Single Number

Solution

B/c duplicates are unwanted, we should recognize the correct data structure to use: set, as used in solutions HashSet and Math.

The bit manipulation solution is most elegant.

HashSet

Add to set if num is not seen yet, otherwise remove it. At the end, set only has 1 element, so just pop it.

Complexity

time: $O(n)$
space: $O(n)$ (due to set)

def singleNumber(self, nums: List[int]) -> int:
    hashset = set()
    for num in nums:
        if num not in hashset:
            hashset.add(num)
        else:
            hashset.remove(num)
    return hashset.pop()

Math

Say c is the single number while a and b appear twice. Then $2*(a+b+c)−(a+a+b+b+c)=c$.

Complexity

time: $O(n)$
space: $O(n)$ (due to set)

def singleNumber(self, nums: List[int]) -> int:
    return 2*sum(set(nums)) - sum(nums)

Bit Manipulation

^ is the associative & communicative XOR operator. These are its features:

• 0^a = a
• a^a = 0
• a^b^a = (a^a)^b = 0^b = b

Complexity

time: $O(n)$
space: $O(1)$

def singleNumber(self, nums: List[int]) -> int:
    res = 0
    for num in nums:
        res ^= num
    return res