Missing Number: the idea to remember.

The core insight

XOR all indices, all array values, and n. Paired values cancel.

Why it works

Each present value appears once in the complete range and once in the array. Only the missing value remains unpaired.

The mistake to avoid

Remember n, which has no corresponding array index. XOR avoids sum overflow.

Commented Java solution

Use java.util.* imports and a surrounding solution class. Tree snippets assume the standard TreeNode definition; linked lists use ListNode and Clone Graph uses a Node with val and neighbors; Copy Random List uses Node with val, next and random. Read the input assumptions above.

int missingNumber(int[] nums) {
    int missing = nums.length;
    for (int i = 0; i < nums.length; i++) missing ^= i ^ nums[i];
    return missing;
}

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