (ind == i)
                cout << 2 << " ";
            else
                cout << ans[i] << " ";
        }
    }
}

// Driver Codea
int main()
{
    int arr[] = { 1, 1, 2, 3, 4, 4 };
    int N = sizeof(arr) / sizeof(arr[0]);
    arrayPartition(arr, N);

    return 0;
}

Java

// Java program for the above approach

import java.util.HashMap;



class GFG{

// Function to partition the array into
// two subsets such that count of unique
// elements in both subsets is the same
public static void arrayPartition(int a[], int n)
{
    // Stores the subset number for
    // each array elements
    int[] ans = new int[n];

    // Stores the count of unique
    // array elements
    int cnt = 0;
    int ind = 0, flag = 0;

    // Stores the frequency of elements
    HashMap<Integer, Integer> mp = new HashMap<Integer, Integer>();

    // Traverse the array
    for (int i = 0; i < n; i++) {
        if(mp.containsKey(a[i])){
            mp.put(a[i], mp.get(a[i]) + 1);
        }else{
            mp.put(a[i], 1);
        }
    }

    // Count of elements having a
    // frequency of 1
    for (int i = 0; i < n; i++) {

        if (mp.get(a[i]) == 1)
            cnt++;

        // Check if there exists any
        // element with frequency > 2
        if (mp.get(a[i]) > 2 && flag == 0) {
            flag = 1;
            ind = i;
        }
    }

    // Count of elements needed to
    // have frequency exactly 1 in
    // each subset
    int p = (cnt + 1) / 2;
    int ans1 = 0;

    // Initialize all values in the
    /// array ans[] as 1
    for (int i = 0; i < n; i++)
        ans[i] = 1;

    // Traverse the array ans[]
    for (int i = 0; i < n; i++) {

        // This array element is a
        // part of first subset
        if (mp.get(a[i]) == 1 && ans1 < p) {
            ans[i] = 1;
            ans1++;
        }

        // Half array elements with
        // frequency 1 are part of
        // the second subset
        else if (mp.get(a[i]) == 1) {
            ans[i] = 2;
        }
    }

    // If count of elements is exactly
    // 1 are odd and has no element
    // with frequency > 2
    if (cnt % 2 == 1 && flag == 0) {
        System.out.println(-1 + "\n");
        return;
    }

    // If count of elements that occurs
    // exactly once are even
    if (cnt % 2 == 0) {

        // Print the result
        for (int i = 0; i < n; i++) {
            System.out.print(ans[i] + " ");
        }
    }

    // If the count of elements has
    // exactly 1 frequency are odd
    // and there is an element with
    // frequency greater than 2
    else {

        // Print the result
        for (int i = 0; i < n; i++) {
            if (ind == i)
            System.out.print(2 + " ");
            else
            System.out.print(ans[i] + " ");
        }
    }
}

// Driver Codea
public static void main(String args[])
{
    int arr[] = { 1, 1, 2, 3, 4, 4 };
    int N = arr.length;
    arrayPartition(arr, N);

}
}

// This code is contributed by gfgking.

Python3

# Python3 program for the above approach

# Function to partition the array into
# two subsets such that count of unique
# elements in both subsets is the same
def arrayPartition(a, n):

    # Stores the subset number for
    # each array elements
    ans = [0] * n

    # Stores the count of unique
    # array elements
    cnt = 0
    ind, flag = 0, 0

    # Stores the frequency of elements
    mp = {}

    # Traverse the array
    for i in a:
        mp[i] = mp.get(i, 0) + 1

    # Count of elements having a
    # frequency of 1
    for i in range(n):
        if ((a[i] in mp) and mp[a[i]] == 1):
            cnt += 1

        # Check if there exists any
        # element with frequency > 2
        if (mp[a[i]] > 2 and flag == 0):
            flag = 1
            ind = i

    # Count of elements needed to
    # have frequency exactly 1 in
    # each subset
    p = (cnt + 1) // 2
    ans1 = 0

    # Initialize all values in the
    # array ans[] as 1
    for i in range(n):
        ans[i] = 1

    # Traverse the array ans[]
    for i in range(n):

        # This array element is a
        # part of first subset
        if ((a[i] in mp) and mp[a[i]] == 1 and
            ans1 < p):
            ans[i] = 1
            ans1 += 1

        # Half array elements with
        # frequency 1 are part of
        # the second subset
        elif ((a[i] in mp) and mp[a[i]] == 1):
            ans[i] = 2

    # If count of elements is exactly
    # 1 are odd and has no element
    # with frequency > 2
    if (cnt % 2 == 1 and flag == 0):
        print (-1)
        return

    # If count of elements that occurs
    # exactly once are even
    if (cnt % 2 == 0):

        # Print the result
        print(*ans)

    # If the count of elements has
    # exactly 1 frequency are odd
    # and there is an element with
    # frequency greater than 2
    else:

        # Print the result
        for i in range(n):
            if (ind == i):
                print(2, end = " ")
            else:
                print(ans[i], end = " ")

# Driver Codea
if __name__ == '__main__':

    arr = [ 1, 1, 2, 3, 4, 4 ]
    N = len(arr)

    arrayPartition(arr, N)

# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Function to partition the array into
// two subsets such that count of unique
// elements in both subsets is the same
static void arrayPartition(int []a, int n)
{
    // Stores the subset number for
    // each array elements
    int []ans = new int[n];

    // Stores the count of unique
    // array elements
    int cnt = 0;
    int ind=0, flag = 0;

    // Stores the frequency of elements
    Dictionary<int,int> mp = new Dictionary<int,int>();

    // Traverse the array
    for (int i = 0; i < n; i++) {
        if(mp.ContainsKey(a[i]))
         mp[a[i]]++;
        else
          mp.Add(a[i],1);
    }

    // Count of elements having a
    // frequency of 1
    for (int i = 0; i < n; i++) {

        if (mp.ContainsKey(a[i]) && mp[a[i]] == 1)
            cnt++;

        // Check if there exists any
        // element with frequency > 2
        if (mp.ContainsKey(a[i]) && mp[a[i]] > 2 && flag == 0) {
            flag = 1;
            ind = i;
        }
    }

    // Count of elements needed to
    // have frequency exactly 1 in
    // each subset
    int p = (cnt + 1) / 2;
    int ans1 = 0;

    // Initialize all values in the
    /// array ans[] as 1
    for (int i = 0; i < n; i++)
        ans[i] = 1;

    // Traverse the array ans[]
    for (int i = 0; i < n; i++) {

        // This array element is a
        // part of first subset
        if (mp.ContainsKey(a[i]) && mp[a[i]] == 1 && ans1 < p) {
            ans[i] = 1;
            ans1++;
        }

        // Half array elements with
        // frequency 1 are part of
        // the second subset
        else if (mp.ContainsKey(a[i]) && mp[a[i]] == 1) {
            ans[i] = 2;
        }
    }

    // If count of elements is exactly
    // 1 are odd and has no element
    // with frequency > 2
    if (cnt % 2 == 1 && flag == 0) {
        Console.Write(-1);
        return;
    }

    // If count of elements that occurs
    // exactly once are even
    if (cnt % 2 == 0) {

        // Print the result
        for (int i = 0; i < n; i++) {
            Console.Write(ans[i] + " ");
        }
    }

    // If the count of elements has
    // exactly 1 frequency are odd
    // and there is an element with
    // frequency greater than 2
    else {

        // Print the result
        for (int i = 0; i < n; i++) {
            if (ind == i)
                Console.Write(2 + " ");
            else
                Console.Write(ans[i] + " ");
        }
    }
}

// Driver Codea
public static void Main()
{
    int []arr = { 1, 1, 2, 3, 4, 4 };
    int N = arr.Length;
    arrayPartition(arr, N);
}
}

// This code is contributed by SURENDRA_GANGWAR.

Javascript

<script>

// JavaScript program for the above approach

// Function to partition the array into
// two subsets such that count of unique
// elements in both subsets is the same
function arrayPartition(a, n) {
    // Stores the subset number for
    // each array elements
    let ans = new Array(n);

    // Stores the count of unique
    // array elements
    let cnt = 0;
    let ind, flag = 0;

    // Stores the frequency of elements
    let mp = new Map();

    // Traverse the array
    for (let i = 0; i < n; i++) {
        if (mp.has(a[i])) {
            mp.set(a[i], mp.get(a[i]) + 1)
        } else {
            mp.set(a[i], 1)
        }
    }

    // Count of elements having a
    // frequency of 1
    for (let i = 0; i < n; i++) {

        if (mp.get(a[i]) == 1)
            cnt++;

        // Check if there exists any
        // element with frequency > 2
        if (mp.get(a[i]) > 2 && flag == 0) {
            flag = 1;
            ind = i;
        }
    }

    // Count of elements needed to
    // have frequency exactly 1 in
    // each subset
    let p = Math.floor((cnt + 1) / 2);
    let ans1 = 0;

    // Initialize all values in the
    /// array ans[] as 1
    for (let i = 0; i < n; i++)
        ans[i] = 1;

    // Traverse the array ans[]
    for (let i = 0; i < n; i++) {

        // This array element is a
        // part of first subset
        if (mp.get(a[i]) == 1 && ans1 < p) {
            ans[i] = 1;
            ans1++;
        }

        // Half array elements with
        // frequency 1 are part of
        // the second subset
        else if (mp.get(a[i]) == 1) {
            ans[i] = 2;
        }
    }

    // If count of elements is exactly
    // 1 are odd and has no element
    // with frequency > 2
    if (cnt % 2 == 1 && flag == 0) {
        document.write(-1 + "<br>");
        return;
    }

    // If count of elements that occurs
    // exactly once are even
    if (cnt % 2 == 0) {

        // Print the result
        for (let i = 0; i < n; i++) {
            document.write(ans[i] + " ");
        }
    }

    // If the count of elements has
    // exactly 1 frequency are odd
    // and there is an element with
    // frequency greater than 2
    else {

        // Print the result
        for (let i = 0; i < n; i++) {
            if (ind == i)
                document.write(2 + " ");
            else
                document.write(ans[i] << " ");
        }
    }
}

// Driver Codea

let arr = [1, 1, 2, 3, 4, 4];
let N = arr.length
arrayPartition(arr, N);

</script>

Output:

1 1 1 2 1 1

Time Complexity: O(NlogN)
Auxiliary Space: O(N) as using extra space for Map