Missing Number

Clarify the problem:

• The problem requires finding the missing number in an array of distinct integers.
• The array contains numbers from 0 to n, but one number is missing.
• We need to implement a function that takes the array as input and returns the missing number.

Analyze the problem:

• Input: An array of distinct integers.
• Output: The missing number.
• Constraints:
  • The array is not empty.
  • The array contains numbers from 0 to n, but one number is missing.
  • The array size is (n-1), where n is the range of numbers.

Design an algorithm:

• We can solve this problem by calculating the sum of the expected numbers and subtracting the sum of the given array.
• The expected sum of numbers from 0 to n can be calculated using the formula (n * (n + 1)) / 2.
• We will iterate through the given array and calculate the sum of its elements.
• Finally, we will subtract the sum of the given array from the expected sum to find the missing number.

Explain your approach:

• We will implement a function called missingNumber that takes an array as input.
• We will initialize a variable expectedSum to calculate the sum of expected numbers using the formula (n * (n + 1)) / 2, where n is the length of the array plus one.
• We will iterate through the array using a loop and calculate the sum of its elements.
• We will subtract the sum of the array from the expected sum and return the result, which will be the missing number.

Write clean and readable code:

python

def missingNumber(nums):
    n = len(nums) + 1
    expectedSum = (n * (n + 1)) // 2

    actualSum = 0
    for num in nums:
        actualSum += num

    return expectedSum - actualSum

Test your code:

python

# Test case 1
nums = [3, 0, 1]
# The missing number is 2.
assert missingNumber(nums) == 2

# Test case 2
nums = [0, 1, 2, 4, 5, 6]
# The missing number is 3.
assert missingNumber(nums) == 3

# Test case 3
nums = [9, 6, 4, 2, 3, 5, 7, 0, 1]
# The missing number is 8.
assert missingNumber(nums) == 8

Optimize if necessary:

• The provided solution already has an efficient algorithm for finding the missing number using constant space and linear time complexity.
• There is no further optimization possible for this problem.

Handle error cases:

• The given code assumes that the input nums is a valid list of integers. If the input is not a list or contains non-integer elements, it may result in a TypeError.

Discuss complexity analysis:

• The time complexity of the solution is O(n) because we need to iterate through the given array once to calculate the sum of its elements.
• The space complexity is O(1) as we only use a constant amount of space to store the expected sum and the actual sum.