What is the time complexity of Find Subarrays With Equal Sum?

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

What data structures are used to solve Find Subarrays With Equal Sum?

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 Subarrays With Equal Sum?

Insight 1: The problem can be efficiently solved using a hash set to track the sums of subarrays of length 2. Insight 2: A hash set (or similar data structure like a set) provides constant-time average-case lookup (`contains()` operation), which is crucial for achieving linear time complexity.

Which companies ask LeetCode 2395. Find Subarrays With Equal Sum in interviews?

This problem is frequently asked at Morgan Stanley.

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Find Subarrays With Equal Sum - LeetCode 2395 Solution

Find Subarrays With Equal Sum - Complete Solution Guide

Find Subarrays With Equal Sum is LeetCode problem 2395, 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 a 0-indexed integer array nums , determine whether there exist two subarrays of length 2 with equal sum. Note that the two subarrays must begin at different indices. Return true if these subarrays exist, and false otherwise. A subarray is a contiguous non-empty sequence of elements within an array. Example 1: Input: nums = [4,2,4] Output: true Explanation: The subarrays with elements [4,2] and [2,4] have the same sum of 6. Example 2: Input: nums = [1,2,3,4,5] Output: false Explanation: No

Detailed Explanation

The problem asks whether there exist two subarrays of length 2 within a given integer array `nums` that have the same sum. The subarrays must start at different indices. For example, in `[4, 2, 4]`, the subarrays `[4, 2]` and `[2, 4]` both sum to 6, so the function should return `true`. The input is a 0-indexed integer array, and the output is a boolean value indicating whether such subarrays exist. The constraints specify that the array length is between 2 and 1000, inclusive, and the array elements are within the range -10<sup>9</sup> to 10<sup>9</sup>.

Solution Approach

The provided solution uses a hash set (`sums` in Python/Java/C++ and an array `sums` in C) to store the sums of all subarrays of length 2. It iterates through the input array, calculating the sum of each consecutive pair of elements. If a sum is already present in the hash set, it means we've found two subarrays with the same sum, and the function returns `true`. Otherwise, the sum is added to the hash set, and the iteration continues. If the loop completes without finding any duplicate sums, the function returns `false`.

Step-by-Step Algorithm

Step 1: Initialize an empty hash set (or array in the C solution) called `sums`.
Step 2: Iterate through the input array `nums` from index 0 to `nums.length - 2`.
Step 3: For each index `i`, calculate the sum of the subarray `nums[i], nums[i+1]`.
Step 4: Check if the calculated sum is already present in the `sums` hash set.
Step 5: If the sum is present, return `true` (two subarrays with the same sum found).
Step 6: If the sum is not present, add it to the `sums` hash set.
Step 7: After the loop completes, return `false` (no two subarrays with equal sum were found).

Key Insights

Insight 1: The problem can be efficiently solved using a hash set to track the sums of subarrays of length 2.
Insight 2: A hash set (or similar data structure like a set) provides constant-time average-case lookup (`contains()` operation), which is crucial for achieving linear time complexity.
Insight 3: The solution only needs to consider subarrays of length 2; iterating through all possible pairs of subarrays is unnecessary and would result in quadratic time complexity.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table.

Companies

Asked at: Morgan Stanley.

Find Subarrays With Equal Sum | LeetCode 2395

Easy

Array Hash Table

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

Solution Code

Available in:

import java.util.HashSet;
import java.util.Set;

class Solution {
    public boolean findSubarrays(int[] nums) {
        Set<Integer> sums = new HashSet<>();
        for (int i = 0; i < nums.length - 1; i++) {
            int sum = nums[i] + nums[i + 1];
            if (sums.contains(sum)) {
                return true;
            }
            sums.add(sum);
        }
        return false;
    }
}

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Problem Info

Description

Problem 2395: Find Subarrays With Equal Sum - Detailed explanation and solution approaches.

Topics

Array Hash Table

Companies

Morgan Stanley

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2395

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: Initialize an empty hash set (or array in the C solution) called `sums`.
2
Step 2: Iterate through the input array `nums` from index 0 to `nums.length - 2`.
3
Step 3: For each index `i`, calculate the sum of the subarray `nums[i], nums[i+1]`.
4
Step 4: Check if the calculated sum is already present in the `sums` hash set.
5
Step 5: If the sum is present, return `true` (two subarrays with the same sum found).
6
Step 6: If the sum is not present, add it to the `sums` hash set.
7
Step 7: After the loop completes, return `false` (no two subarrays with equal sum were found).

💡

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 algorithm iterates through the input array once, which takes O(n) time. The hash set operations (insertion and lookup) have an average time complexity of O(1). In the worst-case scenario (all subarray sums are unique), the hash set will store up to n-1 elements, resulting in O(n) space complexity. The C solution uses an array of size 1000, which is a fixed space. However, it has O(n^2) time complexity due to nested loops. The other three solutions (Python, Java, C++) have optimized time and space complexities.

📖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

Brute Force

Compare the sum of every possible subarray of length 2 with every other subarray of length 2. This involves nested loops.

Time: O(n^2)Space: O(1)

Trade-offs: This approach is less efficient than the hash set approach, especially for larger input arrays. It's simpler to understand but significantly slower.

✨

Key Insights

1Insight 1: The problem can be efficiently solved using a hash set to track the sums of subarrays of length 2.
2Insight 2: A hash set (or similar data structure like a set) provides constant-time average-case lookup (`contains()` operation), which is crucial for achieving linear time complexity.
3Insight 3: The solution only needs to consider subarrays of length 2; iterating through all possible pairs of subarrays is unnecessary and would result in quadratic time complexity.

📚

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 array or array with less than 2 elements. The solution handles this implicitly because the loop condition `i < nums.length - 1` prevents any processing if the array is too short. It correctly returns `false`.
Edge case 2: Array with all elements being the same. The solution correctly handles this case by detecting the duplicate sums. For example, `[0, 0, 0]` will result in `true` because [0,0] and [0,0] have the same sum, even though they are in different positions.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to check if the subarrays start at different indices. This is implicitly handled in the code by checking if the sums are duplicate using a hash set.

✗Common mistake 2: Using an inefficient data structure (like a list) to store sums, leading to O(n) lookup time instead of O(1) average-case, resulting in an overall O(n^2) time complexity.

✅

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 analysis tasks involving finding patterns in sequential data. For example, identifying consecutive periods with similar activity levels.

🏦Real-world scenario 2: Signal processing, where you might need to detect repeating patterns or segments in a signal with similar characteristics.

💡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.

👨‍💻 From Experience

This is one of the first problems I solved when learning Array. It's a great foundation for more complex problems.

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: July 26, 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

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 14

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

@AlgoMasterJul 7

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

@InterviewProJun 30

❓

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.

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

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 Subarrays With Equal Sum"?

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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