DSA TrainerFind All Numbers Disappeared in an Array
Given an array of n integers where each integer is in the range [1, n], return all integers in [1, n] that do not appear in the array. Some numbers may appear twice.
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Problem
Given an array nums of n integers where nums[i] is in the range [1, n], return an array of all the integers in the range [1, n] that do not appear in nums.
Input
An integer array `nums` of length n where each element is in [1, n].
Output
A list of all integers from 1 to n that are missing from `nums`.
Examples
Input: nums = [4,3,2,7,8,2,3,1]
Output: [5,6]
Input: nums = [1,1]
Output: [2]
The brute-force approach
Use a hash set of all numbers in nums. Scan 1 to n, collect those not in the set.
seen = set(nums)
return [i for i in range(1, n+1) if i not in seen]O(n) time but O(n) extra space. Cyclic sort achieves O(n) time and O(1) extra space.
Spotting the pattern
This is a Cyclic Sort problem. The key question to ask yourself:
After the cyclic sort, why does nums[i] != i+1 at some index tell you exactly which number is missing? What should nums[i] equal if the array were complete?
Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.
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