MissingNumber.java

class Solution {
    
    /* 
     use XOR operation. We all know that a^b^b =a,
     
     which means two xor operations with the same number will eliminate the number and reveal the original number.
    
     In this solution, I apply XOR operation to both the index and value of the array. In a complete array with no missing numbers, the index and value should be perfectly corresponding( nums[index] = index), so in a missing array, what left finally is the missing number.*/
    
     public int missingNumber(int[] nums) {
         int xor = 0,  
            i = 0;
        
        for (i = 0; i < nums.length; i++) {  
            xor = xor ^ i ^ nums[i];
        }

        return xor ^ i;
    }
}