What is the time complexity of Find All Numbers Disappeared in an Array?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Find All Numbers Disappeared in an Array?

This problem uses Array, Hash Table. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Find All Numbers Disappeared in an Array?

Insight 1: The problem leverages the fact that the numbers in the input array are within a specific range ([1, n]) which can be used as indices. Insight 2: Using a set or a boolean array allows efficient checking of the presence of each number in the specified range.

Which companies ask LeetCode 448. Find All Numbers Disappeared in an Array in interviews?

This problem is frequently asked at Tinkoff.

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Find All Numbers Disappeared in an Array - LeetCode 448 Solution

Q: How to solve Find All Numbers Disappeared in an Array?

The provided solutions use a hash set (or a boolean array) to keep track of the numbers present in the input array. After iterating through the array and adding each number to the set, the code iterates from 1 to `n` (inclusive), checking if each number is present in the set. If a number is *not* present in the set, it is added to the result list. The C solution is a variation which utilizes in-place modification to achieve O(1) extra space.

Find All Numbers Disappeared in an Array - Complete Solution Guide

Find All Numbers Disappeared in an Array is LeetCode problem 448, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

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 . Example 1: Input: nums = [4,3,2,7,8,2,3,1] Output: [5,6] Example 2: Input: nums = [1,1] Output: [2] Constraints: n == nums.length 1 <= n <= 10 5 1 <= nums[i] <= n Follow up: Could you do it without extra space and in O(n) runtime? You may assume the returned list does not count as extra space.

Detailed Explanation

The problem asks us to find all numbers within the range [1, n] (inclusive) that are *missing* from a given array `nums` of `n` integers. Each element in the `nums` array is guaranteed to be within the same range [1, n]. The goal is to return a list of these missing numbers. For example, if `nums` is [4,3,2,7,8,2,3,1], the missing numbers are 5 and 6, since they are the only numbers within the range [1, 8] that are not present in the array.

Solution Approach

The provided solutions use a hash set (or a boolean array) to keep track of the numbers present in the input array. After iterating through the array and adding each number to the set, the code iterates from 1 to `n` (inclusive), checking if each number is present in the set. If a number is *not* present in the set, it is added to the result list. The C solution is a variation which utilizes in-place modification to achieve O(1) extra space.

Step-by-Step Algorithm

Step 1: Create a hash set (or boolean array) to store the numbers present in the input array `nums`.
Step 2: Iterate through the `nums` array and add each number to the hash set (or set the corresponding index in the boolean array to true).
Step 3: Create an empty list to store the missing numbers.
Step 4: Iterate from 1 to `n` (inclusive).
Step 5: For each number `i` in the range [1, n], check if it is present in the hash set (or if the corresponding index in the boolean array is true).
Step 6: If the number `i` is *not* present in the hash set (or the corresponding index in the boolean array is false), add it to the list of missing numbers.
Step 7: Return the list of missing numbers.

Key Insights

Insight 1: The problem leverages the fact that the numbers in the input array are within a specific range ([1, n]) which can be used as indices.
Insight 2: Using a set or a boolean array allows efficient checking of the presence of each number in the specified range.
Insight 3: The 'in-place' modification of the input array (as done in the C solution) is a clever way to achieve O(1) space complexity (excluding the output array), by utilizing the existing array as a hash table.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table.

Companies

Asked at: Tinkoff.

Find All Numbers Disappeared in an Array | LeetCode 448

Easy

Array Hash Table

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

Solution Code

Available in:

import java.util.*;
class Solution {
    public List<Integer> findDisappearedNumbers(int[] nums) {
        Set<Integer> numSet = new HashSet<>();
        for(int num : nums){
            numSet.add(num);
        }
        List<Integer> result = new ArrayList<>();
        for(int i = 1; i <= nums.length; i++){
            if(!numSet.contains(i)){
                result.add(i);
            }
        }
        return result;
    }
}

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Problem Info

Description

Problem 448: Find All Numbers Disappeared in an Array - Detailed explanation and solution approaches.

Topics

Array Hash Table

Companies

Tinkoff

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:448

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

7 steps

1
Step 1: Create a hash set (or boolean array) to store the numbers present in the input array `nums`.
2
Step 2: Iterate through the `nums` array and add each number to the hash set (or set the corresponding index in the boolean array to true).
3
Step 3: Create an empty list to store the missing numbers.
4
Step 4: Iterate from 1 to `n` (inclusive).
5
Step 5: For each number `i` in the range [1, n], check if it is present in the hash set (or if the corresponding index in the boolean array is true).
6
Step 6: If the number `i` is *not* present in the hash set (or the corresponding index in the boolean array is false), add it to the list of missing numbers.
7
Step 7: Return the list of missing numbers.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is determined by the two loops that iterate through the array and the range [1,n] respectively. The space complexity is determined by the size of the set (or boolean array) used to store the numbers present in the array. The C solution avoids this extra space by modifying the input array in place.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

In-place Modification (Optimized Space)

Iterate through the array. For each number `num`, change the sign of the element at index `abs(num) - 1`. Then, iterate through the array again, and any index `i` whose value is positive indicates that the number `i + 1` is missing. This approach modifies the input array directly to use it as a hash table. This is what the C solution does.

Time: O(n)Space: O(1) (excluding the output array)

Trade-offs: This approach modifies the input array in place. If the caller needs to preserve the original array, a copy needs to be made first, which would increase the space complexity to O(n). It avoids the need for an extra set or boolean array.

✨

Key Insights

1Insight 1: The problem leverages the fact that the numbers in the input array are within a specific range ([1, n]) which can be used as indices.
2Insight 2: Using a set or a boolean array allows efficient checking of the presence of each number in the specified range.
3Insight 3: The 'in-place' modification of the input array (as done in the C solution) is a clever way to achieve O(1) space complexity (excluding the output array), by utilizing the existing array as a hash table.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Edge Cases

Edge case 1: Empty input array. The provided solutions will return a list of numbers from 1 to 0 (which is an empty list in the first place). This handles this case gracefully.
Edge case 2: All numbers from 1 to n are present in the input array. In this case, the code will correctly return an empty list, as no numbers are missing.
Edge case 3: Duplicate numbers in the input array. The use of a set (or boolean array) handles duplicates correctly, as it only stores each number once. So duplicate numbers in the input don't affect the logic.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling duplicate numbers correctly. Using a list instead of a set (or boolean array) to track the numbers present in the array will lead to incorrect results when there are duplicate numbers in the input.

✗Common mistake 2: Incorrectly calculating the index for the in-place modification approach. Remember that the numbers are in the range [1, n], so you need to subtract 1 to get the correct index (i.e., `index = abs(num) - 1`).

✗Common mistake 3: Confusing the index with the number itself. Be careful to return `i+1` for the missing number in the in-place approach, as `i` represents the index.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Data validation. This algorithm can be used to validate data in a database or spreadsheet to ensure that all expected values are present and no data is missing.

🏦Real-world scenario 2: Resource allocation. In resource allocation scenarios, this can be used to find available resource IDs or identify gaps in a sequence of allocated resources.

🎮Real-world scenario 3: Error Detection: Useful in debugging software, especially when dealing with numbered entities (e.g., process IDs, sequence numbers) to quickly find missing or skipped values.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: August 28, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Find All Numbers Disappeared in an Array"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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