//Given an array of numbers where all numbers except one have a pair, //find the number that appears only once // // // <= [1, 0, 3, -2, 9, 9, 1, -2, 0] // // => 3 int find(int[] arr){ Map<Integer,

Task: find the single number in an array that does not have a pair (all others appear twice).

The optimal solution is to use the XOR operation (exclusive OR). Properties of XOR:

• a ^ a = 0
• a ^ 0 = a
• XOR is commutative and associative

Therefore, if you perform XOR on all elements of the array, pairs will cancel each other out, leaving only the number without a pair.

Example in Java:

int find(int[] arr) {
    int result = 0;
    for (int num : arr) {
        result ^= num;
    }
    return result;
}

// Example usage: // int[] arr = {1, 0, 3, -2, 9, 9, 1, -2, 0}; // find(arr) will return 3

This solution works in O(n) time and O(1) space.