MissingNumber

Problem

https://leetcode.com/problems/missing-number/

Solution

Let \(m \in \{1, ..., n\}\) be the missing number. Since nums \(= \{1, ..., n\} - \{m\}\),

\[\begin{split}\begin{align} \DeclareMathOperator{\sumof}{sumof} \sumof(nums) &= \left( \sum_{i=1}^{n} i \right) - m \\ m &= \sum_{i=1}^{n} i - \sumof(nums) \end{align}\end{split}\]

Use the formula

\[\sum_{i=1}^{n} i = \frac{n(n+1)}{2}\]

to calculate the the sum from 1 to \(n\) quickly. Note that \(n\) is one more than the number of elements in nums.

Code

https://github.com/GeorgeRPu/tech-interview-prep/blob/main/solutions/MissingNumber.py

from typing import List


def missingNumber(nums: List[int]) -> int:
    """Find the single missing number in a list of integers.
    """
    n = len(nums)
    s = sum(nums)
    return n * (n + 1) // 2 - s

Test

>>> from MissingNumber import missingNumber
>>> list1 = list(range(4))
>>> list1.remove(2)
>>> missingNumber(list1)
2
>>> list2 = list(range(100))
>>> list2.remove(47)
>>> missingNumber(list2)
47

Functions

missingNumber(nums)

Find the single missing number in a list of integers.