Binary Subarrays With Sum: Leveraging At Most Strategy

Day 21 of 30-day Coding Sprint Today I solved Binary Subarrays With Sum, using one of the most clever mathematical tricks in the Sliding Window handbook. 930. Binary Subarrays With Sum - The Problem: Find the number of non-empty subarrays with a sum equal to a specific goal. - The Challenge: In a binary array (containing 0s and 1s), multiple windows can satisfy the same sum because zeros don't increase the sum but do create new subarrays. This makes a direct "exactly K" sliding window difficult to implement. - The Strategy: The Difference of "At Most" Instead of calculating "exactly goal" directly, I created a helper function to find subarrays with a sum at most goal. The Formula: Exactly(K) = AtMost(K) - AtMost(K-1) By subtracting the count of subarrays that sum to K-1 from those that sum to K, we are left with exactly the ones that equal K. Result: O(N) time complexity and O(1) space. Note: This "At Most" pattern is a life-saver for subarray problems involving counts. It simplifies the logic significantly—instead of managing complex pointers for a fixed sum, you're just measuring how many windows fit within a limit. #30DaysOfCode #DSASprint #LeetCode #JavaScript #SlidingWindow #BinaryArrays #Algorithms #Consistency

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