What is the best approach to solve Subarray Sum Equals K?

The optimal approach for Subarray Sum Equals K is the "Optimal — Prefix Sum + Hash Map" technique. It runs in O(n) time and uses O(n) space. Key insight: if prefixSum[j] - prefixSum[i] = k, then subarray (i+1...j) sums to k. Track how many times each prefix sum value has occurred. For each new prefix sum, check if prefixSum - k exists in t

What is the time complexity of Subarray Sum Equals K?

The optimal solution for Subarray Sum Equals K has a time complexity of O(n) and a space complexity of O(n), achieved using the Prefix Sum pattern.

Is Subarray Sum Equals K a Medium LeetCode problem?

Yes, LeetCode #560 (Subarray Sum Equals K) is rated Medium. It uses the Prefix Sum pattern and is commonly asked in interviews at Facebook, Google, Amazon.

How to solve Subarray Sum Equals K in Python, Java, C++, and JavaScript?

LumiChats provides complete solutions for Subarray Sum Equals K in Python, Java, C++, and JavaScript, along with step-by-step visual animations and time/space complexity analysis. All solutions are free to view.

#560MediumPrefix Sum

Subarray Sum Equals K

Track prefix sum frequencies to count subarrays summing to K in O(n).

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Problem Statement

Given an array of integers nums and an integer k, return the total number of subarrays whose sum equals to k.

Examples

Example 1

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

Output:2

Explanation: Subarrays [1,1] (indices 0-1) and [1,1] (indices 1-2) both sum to 2.

Example 2

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

Output:2

Constraints

1 ≤ nums.length ≤ 2 × 10⁴
-1000 ≤ nums[i] ≤ 1000
-10⁷ ≤ k ≤ 10⁷

Solutions

Brute Force — All subarrays

TimeO(n²)SpaceO(1)

For every (i,j) pair, compute the subarray sum and count those equal to k. O(n²).

Visual Animation

def subarraySum(nums: list[int], k: int) -> int:
    count = 0
    for i in range(len(nums)):
        total = 0
        for j in range(i, len(nums)):
            total += nums[j]
            if total == k: count += 1
    return count

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