What is the time complexity of Missing Number?

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

What data structures are used to solve Missing Number?

This problem uses Array, Hash Table, Math, Binary Search, Bit Manipulation, Sorting. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Missing Number?

Insight 1: The sum of numbers from 0 to n is easily calculated using the formula n*(n+1)/2. Insight 2: The difference between the expected sum (calculated using the formula) and the actual sum of the numbers in the array gives the missing number.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Missing Number - LeetCode 268 Solution

Q: Which companies ask LeetCode 268. Missing Number in interviews?

This problem is frequently asked at AQR Capital Management, Arista Networks, Cisco, Genpact, Goldman Sachs and 7 more companies.

Missing Number - Complete Solution Guide

Missing Number is LeetCode problem 268, 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 containing n distinct numbers in the range [0, n] , return the only number in the range that is missing from the array. Example 1: Input: nums = [3,0,1] Output: 2 Explanation: n = 3 since there are 3 numbers, so all numbers are in the range [0,3] . 2 is the missing number in the range since it does not appear in nums . Example 2: Input: nums = [0,1] Output: 2 Explanation: n = 2 since there are 2 numbers, so all numbers are in the range [0,2] . 2 is the missing number in the r

Detailed Explanation

The problem asks you to find the single missing number within a given array of numbers. The array contains 'n' distinct numbers, and these numbers are within the range [0, n]. This means the array should ideally contain all numbers from 0 to n, but exactly one number is missing. The task is to identify this missing number. For example, if the input is `[3, 0, 1]`, the missing number is 2 because the range is [0, 3] and 2 is absent.

Solution Approach

The solution uses a mathematical approach based on the sum of integers. It calculates the expected sum of numbers from 0 to n using the formula `n*(n+1)/2`, where n is the length of the input array. Then, it calculates the actual sum of the numbers present in the input array. The difference between the expected sum and the actual sum is the missing number. This works because the missing number is the only discrepancy between the expected and actual sum.

Step-by-Step Algorithm

Step 1: Calculate the length of the input array and store it in variable 'n'.
Step 2: Calculate the expected sum of numbers from 0 to n using the formula `n * (n + 1) / 2`.
Step 3: Calculate the actual sum of the numbers in the input array by iterating through the array and summing up its elements.
Step 4: Subtract the actual sum from the expected sum. The result is the missing number.

Key Insights

Insight 1: The sum of numbers from 0 to n is easily calculated using the formula n*(n+1)/2.
Insight 2: The difference between the expected sum (calculated using the formula) and the actual sum of the numbers in the array gives the missing number.
Insight 3: This approach efficiently solves the problem using constant extra space (O(1)) because it only needs a few integer variables to store sums and the array length.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Hash Table, Math, Binary Search, Bit Manipulation, Sorting.

Companies

Asked at: AQR Capital Management, Arista Networks, Cisco, Genpact, Goldman Sachs, Google, Infosys, Nvidia, Revolut, Tesla, Warnermedia, tcs.

Missing Number | LeetCode 268

Easy

Array Hash Table Math Binary Search Bit Manipulation Sorting

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public int missingNumber(int[] nums) {
        int n = nums.length;
        int expectedSum = n * (n + 1) / 2;
        int actualSum = 0;
        for (int num : nums) {
            actualSum += num;
        }
        return expectedSum - actualSum;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 268: Missing Number - Detailed explanation and solution approaches.

Topics

Array Hash Table Math Binary Search Bit Manipulation Sorting

Companies

AQR Capital ManagementArista NetworksCiscoGenpactGoldman SachsGoogleInfosysNvidia

Stats

Difficulty:Easy

Languages:4

Companies:12

Problem #:268

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

4 steps

1
Step 1: Calculate the length of the input array and store it in variable 'n'.
2
Step 2: Calculate the expected sum of numbers from 0 to n using the formula `n * (n + 1) / 2`.
3
Step 3: Calculate the actual sum of the numbers in the input array by iterating through the array and summing up its elements.
4
Step 4: Subtract the actual sum from the expected sum. The result is the missing number.

💡

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(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(n) because we iterate through the array once to calculate the actual sum. The space complexity is O(1) because we only use a few integer variables to store the length of the array, expected sum, and actual sum. No extra data structures proportional to the input size are used.

📖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

Bit Manipulation

Use bit manipulation (XOR) to find the missing number. XORing all numbers from 0 to n with the numbers in the array will result in the missing number.

Time: O(n)Space: O(1)

Trade-offs: Bit manipulation can be slightly faster than the sum approach in some cases but might be less intuitive for beginners.

Sorting

Sort the array and then iterate to find the missing number.

Time: O(n log n)Space: O(1) (in-place sort) or O(n) (for some sorting algorithms)

Trade-offs: Sorting is less efficient than the sum approach in terms of time complexity but can be simpler to understand for beginners.

✨

Key Insights

1Insight 1: The sum of numbers from 0 to n is easily calculated using the formula n*(n+1)/2.
2Insight 2: The difference between the expected sum (calculated using the formula) and the actual sum of the numbers in the array gives the missing number.
3Insight 3: This approach efficiently solves the problem using constant extra space (O(1)) because it only needs a few integer variables to store sums and the array length.

📚

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!

Binary Search

Halving the search space each step. Like finding a word in a dictionary!

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty array: The code correctly handles an empty array by returning 0 (expected sum - actual sum = 0 - 0 = 0).
Edge case 2: Array with only one element: If the array contains a single element, say [0], the code correctly determines that the missing number is 1 (expected sum for n=1 is 1, actual sum is 0; 1-0=1)

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Off-by-one errors: Incorrectly calculating the expected sum or handling array indices can lead to wrong results.

✗Common mistake 2: Integer overflow: For very large arrays, the sums might exceed the maximum value of the integer data type. Using long integers could prevent overflow.

✅

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: Checking for missing data entries in a dataset.

🏦Real-world scenario 2: Network packet sequencing: Ensuring all packets in a sequence have arrived.

💡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 "Missing Number"?

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.

🤖 Need help with this problem?