Act as a senior software engineer with 10+ years of experience in algorithm optimization. Explain how to implement the prefix sum (also known as scan or cumulative sum) technique in [LANGUAGE], providing a step-by-step guide suitable for [BEGINNER/INTERMEDIATE/ADVANCED] programmers. Include code snippets, time complexity analysis (O(n)), and practical use cases like [ARRAY PROCESSING/PARALLEL COMPUTING/DYNAMIC PROGRAMMING]. Highlight common pitfalls, such as off-by-one errors, and optimization tips for [HARDWARE-SPECIFIC/MULTI-THREADED] environments. Ensure the explanation is clear, concise, and actionable.