Minimum Bitwise XOR operations to make any two array elements equal
Last Updated :
05 Sep, 2022
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Given an array arr[] of integers of size N and an integer K. One can perform the Bitwise XOR operation between any array element and K any number of times. The task is to print the minimum number of such operations required to make any two elements of the array equal. If it is not possible to make any two elements of the array equal after performing the above-mentioned operation then print -1.
Examples:
Input : arr[] = {1, 9, 4, 3}, K = 3
Output :-1
Explanation : No possible to make any two elements equal
Input : arr[] = {13, 13, 21, 15}, K = 13
Output :0
Explanation : Already exists two same elements
Approach: The key observation is that if it is possible to make the desired array then the answer will be either 0, 1 or 2. It will never exceed 2.
Because, if (x ^ k) = y
then, performing (y ^ k) will give x again
- The answer will be 0, if there are already equal elements in the array.
- For the answer to be 1, we will create a new array b[] which holds b[i] = (a[i] ^ K),
Now, for each a[i] we will check if there is any index j such that i != j and a[i] = b[j].
If yes, then the answer will be 1. - For the answer to be 2, we will check for an index i in the new array b[], If there is any index j such that i != j and b[i] = b[j].
If yes, then the answer will be 2. - If any of the above conditions is not satisfied then the answer will be -1.
Below is the implementation of the above approach:
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Function to return the count of
// minimum operations required
int minOperations(int a[], int n, int K)
{
unordered_map<int, bool> map;
for (int i = 0; i < n; i++) {
// Check if the initial array
// already contains an equal pair
if (map[a[i]])
return 0;
map[a[i]] = true;
}
// Create new array with XOR operations
int b[n];
for (int i = 0; i < n; i++)
b[i] = a[i] ^ K;
// Clear the map
map.clear();
// Check if the solution
// is a single operation
for (int i = 0; i < n; i++) {
// If Bitwise XOR operation between
// 'k' and a[i] gives
// a number other than a[i]
if (a[i] != b[i])
map[b[i]] = true;
}
// Check if any of the a[i]
// gets equal to any other element
// of the array after the operation
for (int i = 0; i < n; i++)
// Single operation
// will be enough
if (map[a[i]])
return 1;
// Clear the map
map.clear();
// Check if the solution
// is two operations
for (int i = 0; i < n; i++) {
// Check if the array 'b'
// contains duplicates
if (map[b[i]])
return 2;
map[b[i]] = true;
}
// Otherwise it is impossible to
// create such an array with
// Bitwise XOR operations
return -1;
}
// Driver code
int main()
{
int K = 3;
int a[] = { 1, 9, 4, 3 };
int n = sizeof(a) / sizeof(a[0]);
// Function call to compute the result
cout << minOperations(a, n, K);
return 0;
}
// Java implementation of the approach
import java.util.HashMap;
class GFG
{
// Function to return the count of
// minimum operations required
static int minOperations(int[] a, int n, int k)
{
HashMap<Integer,
Boolean> map = new HashMap<>();
for (int i = 0; i < n; i++)
{
// Check if the initial array
// already contains an equal pair
if (map.containsKey(a[i]) &&
map.get(a[i]))
return 0;
map.put(a[i], true);
}
// Create new array with XOR operations
int[] b = new int[n];
for (int i = 0; i < n; i++)
b[i] = a[i] ^ k;
// Clear the map
map.clear();
// Check if the solution
// is a single operation
for (int i = 0; i < n; i++)
{
// If Bitwise XOR operation between
// 'k' and a[i] gives
// a number other than a[i]
if (a[i] != b[i])
map.put(b[i], true);
}
// Check if any of the a[i]
// gets equal to any other element
// of the array after the operation
for (int i = 0; i < n; i++)
// Single operation
// will be enough
if (map.containsKey(a[i]) &&
map.get(a[i]))
return 1;
// Clear the map
map.clear();
// Check if the solution
// is two operations
for (int i = 0; i < n; i++)
{
// Check if the array 'b'
// contains duplicates
if (map.containsKey(b[i]) &&
map.get(b[i]))
return 2;
map.put(b[i], true);
}
// Otherwise it is impossible to
// create such an array with
// Bitwise XOR operations
return -1;
}
// Driver Code
public static void main(String[] args)
{
int K = 3;
