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# LC560 - Subarray Sum Equals K

## Problem

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.

### Example

**Example 1:**

**Input:** nums = \[1,1,1], k = 2

**Output:** 2

**Example 2:**

**Input:** nums = \[1,2,3], k = 3

**Output:** 2

## Solution

Use a hash map to keep track of prefix sums as we iterate through the array. This allows us to process the entire array in T(O(n)) and S(O(n)).

```cpp
int subarraySum(vector<int>& nums, int k) {
	unordered_map<int, int> prefixSums;
	prefixSums[0] = 1;
	
	auto sum = 0;
	auto count = 0;
	
	for (auto num : nums) {
		sum += num;
		
		// Check if prefix sum exists such that delta(cSum, pSum) ==k
		if (prefixSums.find(sum - k) != prefixSums.end()) {
			count += prefixSums[sum - k];
		}
		
		prefixSums[sum]++;
	}
	
	return count;
}
```