Set Mismatch

Problem Description

You have a set of integers s, which originally contains all the numbers from 1 to n. Unfortunately, due to some error, one of the numbers in s got duplicated to another number in the set, which results in repetition of one number and loss of another number. You are given an integer array nums representing the data status of this set after the error. Find the number that occurs twice and the number that is missing and return them in the form of an array.

Key Insights

• The array contains integers from 1 to n, with one number duplicated and one number missing.
• The sum of the first n natural numbers can be used to find the missing number.
• Using a hash table (or set) can help track seen numbers and identify the duplicate quickly.
• The problem can be solved in a single pass through the array.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve the problem, we can utilize a hash table (or set) to keep track of the numbers we encounter as we iterate through the array. As we check each number, we can determine if it has already been seen (indicating it's the duplicate) and calculate the expected sum to find the missing number.

1. Initialize an empty set to keep track of seen numbers.
2. Initialize variables for the duplicate and the expected sum.
3. Iterate through the array:
   • If a number is already in the set, it is the duplicate.
   • Otherwise, add it to the set.
4. Calculate the expected sum of numbers from 1 to n.
5. The missing number can be found by subtracting the sum of the numbers in the array from the expected sum.

Code Solutions