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Unique element in an array where all elements occur K times except one | Set 2
• Last Updated : 01 Dec, 2020

Given an array arr[] where every element occurs K times except one element which occurs only once, the task is to find that unique element.
Examples:

Input: arr[] = {12, 1, 12, 3, 12, 1, 1, 2, 3, 2, 2, 3, 7}, k = 3
Output:
Explanation:
7 is the only element which occurs once while others occurs k times.
Input: arr[] = {12, 12, 2, 2, 3}, k = 2
Output:
Explanation:
3 is the only element which occurs once while others occurs k times.

Naive Approach: Suppose we have every element K times then the difference between the sum of all elements in the given array and the K*sum of all unique elements is (K-1) times the unique element.
For Example:

arr[] = {a, a, a, b, b, b, c, c, c, d}, k = 3
unique elements = {a, b, c, d}
Difference = 3*(a + b + c + d) – (a + a + a + b + b + b + c + c + c + d) = 2*d
Therefore, Generalizing the equation:
The unique element can be given by: Below are the steps:

1. Store all the elements of the given array in the set to get the unique elements.
2. Find the sum of all elements in the array (say sum_array) and the sum of all the elements in the set(say sum_set).
3. The unique element is given by (K*sum_set – sum_array)/(K – 1).

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach   #include  using namespace std;   // Function that find the unique element // in the array arr[] int findUniqueElements(int arr[], int N,                        int K) {     // Store all unique element in set     unordered_set<int> s(arr, arr + N);       // Sum of all element of the array     int arr_sum = accumulate(arr, arr + N, 0);       // Sum of element in the set     int set_sum = accumulate(s.begin(),                              s.end(),                              0);       // Print the unique element using formula     cout << (K * set_sum - arr_sum) / (K - 1); }   // Driver Code int main() {       int arr[] = { 12, 1, 12, 3, 12, 1,                   1, 2, 3, 2, 2, 3, 7 };     int N = sizeof(arr) / sizeof(arr);     int K = 3;       // Function call     findUniqueElements(arr, N, K);       return 0; }

## Java

 // Java program for the above approach import java.util.*;   class GFG{       // Function that find the unique element // in the array arr[] static void findUniqueElements(int arr[],                                 int N, int K) {           // Store all unique element in set     Set s = new HashSet<>();     for(int i = 0; i < N; i++)         s.add(arr[i]);       // Sum of all element of the array     int arr_sum = 0;     for(int i = 0; i < N; i++)         arr_sum += arr[i];       // Sum of element in the set     int set_sum = 0;     Iterator it = s.iterator();       while (it.hasNext())      {         set_sum += (int)it.next();     }       // Print the unique element using formula     System.out.println((K * set_sum - arr_sum) /                        (K - 1)); }   // Driver code public static void main(String[] args) {     int arr[] = { 12, 1, 12, 3, 12, 1,                   1, 2, 3, 2, 2, 3, 7 };     int N = arr.length;     int K = 3;       // Function call     findUniqueElements(arr, N, K); } }   // This code is contributed by offbeat

## Python3

 # Python3 program for the above approach   # Function that find the unique element # in the array arr[] def findUniqueElements(arr, N, K):           # Store all unique element in set     s = set()     for x in arr:         s.add(x)       # Sum of all element of the array     arr_sum = sum(arr)       # Sum of element in the set     set_sum = 0     for x in s:         set_sum += x       # Print the unique element using formula     print((K * set_sum - arr_sum) // (K - 1))   # Driver Code if __name__ == '__main__':           arr = [ 12, 1, 12, 3, 12, 1,             1, 2, 3, 2, 2, 3, 7 ]     N = len(arr)     K = 3       # Function call     findUniqueElements(arr, N, K)   # This code is contributed by Samarth

## C#

 // C# program for the above approach using System; using System.Collections.Generic; class GFG{       // Function that find the unique element // in the array []arr static void findUniqueElements(int []arr,                                 int N, int K) {           // Store all unique element in set     HashSet<int> s = new HashSet<int>();     for(int i = 0; i < N; i++)         s.Add(arr[i]);       // Sum of all element of the array     int arr_sum = 0;     for(int i = 0; i < N; i++)         arr_sum += arr[i];       // Sum of element in the set     int set_sum = 0;     foreach(int i in s)         set_sum += i;         // Print the unique element using formula     Console.WriteLine((K * set_sum - arr_sum) /                       (K - 1)); }   // Driver code public static void Main(String[] args) {     int []arr = { 12, 1, 12, 3, 12, 1,                   1, 2, 3, 2, 2, 3, 7 };     int N = arr.Length;     int K = 3;       // Function call     findUniqueElements(arr, N, K); } }   // This code is contributed by gauravrajput1

Output

7

Time Complexity: O(N), where N is the number of elements in the array
Auxiliary Space Complexity: O(N/K), where K is the frequency.

Another Approach:  The idea is to use hashing but it will take O(n) time and requires extra space. We can also do it by sorting but it will take O(N log N) time.

