Missing Number
To solve this coding challenge, we need to determine which number is missing from a given array of
distinct numbers in the range
. This problem can be efficiently solved using a mathematical approach that leverages the property of the sum of the first
natural numbers.
natural numbers is given by the formula:
\[ S = \frac{n \times (n + 1)}{2} \]
where
is the length of the given array of numbers.
Given that the numbers in the array range from
to
and are distinct, the sum of the numbers in the array should be equal to this calculated sum if no number were missing. However, since one number is missing, the actual sum of the numbers in the array will be less than this calculated sum by the value of the missing number.
Therefore, the missing number can be found by:
\[ \text{Missing Number} = S - \text{Actual Sum} \]
where
is the sum of the elements in the given array.
n
[0, n]
n
Explanation
The sum of the firstn
n
0
n
Actual Sum
Pseudocode with Comments
# Begin by calculating the expected sum using the formula.
expected_sum = n * (n + 1) // 2
# The sum function provides the actual sum of numbers in the array.
actual_sum = sum(nums)
# The missing number is simply the difference between the expected_sum and actual_sum.
missing_number = expected_sum - actual_sum
# Return the missing number to the caller.
return missing_number
Detailed Steps in Pseudocode
- Calculate the length of the input array:
-
This will tell us the value of
n
[0, n]
-
Compute the expected sum of the first
n
-
Use the formula for the sum of the first
n
- Calculate the actual sum of the elements in the array:
- Sum all the numbers present in the given array using a summation function.
- Determine the missing number:
- The missing number is the difference between the expected sum and the actual sum computed.
n = length_of(nums) # Get the length of nums array
expected_sum = n * (n + 1) // 2 # Calculate the expected sum
actual_sum = sum(nums) # Compute the sum of all elements in the array
missing_number = expected_sum - actual_sum # Derive the missing number