What is the time complexity of Running Sum of 1d Array?

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

What data structures are used to solve Running Sum of 1d Array?

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

What are the key insights for solving Running Sum of 1d Array?

Insight 1: The running sum at each index is simply the running sum at the previous index plus the current element. This allows for a single-pass solution. Insight 2: A simple iterative approach using a loop is sufficient and efficient to solve this problem. No advanced data structures are needed.

Which companies ask LeetCode 1480. Running Sum of 1d Array in interviews?

This problem is frequently asked at EPAM Systems.

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Running Sum of 1d Array - LeetCode 1480 Solution

Running Sum of 1d Array - Complete Solution Guide

Running Sum of 1d Array is LeetCode problem 1480, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3.

Problem Statement

Given an array nums . We define a running sum of an array as runningSum[i] = sum(nums[0]…nums[i]) . Return the running sum of nums . Example 1: Input: nums = [1,2,3,4] Output: [1,3,6,10] Explanation: Running sum is obtained as follows: [1, 1+2, 1+2+3, 1+2+3+4]. Example 2: Input: nums = [1,1,1,1,1] Output: [1,2,3,4,5] Explanation: Running sum is obtained as follows: [1, 1+1, 1+1+1, 1+1+1+1, 1+1+1+1+1]. Example 3: Input: nums = [3,1,2,10,1] Output: [3,4,6,16,17] Constraints: 1 <= nums.lengt

Detailed Explanation

The problem asks you to calculate the running sum of a 1D array. The running sum at index `i` is the sum of all elements from index 0 up to and including index `i`. The input is an array of integers, `nums`. The output is a new array of the same length, where each element represents the running sum up to that point. For example, if the input is `[1, 2, 3, 4]`, the output should be `[1, 3, 6, 10]` because: 1, 1+2, 1+2+3, 1+2+3+4. The constraints specify that the input array will have a length between 1 and 1000, inclusive, and the elements within the array will be between -10<sup>6</sup> and 10<sup>6</sup>, inclusive.

Solution Approach

The provided Python solution uses a straightforward iterative approach. It initializes an empty list called `running_sum` to store the results. It then iterates through the input array `nums`. In each iteration, it adds the current element to a `current_sum` variable. This `current_sum` is then appended to the `running_sum` list, representing the running sum up to that point. Finally, the `running_sum` list is returned.

Step-by-Step Algorithm

Step 1: Initialize an empty list called `running_sum` to store the running sums.
Step 2: Initialize a variable `current_sum` to 0.
Step 3: Iterate through the input array `nums`.
Step 4: In each iteration, add the current element `num` to `current_sum`.
Step 5: Append `current_sum` to the `running_sum` list.
Step 6: After iterating through all elements, return the `running_sum` list.

Key Insights

Insight 1: The running sum at each index is simply the running sum at the previous index plus the current element. This allows for a single-pass solution.
Insight 2: A simple iterative approach using a loop is sufficient and efficient to solve this problem. No advanced data structures are needed.
Insight 3: Handling an empty input array is not explicitly mentioned, but a robust solution should gracefully handle this edge case by returning an empty array.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Prefix Sum.

Companies

Asked at: EPAM Systems.

Running Sum of 1d Array | LeetCode 1480

Easy

Array Prefix Sum

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

Solution Code

Available in:

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 1480: Running Sum of 1d Array - Detailed explanation and solution approaches.

Topics

Array Prefix Sum

Companies

EPAM Systems

Stats

Difficulty:Easy

Languages:2

Companies:1

Problem #:1480

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

6 steps

1
Step 1: Initialize an empty list called `running_sum` to store the running sums.
2
Step 2: Initialize a variable `current_sum` to 0.
3
Step 3: Iterate through the input array `nums`.
4
Step 4: In each iteration, add the current element `num` to `current_sum`.
5
Step 5: Append `current_sum` to the `running_sum` list.
6
Step 6: After iterating through all elements, return the `running_sum` list.

💡

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 O(n) because the code iterates through the input array once. The space complexity is O(n) because the solution creates a new array of the same size as the input array to store the running sums.

📖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

Modify the input array directly instead of creating a new array. This would reduce space complexity.

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

Trade-offs: This approach modifies the original array, which might not be desirable in all situations. It improves space complexity at the cost of potentially altering the input data.

✨

Key Insights

1Insight 1: The running sum at each index is simply the running sum at the previous index plus the current element. This allows for a single-pass solution.
2Insight 2: A simple iterative approach using a loop is sufficient and efficient to solve this problem. No advanced data structures are needed.
3Insight 3: Handling an empty input array is not explicitly mentioned, but a robust solution should gracefully handle this edge case by returning an empty array.

📚

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: Empty input array. The solution handles this correctly by returning an empty list.
Edge case 2: Array with all zeros. The solution correctly produces an array with the same number of zeros and cumulative sums of zero.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly accumulating the sum. Beginners might forget to add the current element to the running sum in each iteration.

✗Common mistake 2: Off-by-one errors. Incorrectly handling the starting index or the loop termination condition.

✅

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: Tracking cumulative sales figures over time. Each element in the array represents daily sales, and the running sum shows the total sales up to that day.

🏦Real-world scenario 2: Calculating cumulative network traffic. Each element could be the amount of data transferred in a time interval, and the running sum provides the total data transferred so far.

💡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 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

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

❓

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.

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 "Running Sum of 1d 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 prefix sum techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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