Number of unique triplets whose XOR is zero
Given N numbers with no duplicates, count the number of unique triplets (ai, aj, ak) such that their XOR is 0. A triplet is said to be unique if all of the three numbers in the triplet are unique.
Examples:
Input : a[] = {1, 3, 5, 10, 14, 15};
Output : 2
Explanation : {1, 14, 15} and {5, 10, 15} are the
unique triplets whose XOR is 0.
{1, 14, 15} and all other combinations of
1, 14, 15 are considered as 1 only.Input : a[] = {4, 7, 5, 8, 3, 9};
Output : 1
Explanation : {4, 7, 3} is the only triplet whose XOR is 0
Naive Approach: A naive approach is to run three nested loops, the first runs from 0 to n, the second from i+1 to n, and the last one from j+1 to n to get the unique triplets. Calculate the XOR of ai, aj, ak, check if it equals 0. If so, then increase the count.
Below is the implementation of the above idea:
C++
// CPP program to count the number of // unique triplets whose XOR is 0 #include <bits/stdc++.h> using namespace std; // function to count the number of // unique triplets whose xor is 0 int countTriplets( int a[], int n) { // stores the count of unique triplets int count = 0; // traverse for all i, j, k pairs such that k>j>i for ( int i = 0; i < n - 1; i++) { for ( int j = i + 1; j < n; j++) { for ( int k = j + 1; k < n; k++) { int xorr = a[i] ^ a[j] ^ a[k]; // if xor of a[i], a[j] and a[k] is 0, // increase count by 1 if (xorr == 0) count++; } } } return count; } // Driver code int main() { int a[] = { 1, 3, 5, 10, 14, 15 }; int n = sizeof (a) / sizeof (a[0]); cout << countTriplets(a, n); return 0; } |
Java
// JAVA program to count the number of // unique triplets whose XOR is 0 public class GFG { // function to count the number of // unique triplets whose xor is 0 static int countTriplets( int a[], int n) { // stores the count of unique triplets int count = 0 ; // traverse for all i, j, k pairs such that k>j>i for ( int i = 0 ; i < n - 1 ; i++) { for ( int j = i + 1 ; j < n; j++) { for ( int k = j + 1 ; k < n; k++) { int xorr = a[i] ^ a[j] ^ a[k]; // if xor of a[i], a[j] and a[k] is 0, // increase count by 1 if (xorr == 0 ) count++; } } } return count; } public static void main(String[] args) { int a[] = { 1 , 3 , 5 , 10 , 14 , 15 }; int n = 6 ; System.out.println(countTriplets(a, n)); } } |
Python3
# Python program to count the number of # unique triplets whose XOR is 0 class GFG : # function to count the number of # unique triplets whose xor is 0 @staticmethod def countTriplets( a, n) : # stores the count of unique triplets count = 0 # traverse for all i, j, k pairs such that k>j>i i = 0 while (i < n - 1 ) : j = i + 1 while (j < n) : k = j + 1 while (k < n) : xorr = a[i] ^ a[j] ^ a[k] # if xor of a[i], a[j] and a[k] is 0, # increase count by 1 if (xorr = = 0 ) : count + = 1 k + = 1 j + = 1 i + = 1 return count @staticmethod def main( args) : a = [ 1 , 3 , 5 , 10 , 14 , 15 ] n = 6 print (GFG.countTriplets(a, n)) if __name__ = = "__main__" : GFG.main([]) # This code is contributed y aadityaburujwale. |
C#
using System; class GFG { static int countTriplets( int [] a, int n) { // stores the count of unique triplets int count = 0; // traverse for all i, j, k pairs such that k>j>i for ( int i = 0; i < n - 1; i++) { for ( int j = i + 1; j < n; j++) { for ( int k = j + 1; k < n; k++) { int xorr = a[i] ^ a[j] ^ a[k]; // if xor of a[i], a[j] and a[k] is 0, // increase count by 1 if (xorr == 0) count++; } } } return count; } // Driver's code public static void Main( string [] args) { int [] a = { 1, 3, 5, 10, 14, 15 }; int n = 6; // Function call Console.Write(countTriplets(a, n)); } } // This code is contributed garg28harsh. |
Javascript
// Javascript program to count the number of // unique triplets whose XOR is 0 // function to count the number of // unique triplets whose xor is 0 function countTriplets(a, n) { // stores the count of unique triplets let count = 0; // traverse for all i, j, k pairs such that k>j>i for (let i = 0; i < n - 1; i++) { for (let j = i + 1; j < n; j++) { for (let k = j + 1; k < n; k++) { let xorr = a[i] ^ a[j] ^ a[k]; // if xor of a[i], a[j] and a[k] is 0, // increase count by 1 if (xorr == 0) count++; } } } return count; } // Driver code let a = [ 1, 3, 5, 10, 14, 15 ]; let n = 6; console.log(countTriplets(a, n)); // This code is contributed by garg28harsh. |
2
Time Complexity: O(n3), as we will be using nested loops for traversing n3 times.
Auxiliary Space: O(1), as we will not use extra space.
Efficient Approach: An efficient approach is to use one of the properties of XOR: the XOR of two of the same numbers gives 0. So we need to calculate the XOR of unique pairs only, and if the calculated XOR is one of the array elements, then we get the triplet whose XOR is 0. Given below are the steps for counting the number of unique triplets:
Below is the complete algorithm for this approach:
- With the map, mark all the array elements.
