*1.4K*

Question:-We are given a list of n-1 integers and these integers are in the range of 1 to n. There are no duplicates in list. One of the integers is missing. Give an algorithm to find the missing integer.

Input:-1, 2, 4, 6, 3, 7, 8

Output:-5

We solved this problem using array summation here. We can also utilize the property of XOR to solve this problem. The major property of XOR that we will be using is A XOR A = 0.

Thus, the steps involved are:-

- XOR all the numbers from 1 to n. Get a value ‘num1’.
- XOR all the elements of the array. Get a value ‘num2’.
- Get the XOR of num1 and num2.

Since all the elements are repeated, the XOR becomes 0 and the only numbers that does not becomes zero is the missing number. Thus we get our number. Here is an implementation of the algorithm:-

//find missing number in array of size 'size' range is 1-n int findMissingNumberXOR(int arr[], int size, int n) { int i; int xor1 = 0; //get the XOR of all the numbers from 1 to n for(i=1;i<=n;i++) xor1 ^= i; int xor2 = 0; //loop through the array and get the XOR of elements for(i = 0;i<size;i++) { xor2 ^= arr[i]; } return (xor1 ^ xor2); }

* Time Complexity:-* O(n) to scan the array

*Space Complexity:-* O(1)