Efficient Approach: The above problem can be optimized in terms of constant space complexity. Use bit manipulation approach for this problem.

• Let’s assume we have a case where all the elements appear k times except 1 element.
• So, count the bit of every element for 32 bits.
• Count 0th bit of every element and take modulo by k will eliminate the bit of elements which present k times and we remain with the only bit of element which presents one time.
• Apply this process for all the 32 bits and by taking modulo by k we will eliminate repeated elements bits.
• At every step, generate the results from these remaining bits.
• To handle any negative number, check if the result is present in the array or not if present then print it. Else print negative of the result.

For Example arr[] = {2, 2, 4, 2, 2, 2, 1, 1, 1, 1, 1} , k = 5

Our result is (100) in binary = 4 in decimal. So the final answer will be 4, because it presents 1 time.

Below is the implementation of the above approach:

## C++

 // CPP program for the above approach #include  using namespace std;   // Function to find single occurance element int findunique(vector<int>& a, int k) {     int res = 0;       for (int i = 0; i < 32; i++) {         int p = 0;           for (int j = 0; j < a.size(); j++) {             // By shifting 1 to left ith             // time and taking and with 1             // will give us that ith             // bit of a[j] is 1 or 0             p += (abs(a[j]) & (                   1 << i)) != 0 ? 1 : 0;         }           // Taking modulo of p with k         p %= k;           // Generate result         res += pow(2, i) * p;     }       int c = 0;       // Loop for negative numbers     for (auto x : a)           if (x == res) {             c = 1;             break;         }         // Check if the calculated value res     // is present in array, then mark c=1     // and if c = 1 return res     // else res must be -ve     return c == 1 ? res : -res; }   // Driver code int main() {       vector<int> a = { 12, 12, 2, 2, 3 };     int k = 2;       // Function call     cout << findunique(a, k) << "\n"; } // This article is contributed by ajaykr00kj

## Java

 // Java program for the above approach import java.util.Arrays; class Main{       // Function to find single  // occurance element public static int findunique(int a[],                               int k) {   int res = 0;     for (int i = 0; i < 32; i++)    {     int p = 0;       for (int j = 0; j < a.length; j++)      {       // By shifting 1 to left ith       // time and taking and with 1       // will give us that ith       // bit of a[j] is 1 or 0       p += (Math.abs(a[j]) &            (1 << i)) != 0 ? 1 : 0;     }       // Taking modulo of p with k     p %= k;       // Generate result     res += Math.pow(2, i) * p;   }     int c = 0;     // Loop for negative numbers   for (int x = 0; x < a.length; x++)       if (a[x] == res)      {       c = 1;       break;     }     // Check if the calculated value res   // is present in array, then mark c=1   // and if c = 1 return res   // else res must be -ve   return c == 1 ? res : -res; }   // Driver code public static void main(String[] args)  {   int a[] = {12, 12, 2, 2, 3};   int k = 2;     // Function call   System.out.println(findunique(a, k)); } }   // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 program for the above approach   # Function to find single occurance element def findunique(a, k):       res = 0       for i in range(32):         p = 0           for j in range(len(a)):                         # By shifting 1 to left ith             # time and taking and with 1             # will give us that ith             # bit of a[j] is 1 or 0             if (abs(a[j]) & (1 << i)) != 0 :                 p += 1           # Taking modulo of p with k         p %= k           # Generate result         res += pow(2, i) * p       c = 0       # Loop for negative numbers     for x in a:           if (x == res) :             c = 1             break       # Check if the calculated value res     # is present in array, then mark c=1     # and if c = 1 return res     # else res must be -ve     if c == 1 :         return res     else :         return -res   # Driver code a = [ 12, 12, 2, 2, 3 ] k = 2   # Function call print(findunique(a, k))   # This code is contributed by divyesh072019

## C#

 // C# program for the // above approach using System; class GFG{        // Function to find single  // occurance element public static int findunique(int []a,                               int k) {   int res = 0;      for (int i = 0; i < 32; i++)    {     int p = 0;        for (int j = 0; j < a.Length; j++)      {       // By shifting 1 to left ith       // time and taking and with 1       // will give us that ith       // bit of a[j] is 1 or 0       p += (Math.Abs(a[j]) &            (1 << i)) != 0 ? 1 : 0;     }        // Taking modulo of p with k     p %= k;        // Generate result     res += (int)Math.Pow(2, i) * p;   }      int c = 0;      // Loop for negative numbers   for (int x = 0; x < a.Length; x++)        if (a[x] == res)      {       c = 1;       break;     }      // Check if the calculated value res   // is present in array, then mark c=1   // and if c = 1 return res   // else res must be -ve   return c == 1 ? res : -res; }    // Driver code  public static void Main(string []args)  {   int []a = {12, 12, 2, 2, 3};   int k = 2;      // Function call   Console.Write(findunique(a, k)); } }   // This code is contributed by Rutvik_56

Output

3

Time Complexity: O(32 * n) = O(n)
Auxiliary Space: O(1)

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