- Run two nested loops, one from i-n-1, and the other from i+1-n to get all the pairs.
- Obtain the XOR of the pair.
- Check if the XOR is an array element and not one of ai or aj.
- Increase the count if the condition holds.
- Return count/3 as we only want unique triplets. Since i-n and j+1-n give us unique pairs but not triplets, we do a count/3 to remove the other two possible combinations.
Below is the implementation of the above idea:
C++
// CPP program to count the number of // unique triplets whose XOR is 0 #include <bits/stdc++.h> using namespace std; // function to count the number of // unique triplets whose xor is 0 int countTriplets( int a[], int n) { // To store values that are present unordered_set< int > s; for ( int i = 0; i < n; i++) s.insert(a[i]); // stores the count of unique triplets int count = 0; // traverse for all i, j pairs such that j>i for ( int i = 0; i < n-1; i++) { for ( int j = i + 1; j < n; j++) { // xor of a[i] and a[j] int xr = a[i] ^ a[j]; // if xr of two numbers is present, // then increase the count if (s.find(xr) != s.end() && xr != a[i] && xr != a[j]) count++; } } // returns answer return count / 3; } // Driver code to test above function int main() { int a[] = {1, 3, 5, 10, 14, 15}; int n = sizeof (a) / sizeof (a[0]); cout << countTriplets(a, n); return 0; } |
Java
// Java program to count // the number of unique // triplets whose XOR is 0 import java.io.*; import java.util.*; class GFG { // function to count the // number of unique triplets // whose xor is 0 static int countTriplets( int []a, int n) { // To store values // that are present ArrayList<Integer> s = new ArrayList<Integer>(); for ( int i = 0 ; i < n; i++) s.add(a[i]); // stores the count // of unique triplets int count = 0 ; // traverse for all i, // j pairs such that j>i for ( int i = 0 ; i < n; i++) { for ( int j = i + 1 ; j < n; j++) { // xor of a[i] and a[j] int xr = a[i] ^ a[j]; // if xr of two numbers // is present, then // increase the count if (s.contains(xr) && xr != a[i] && xr != a[j]) count++; } } // returns answer return count / 3 ; } // Driver code public static void main(String srgs[]) { int []a = { 1 , 3 , 5 , 10 , 14 , 15 }; int n = a.length; System.out.print(countTriplets(a, n)); } } // This code is contributed by // Manish Shaw(manishshaw1) |
Python3
# Python 3 program to count the number of # unique triplets whose XOR is 0 # function to count the number of # unique triplets whose xor is 0 def countTriplets(a, n): # To store values that are present s = set () for i in range (n): s.add(a[i]) # stores the count of unique triplets count = 0 # traverse for all i, j pairs such that j>i for i in range (n): for j in range (i + 1 , n, 1 ): # xor of a[i] and a[j] xr = a[i] ^ a[j] # if xr of two numbers is present, # then increase the count if (xr in s and xr ! = a[i] and xr ! = a[j]): count + = 1 ; # returns answer return int (count / 3 ) # Driver code if __name__ = = '__main__' : a = [ 1 , 3 , 5 , 10 , 14 , 15 ] n = len (a) print (countTriplets(a, n)) # This code is contributed by # Surendra_Gangwar |
C#
// C# program to count // the number of unique // triplets whose XOR is 0 using System; using System.Collections.Generic; class GFG { // function to count the // number of unique triplets // whose xor is 0 static int countTriplets( int []a, int n) { // To store values // that are present List< int > s = new List< int >(); for ( int i = 0; i < n; i++) s.Add(a[i]); // stores the count // of unique triplets int count = 0; // traverse for all i, // j pairs such that j>i for ( int i = 0; i < n; i++) { for ( int j = i + 1; j < n; j++) { // xor of a[i] and a[j] int xr = a[i] ^ a[j]; // if xr of two numbers // is present, then // increase the count if (s.Exists(item => item == xr) && xr != a[i] && xr != a[j]) count++; } } // returns answer return count / 3; } // Driver code static void Main() { int []a = new int []{1, 3, 5, 10, 14, 15}; int n = a.Length; Console.Write(countTriplets(a, n)); } } // This code is contributed by // Manish Shaw(manishshaw1) |
Javascript
<script> // javascript program to count // the number of unique // triplets whose XOR is 0 // function to count the // number of unique triplets // whose xor is 0 function countTriplets(a , n) { // To store values // that are present var s = []; for (i = 0; i < n; i++) s.push(a[i]); // stores the count // of unique triplets var count = 0; // traverse for all i, // j pairs such that j>i for (i = 0; i < n; i++) { for (j = i + 1; j < n; j++) { // xor of a[i] and a[j] var xr = a[i] ^ a[j]; // if xr of two numbers // is present, then // increase the count if (s.includes(xr) && xr != a[i] && xr != a[j]) count++; } } // returns answer return count / 3; } // Driver code var a = [ 1, 3, 5, 10, 14, 15 ]; var n = a.length; document.write(countTriplets(a, n)); // This code contributed by Rajput-Ji </script> |
2
Time Complexity: O(N*N), as we are using a loop to traverse N*N times.
Auxiliary Space: O(N), as we are using extra space for set s.
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