Find Unique pair in an array with pairs of numbers
Last Updated : 19 Jul, 2022
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Given an array where every element appears twice except a pair (two elements). Find the elements of this unique pair.
Examples:
Input : 6, 1, 3, 5, 1, 3, 7, 6 Output : 5 7 All elements appear twice except 5 and 7 Input : 1 3 4 1 Output : 3 4
The idea is based on below post.
Find Two Missing Numbers | Set 2 (XOR based solution)
- XOR each element of the array and you will left with the XOR of two different elements which are going to be our result. Let this XOR be "XOR"
- Now find a set bit in XOR.
- Now divide array elements in two groups. One group that has the bit found in step 2 as set and other group that has the bit as 0.
- XOR of elements present in first group would be our first element. And XOR of elements present in second group would be our second element.
Implementation:
// C program to find a unique pair in an array
// of pairs.
#include <stdio.h>
void findUniquePair(int arr[], int n)
{
// XOR each element and get XOR of two unique
// elements(ans)
int XOR = arr[0];
for (int i = 1; i < n; i++)
XOR = XOR ^ arr[i];
// Now XOR has XOR of two missing elements. Any set
// bit in it must be set in one missing and unset in
// other missing number
// Get a set bit of XOR (We get the rightmost set bit)
int set_bit_no = XOR & ~(XOR-1);
// Now divide elements in two sets by comparing rightmost
// set bit of XOR with bit at same position in each element.
int x = 0, y = 0; // Initialize missing numbers
for (int i = 0; i < n; i++)
{
if (arr[i] & set_bit_no)
x = x ^ arr[i]; /*XOR of first set in arr[] */
else
y = y ^ arr[i]; /*XOR of second set in arr[] */
}
printf("The unique pair is (%d, %d)", x, y);
}
// Driver code
int main()
{
int a[] = { 6, 1, 3, 5, 1, 3, 7, 6 };
int n = sizeof(a)/sizeof(a[0]);
findUniquePair(a, n);
return 0;
}
// Java program to find a unique pair
// in an array of pairs.
class GFG
{
static void findUniquePair(int[] arr, int n)
{
// XOR each element and get XOR of two
// unique elements(ans)
int XOR = arr[0];
for (int i = 1; i < n; i++)
XOR = XOR ^ arr[i];
// Now XOR has XOR of two missing elements.
// Any set bit in it must be set in one
// missing and unset in other missing number
// Get a set bit of XOR (We get the
// rightmost set bit)
int set_bit_no = XOR & ~(XOR-1);
// Now divide elements in two sets by
// comparing rightmost set bit of XOR with
// bit at same position in each element.
// Initialize missing numbers
int x = 0, y = 0;
for (int i = 0; i < n; i++)
{
if ((arr[i] & set_bit_no)>0)
/*XOR of first set in arr[] */
x = x ^ arr[i];
else
/*XOR of second set in arr[] */
y = y ^ arr[i];
}
System.out.println("The unique pair is (" +
x + "," + y + ")");
}
// Driver code
public static void main (String[] args) {
int[] a = { 6, 1, 3, 5, 1, 3, 7, 6 };
int n = a.length;
findUniquePair(a, n);
}
}
/* This code is contributed by Mr. Somesh Awasthi */
# Python 3 program to find a unique
# pair in an array of pairs.
def findUniquePair(arr, n):
# XOR each element and get XOR
# of two unique elements(ans)
XOR = arr[0]
for i in range(1, n):
XOR = XOR ^ arr[i]
# Now XOR has XOR of two missing
# elements. Any set bit in it
# must be set in one missing and
# unset in other missing number
# Get a set bit of XOR (We get
# the rightmost set bit)
set_bit_no = XOR & ~(XOR - 1)
# Now divide elements in two sets
# by comparing rightmost set bit
# of XOR with bit at same position
# in each element.
x = 0
y = 0 # Initialize missing numbers
for i in range(0, n):
if (arr[i] & set_bit_no):
# XOR of first set in
# arr[]
x = x ^ arr[i]
else:
# XOR of second set
# in arr[]
y = y ^ arr[i]
print("The unique pair is (", x,
", ", y, ")", sep = "")
# Driver code
a = [6, 1, 3, 5, 1, 3, 7, 6 ]
n = len(a)
findUniquePair(a, n)
# This code is contributed by Smitha.
// C# program to find a unique pair
// in an array of pairs.
