Count Subarrays with Sum K | Prefix Sum + Hashing Pattern | Optimal Solution

Today, I’m breaking down one of the most important subarray problems in DSA - Count Subarrays with Sum = K, explained from absolute scratch with deep intuition and clear reasoning.

In this video, I focus on how to think, not just how to code, and explain why counting subarrays is different from finding the longest subarray, even though both use Prefix Sum.

I start with the brute-force idea that works for all cases, then move step by step to the optimal Prefix Sum + Hashing approach, which handles both positive and negative numbers efficiently.

In this video, I explain everything in a simple and beginner-friendly way, covering:

✔ Problem understanding & brute-force approach (O(n²), works for all cases)
✔ Prefix Sum concept explained from scratch
✔ Key observation: prefixSum[j] - prefixSum[i] = K
✔ How Prefix Sum + Hashing counts subarrays optimally
✔ Why we store frequencies of prefix sums (not indices)
✔ Why map[0] = 1 is required (handling subarrays starting at index 0)
✔ How repeated prefix sums directly increase the count
✔ Why Sliding Window fails for this problem
✔ Time & space complexity analysis

📌 GitHub Code (Subarray Problems – Prefix Sum & Sliding Window):
👉 https://github.com/Aadi0729/Data-Stru...

This series documents everything I learn daily as I improve my DSA skills - and I explain each concept exactly the way I understand it, step by step, without skipping logic.

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