Decoded

Subarray Sum Equals K

Given an array of integers nums and an integer k, return the total number of subarrays whose sum equals to k. A subarray is a contiguous non-empty sequence of elements within an array.

Sample Input:   nums = [1, 2, 3], k = 3

Expected Output: 2

The subarrays are [1, 2] and [3].

Constraints

  • 1 <= nums.length <= 2 * 104
  • -1000 <= nums[i] <= 1000
  • -107 <= k <= 107

How We Solve This

  • Compute running sums (prefix sums) as we iterate through the array.
  • Use a HashMap to remember how many times each prefix sum has occurred.
  • For each new prefix sum, check if (currentSum - k) exists in the HashMap:
    • If yes, add its count to the answer (it represents subarrays ending at the current index that sum to k).
  • Update the HashMap with the current prefix sum.

Edge Cases to Consider

Empty Array

Input: []
k: 3
Output: 0

No subarrays can be formed, so the count is 0.

No Matching Subarrays

Input: [1, 2, 4]
k: 10
Output: 0

Correctly returns 0 when no subarray sums to k.

All Zeros

Input: [0, 0, 0]
k: 0
Output: 6

Counts multiple overlapping subarrays of zeros.

Includes Negatives

Input: [1, -1, 2]
k: 2
Output: 2

Handles negative numbers correctly in prefix sums.

Single Element Array

Input: [3]
k: 3
Output: 1

A single element can be a valid subarray.