using System;
class GFG {
static void findUniquePair(int[] arr, int n)
{
// XOR each element and get XOR of two
// unique elements(ans)
int XOR = arr[0];
for (int i = 1; i < n; i++)
XOR = XOR ^ arr[i];
// Now XOR has XOR of two missing
// elements. Any set bit in it must
// be set in one missing and unset
// in other missing number
// Get a set bit of XOR (We get the
// rightmost set bit)
int set_bit_no = XOR & ~(XOR - 1);
// Now divide elements in two sets by
// comparing rightmost set bit of XOR
// with bit at same position in each
// element. Initialize missing numbers
int x = 0, y = 0;
for (int i = 0; i < n; i++)
{
if ((arr[i] & set_bit_no) > 0)
/*XOR of first set in arr[] */
x = x ^ arr[i];
else
/*XOR of second set in arr[] */
y = y ^ arr[i];
}
Console.WriteLine("The unique pair is ("
+ x + ", " + y + ")");
}
// Driver code
public static void Main ()
{
int[] a = { 6, 1, 3, 5, 1, 3, 7, 6 };
int n = a.Length;
findUniquePair(a, n);
}
}
// This code is contributed by vt_m.
<?php
// PHP program to find a
// unique pair in an array
// of pairs.
function findUniquePair($arr, $n)
{
// XOR each element and
// get XOR of two unique
// elements(ans)
$XOR = $arr[0];
for ($i = 1; $i < $n; $i++)
$XOR = $XOR ^ $arr[$i];
// Now XOR has XOR of two
// missing elements. Any set
// bit in it must be set in
// one missing and unset in
// other missing number
// Get a set bit of XOR
// (We get the rightmost set bit)
$set_bit_no = $XOR & ~($XOR-1);
// Now divide elements in two
// sets by comparing rightmost
// set bit of XOR with bit at
// same position in each element.
// Initialize missing numbers
$x = 0;
$y = 0;
for ($i = 0; $i < $n; $i++)
{
if ($arr[$i] & $set_bit_no)
// XOR of first set in arr[]
$x = $x ^ $arr[$i];
else
// XOR of second set in arr[]
$y = $y ^ $arr[$i];
}
echo"The unique pair is ", "(",$x," ", $y,")";
}
// Driver code
$a = array(6, 1, 3, 5, 1, 3, 7, 6);
$n = count($a);
findUniquePair($a, $n);
// This code is contributed by anuj_67.
?>
<script>
// Javascript program to find a unique pair
// in an array of pairs.
function findUniquePair(arr, n)
{
// XOR each element and get XOR of two
// unique elements(ans)
let XOR = arr[0];
for (let i = 1; i < n; i++)
XOR = XOR ^ arr[i];
// Now XOR has XOR of two missing elements.
// Any set bit in it must be set in one
// missing and unset in other missing number
// Get a set bit of XOR (We get the
// rightmost set bit)
let set_bit_no = XOR & ~(XOR-1);
// Now divide elements in two sets by
// comparing rightmost set bit of XOR with
// bit at same position in each element.
// Initialize missing numbers
let x = 0, y = 0;
for (let i = 0; i < n; i++)
{
if ((arr[i] & set_bit_no)>0)
/*XOR of first set in arr[] */
x = x ^ arr[i];
else
/*XOR of second set in arr[] */
y = y ^ arr[i];
}
document.write("The unique pair is (" +
x + "," + y + ")" + "<br/>");
}
// driver function
let a = [ 6, 1, 3, 5, 1, 3, 7, 6 ];
let n = a.length;
findUniquePair(a, n);
</script>
Output
The unique pair is (7, 5)
Time Complexity: O(n)
Auxiliary Space: O(1)
