Single Number

Clarify the problem:

• The problem requires finding the single number in an array where all other elements appear twice.
• We need to implement a function that takes an array of integers as input and returns the single number.

Analyze the problem:

• Input: An array of integers.
• Output: The single number that appears only once.
• Constraints:
  • The number of elements in the array is odd.
  • Each element appears twice except for one.

Design an algorithm:

• To find the single number, we can use the XOR operation.
• XOR of two same numbers is 0, so XORing all the elements in the array will give us the single number.

Explain your approach:

• We will implement a function called singleNumber that takes an array of integers as input.
• Initialize a variable result to 0.
• Iterate through the array and perform XOR operation between result and each element.
• The final value of result will be the single number.

Write clean and readable code:

python

def singleNumber(nums):
    result = 0
    for num in nums:
        result ^= num
    return result

Test your code:

python

# Test case 1
# Input: [2, 2, 1]
# The single number is 1.
assert singleNumber([2, 2, 1]) == 1

# Test case 2
# Input: [4, 1, 2, 1, 2]
# The single number is 4.
assert singleNumber([4, 1, 2, 1, 2]) == 4

# Test case 3
# Input: [1]
# The single number is 1.
assert singleNumber([1]) == 1

Optimize if necessary:

• The provided solution has a time complexity of O(n), where n is the length of the input array. We iterate through the array once.
• The space complexity is O(1) since we are using a constant amount of extra space.

Handle error cases:

• The given code assumes that the input nums is a valid array of integers. If the input is not a valid array or contains invalid values, it may result in unexpected behavior.

Discuss complexity analysis:

• The time complexity of the solution is O(n), where n is the length of the input array. We iterate through the array once to perform the XOR operation.
• The space complexity is O(1) since we use a constant amount of extra space to store the result.