int[] a = { 1, 9, 4, 3 };
int n = a.length;
System.out.println(minOperations(a, n, K));
}
}
// This code is contributed by
// Vivek Kumar Singh
# Python3 implementation of the approach
# Function to return the count of
# minimum operations required
def minOperations(a, n, K) :
map = dict.fromkeys(a, False);
for i in range(n) :
# Check if the initial array
# already contains an equal pair
if (map[a[i]]) :
return 0;
map[a[i]] = True;
# Create new array with XOR operations
b = [0] * n;
for i in range(n) :
b[i] = a[i] ^ K;
# Clear the map
map.clear();
# Check if the solution
# is a single operation
for i in range(n) :
# If Bitwise XOR operation between
# 'k' and a[i] gives
# a number other than a[i]
if (a[i] != b[i]) :
map[b[i]] = True;
# Check if any of the a[i]
# gets equal to any other element
# of the array after the operation
for i in range(n) :
# Single operation
# will be enough
if a[i] in map :
return 1;
# Clear the map
map.clear();
# Check if the solution
# is two operations
for i in range(n) :
# Check if the array 'b'
# contains duplicates
if b[i] in map :
return 2;
map[b[i]] = True;
# Otherwise it is impossible to
# create such an array with
# Bitwise XOR operations
return -1;
# Driver code
if __name__ == "__main__" :
K = 3;
a = [ 1, 9, 4, 3 ];
n = len(a);
# Function call to compute the result
print(minOperations(a, n, K));
# This code is contributed by AnkitRai01
// C# implementation of the approach
using System;
using System.Collections.Generic;
class GFG
{
// Function to return the count of
// minimum operations required
public static int minOperations(int[] a,
int n, int K)
{
Dictionary<int, Boolean> map =
new Dictionary<int, Boolean>();
for (int i = 0; i < n; i++)
{
// Check if the initial array
// already contains an equal pair
if (map.ContainsKey(a[i]))
return 0;
map.Add(a[i], true);
}
// Create new array with XOR operations
int[] b = new int[n];
for (int i = 0; i < n; i++)
b[i] = a[i] ^ K;
// Clear the map
map.Clear();
// Check if the solution
// is a single operation
for (int i = 0; i < n; i++)
{
// If Bitwise OR operation between
// 'k' and a[i] gives
// a number other than a[i]
if (a[i] != b[i])
map.Add(b[i], true);
}
// Check if any of the a[i]
// gets equal to any other element
// of the array after the operation
for (int i = 0; i < n; i++)
{
// Single operation
// will be enough
if (map.ContainsKey(a[i]))
return 1;
}
// Clear the map
map.Clear();
// Check if the solution
// is two operations
for (int i = 0; i < n; i++)
{
// Check if the array 'b'
// contains duplicates
if (map.ContainsKey(b[i]))
return 2;
map.Add(b[i], true);
}
// Otherwise it is impossible to
// create such an array with
// Bitwise OR operations
return -1;
}
// Driver code
public static void Main(String[] args)
{
int K = 3;
int[] a = { 1, 9, 4, 3 };
int n = a.Length;
Console.WriteLine(minOperations(a, n, K));
}
}
// This code is contributed by Rajput-Ji
<script>
// Javascript implementation of the approach
// Function to return the count of
// minimum operations required
function minOperations(a, n, K)
{
var map = new Map();
for (var i = 0; i < n; i++) {
// Check if the initial array
// already contains an equal pair
if (map[a[i]])
return 0;
map[a[i]] = true;
}
// Create new array with XOR operations
var b = Array(n);
for (var i = 0; i < n; i++)
b[i] = a[i] ^ K;
// Clear the map
map = new Map();
// Check if the solution
// is a single operation
for (var i = 0; i < n; i++) {
// If Bitwise XOR operation between
// 'k' and a[i] gives
// a number other than a[i]
if (a[i] != b[i])
map[b[i]] = true;
}
// Check if any of the a[i]
// gets equal to any other element
// of the array after the operation
for (var i = 0; i < n; i++)
// Single operation
// will be enough
if (map[a[i]])
return 1;
// Clear the map
map = new Map();
// Check if the solution
// is two operations
for (var i = 0; i < n; i++) {
// Check if the array 'b'
// contains duplicates
if (map[b[i]])
return 2;
map[b[i]] = true;
}
// Otherwise it is impossible to
// create such an array with
// Bitwise XOR operations
return -1;
}
// Driver code
var K = 3;
var a = [ 1, 9, 4, 3 ];
var n = a.length;
// Function call to compute the result
document.write( minOperations(a, n, K));
</script>
Output:
-1
Time complexity: O(n) where n is size of input array
Auxiliary space: O(n)
