Prefix Sum + Hash Map Explained Intuitively | Subarray Sum Equals K (Python, LeetCode)

Most people memorize the Prefix Sum + Hash Map solution for Subarray Sum Equals K — but don't truly understand why it works.
In this video, we build the idea from scratch, starting with brute force, fixing mistakes step by step, and slowly arriving at the algebraic insight that makes prefix sums inevitable.
This is not a "jump to the final code" tutorial.
This is a thinking-first, interview-ready, intuition-driven explanation.
What you'll learn in this video:
• Why pair-based thinking fails for subarray problems
• How brute force really works (and why it breaks)
• The key invariant behind prefix sums
• The algebraic reframe that makes hash maps necessary
• Why {0:1} is not a trick
• How multiple subarrays can end at the same index
• A clean, safe Python implementation
• When prefix sums work — and why sliding window sometimes fails
Who this video is for:
• Python programmers learning DSA
• LeetCode / interview candidates
• Anyone who wants deep understanding, not memorization
Covered Pattern:
• Prefix Sum + Hash Map
• History-based hashing
• Subarray counting problems
LeetCode problem: Subarray Sum Equals K
Language: Python

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