What is the time complexity of Find the Integer Added to Array I?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Find the Integer Added to Array I?

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

What are the key insights for solving Find the Integer Added to Array I?

Insight 1: Since the same integer `x` is added to every element of `nums1` to obtain `nums2`, the difference between corresponding elements in `nums2` and `nums1` will always be `x`. Insight 2: No complex data structures or algorithms are needed. A simple subtraction operation is sufficient.

Which companies ask LeetCode 3131. Find the Integer Added to Array I in interviews?

This problem is frequently asked at Mitsogo.

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Find the Integer Added to Array I - LeetCode 3131 Solution

Find the Integer Added to Array I - Complete Solution Guide

Find the Integer Added to Array I is LeetCode problem 3131, 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

You are given two arrays of equal length, nums1 and nums2 . Each element in nums1 has been increased (or decreased in the case of negative) by an integer, represented by the variable x . As a result, nums1 becomes equal to nums2 . Two arrays are considered equal when they contain the same integers with the same frequencies. Return the integer x . Example 1: Input: nums1 = [2,6,4], nums2 = [9,7,5] Output: 3 Explanation: The integer added to each element of nums1 is 3. Example 2: Input: nums1 = [1

Detailed Explanation

The problem asks you to find the integer `x` that, when added to each element in array `nums1`, makes it equal to array `nums2`. Two arrays are considered equal if they contain the same elements with the same frequencies. The input consists of two integer arrays, `nums1` and `nums2`, of equal length. The output is the integer `x`. Constraints specify that the arrays will have lengths between 1 and 100, inclusive, and that elements will be between 0 and 1000, inclusive. The problem guarantees a solution exists.

Solution Approach

The solution leverages the key insight that the difference between any corresponding pair of elements from `nums1` and `nums2` will be equal to `x`. The code directly calculates this difference using the first elements of both arrays (nums2[0] - nums1[0]) as it is the simplest and most efficient way to find x. This works because the problem statement guarantees a consistent difference across all elements.

Step-by-Step Algorithm

Step 1: Access the first element of `nums2` (nums2[0]).
Step 2: Access the first element of `nums1` (nums1[0]).
Step 3: Subtract the first element of `nums1` from the first element of `nums2`.
Step 4: Return the result of the subtraction, which represents the integer `x`.

Key Insights

Insight 1: Since the same integer `x` is added to every element of `nums1` to obtain `nums2`, the difference between corresponding elements in `nums2` and `nums1` will always be `x`.
Insight 2: No complex data structures or algorithms are needed. A simple subtraction operation is sufficient.
Insight 3: The problem's guarantee that a solution exists removes the need for error handling or checks for invalid inputs.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Array.

Companies

Asked at: Mitsogo.

Find the Integer Added to Array I | LeetCode 3131

Easy

Array

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

Solution Code

Available in:

class Solution {
    public int addedInteger(int[] nums1, int[] nums2) {
        return nums2[0] - nums1[0];
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 3131: Find the Integer Added to Array I - Detailed explanation and solution approaches.

Topics

Array

Companies

Mitsogo

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:3131

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: Access the first element of `nums2` (nums2[0]).
2
Step 2: Access the first element of `nums1` (nums1[0]).
3
Step 3: Subtract the first element of `nums1` from the first element of `nums2`.
4
Step 4: Return the result of the subtraction, which represents the integer `x`.

💡

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(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The solution performs a fixed number of arithmetic operations regardless of the input array size. It uses only a constant amount of extra space to store the result of the subtraction.

📖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

Iterative Approach

Iterate through both arrays and calculate the difference between corresponding elements. The difference will be consistent for all pairs. Return the difference of the first pair encountered.

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

Trade-offs: Less efficient than the direct subtraction method. It is useful for educational purposes to show an alternative approach that directly implements the problem's logic of checking each pair, but in practice, the O(1) solution is superior.

✨

Key Insights

1Insight 1: Since the same integer `x` is added to every element of `nums1` to obtain `nums2`, the difference between corresponding elements in `nums2` and `nums1` will always be `x`.
2Insight 2: No complex data structures or algorithms are needed. A simple subtraction operation is sufficient.
3Insight 3: The problem's guarantee that a solution exists removes the need for error handling or checks for invalid inputs.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: When `nums1` and `nums2` are identical. The solution correctly returns 0, representing no integer added.
Edge case 2: When elements in `nums1` and `nums2` are large or small within the constraints. The solution handles this without any issues because standard integer arithmetic is used.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly assuming a more complex solution is needed. Beginners might try to use more sophisticated algorithms or data structures, overlooking the straightforward solution.

✗Common mistake 2: Not handling the edge case of identical arrays. This results in a correct solution only for cases where x is not 0.

✅

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: Detecting a constant offset or bias between two sets of sensor readings. In many applications, sensor data may have a consistent offset, and this algorithm could quickly determine the correction factor.

🏦Real-world scenario 2: Image processing. If two images are essentially the same but one has a constant brightness difference, this algorithm can determine the brightness adjustment needed to match them.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ 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 11, 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

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 6

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

@CodeNinjaJun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Find the Integer Added to Array I"?

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 standard techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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