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okay, let's dive into the leetcode problem 645, "set mismatch," and explore various solutions with detailed explanations and code examples (primarily in python, but the concepts can be easily adapted to other languages). we'll cover a few common and efficient approaches.

*problem statement*

you are given an integer array `nums` of length `n` that represents a set of numbers initially containing all numbers from `1` to `n`. however, due to some error, one number in the set is duplicated and another is missing.

you are given the array `nums`. find the number that occurs twice and the number that is missing and return them in the form of an array.

*example:*



*constraints:*

`2 = n = 10000`
`1 = nums[i] = n`

*understanding the problem*

the core challenge is to identify two specific numbers within the given array:

1. *the duplicate:* the number that appears more than once.
2. *the missing:* the number that is not present in the array, despite being within the expected range of 1 to `n`.

*solution 1: using a hash map (frequency counter)*

this is a straightforward and easy-to-understand approach.

*algorithm:*

1. create a hash map (dictionary) to store the frequency of each number in `nums`.
2. iterate through `nums` and update the frequency count in the hash map.
3. iterate from 1 to `n`:
check if each number `i` exists as a key in the hash map.
if a number `i` doesn't exist in the map, it's the missing number.
while iterating through `nums` we also determine which number is the duplicate (frequency 1).

*python code:*



*explanation:*

`freq = {}`: initializes an empty dictionary to store frequencies.
`freq[num] = freq.get(num, 0) + 1`: for each number `num` in `nums`, this line either increments the existing frequency count for `num` or initializes the count to 1 if it's the first time we've seen `num`. `freq.get(num, 0)` efficiently retrieves the current frequency of `num` (or 0 i ...

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Set mismatch
LeetCode 645
Amazon
Apple
Array manipulation
Duplicate numbers
Missing numbers
Algorithm
Coding interview
Data structures
Problem solving
Python
Java
C++
Complexity analysis