Find the element that appears once in an array where every other element appears twice using Javascript

Software Development
#1

Given an array of integers. All numbers occur twice except one number which occurs once. Find the number in O(n) time & constant extra space.

Example :

Input: ar[] = {7, 3, 5, 4, 5, 3, 4} Output: 7

One solution is to check every element if it appears once or not. Once an element with a single occurrence is found, return it. Time complexity of this solution is O(n2).

A better solution is to use hashing.

  1. Traverse all elements and put them in a hash table. Element is used as key and the count of occurrences is used as the value in the hash table.
  2. Traverse the array again and print the element with count 1 in the hash table.
    This solution works in O(n) time but requires extra space.
    The best solution is to use XOR. XOR of all array elements gives us the number with a single occurrence. The idea is based on the following two facts.
    a) XOR of a number with itself is 0.
    b) XOR of a number with 0 is number itself.

Let us consider the above example. Let ^ be xor operator as in C and C++. res = 7 ^ 3 ^ 5 ^ 4 ^ 5 ^ 3 ^ 4 Since XOR is associative and commutative, above expression can be written as: res = 7 ^ (3 ^ 3) ^ (4 ^ 4) ^ (5 ^ 5) = 7 ^ 0 ^ 0 ^ 0 = 7 ^ 0 = 7

Below are implementations of above algorithm.

<script>

// JavScript program to find the array

// element that appears only once

function findSingle(ar, ar_size)

{

// Do XOR of all elements and return

let res = ar[0];

for (let i = 1; i < ar_size; i++)

res = res ^ ar[i];

return res;

}

// Driver code

let ar = [2, 3, 5, 4, 5, 3, 4];

let n = ar.length;

document.write( "Element occurring once is "

+ findSingle(ar, n));

</script>

Output:

Element occurring once is 2

The time complexity of this solution is O(n) and it requires O(1) extra space.