Single Number (Find the Unique Element)

📌 Definition:

📖 Detailed Explanation:

XOR every element together: identical values cancel (x ^ x = 0) and XOR with 0 leaves the value (x ^ 0 = x), so the unpaired element remains. This is O(n) time and O(1) space, beating a frequency map or sorting.

💻 Solutions:

• Java
• JavaScript
• Python

public static int singleNumber(int[] a) {
    int result = 0;
    for (int x : a) result ^= x;
    return result;
}

function singleNumber(a) {
  return a.reduce((acc, x) => acc ^ x, 0);
}

def single_number(a):
    result = 0
    for x in a:
        result ^= x
    return result

🔑 Key Points:

• x ^ x = 0, x ^ 0 = x — pairs cancel
• XOR the whole array; the loner survives
• O(n) time, O(1) space
• No extra map or sort needed

🌍 Real-World Example: