Single_Number

/*
Single Number 

Given an array of integers, every element appears twice except for one. Find that single one.

Note:
Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory?
*/

class Solution {
public:
    int singleNumber(int A[], int n) {
      if (n==0) return A[0];
      int res = A[0];
      for (int i=1; i<n; ++i)
      {
        res = res ^ A[i];
      }
      return res;
    }
};


REMARK:
1.Have no idea. How to do that in O(n) time without using extra memory?
IDEA:
The requirement is O(n) time and O(1) space.
Thus, the  "first sort and then find " way is not working.
Also the "hash map" way is not working.

Thus, we use XOR: a XOR a = 0, a XOR b XOR a = b 
(Note: for XOR, we have: 
(1)Commutativity: a XOR b = b XOR a
(2)Associativity: (a XOR b) XOR c = a XOR (b XOR c) 
(3)
)

By using XOR, the code becomes very easy. But hard to think of XOR.