Subarray Sum Equals K - Solution & Explanation

This straightforward approach involves checking all possible subarrays in the given array. We calculate the sum for each subarray and check if it equals k. Although simple, it can be inefficient for large arrays due to its O(n^2) time complexity.

This C code implements a nested loop where the outer loop selects the start of the subarray and the inner loop expands it, calculating the sum. If the sum equals k, it increments the count. The time complexity is O(n^2), and the space complexity is O(1).

This optimized approach uses a hashmap to store prefix sums, facilitating the identification of subarrays with the desired sum in constant time. By keeping a count of prefix sums that have been seen, we can determine how many times a specific sum - k has appeared, suggesting that a subarray ending at the current position sums to k.

This C implementation uses a hash table to track the occurrence of prefix sums, adjusted with an offset for negative indices safety, enabling identification of subarrays summing to k. The time complexity reduces to O(n), with space complexity also improving due to the hash table.