Single Number Ii

Problem

https://leetcode.com/problems/single-number-ii/

Given an integer array nums where every element appears three times except for one, which appears exactly once. Find the single element and return it.

You must implement a solution with a linear runtime complexity and use only constant extra space.

Example 1:

Input: nums = [2,2,3,2]
Output: 3

Example 2:

Input: nums = [0,1,0,1,0,1,99]
Output: 99

Constraints:

• 1 <= nums.length <= 3 * 10:sup:`4`

• -2:sup:`31`<= nums[i] <= 2:sup:`31`- 1

• Each element in nums appears exactly three times except for one element which appears once.

Pattern

Array, Bit Manipulation

Approaches

Bit Counting

Explanation

For each bit position, we sum the bits in that position across nums. For the integers in nums that appear 3 times, the number of 1s in each position will be a multiple of 3. For each position, we can extract the bit value of the integer \(x\) that appears once by modding the sum by 3. If \(x\) is negative, then the bit values will be in 2’s complement form. We can convert unsigned integers to 2’s complement by subtracting \(2^{32}\).

Code

def singleNumber(nums: list[int]) -> int:
    """Finds the integer that appears once in ``nums`` where all other integers
    appear 3 times.
    """
    bits = 32 * [0]
    for num in nums:
        for i in range(32):
            bits[i] += getBit(num, i)

    bits = [bit % 3 for bit in bits]

    ans = 0
    for i in range(32):
        ans += bits[i] << i

    return ans if ans < 2**31 else ans - 2**32


def getBit(num, i):
    """Gets the ``i``-th bit of ``num``."""
    return (num >> i) & 1

Test

>>> from single_number_ii__bit_counting import singleNumber
>>> singleNumber([2, 2, 3, 2])
3
>>> singleNumber([0, 1, 0, 1, 0, 1, 99])
99

Complexity

\(n\) is the length of the input array

Measure	Complexity	Notes
Time	\(O(n)\)	single pass through the array
Auxiliary Space	\(O(1)\)	fixed 32-bit array to store sum

single_number_ii__bit_counting.singleNumber(nums: list[int]) → int

Finds the integer that appears once in nums where all other integers appear 3 times.

single_number_ii__bit_counting.getBit(num, i)

Gets the i-th bit of num.