To solve Subarray Sum Equals K, iterate through nums while maintaining a prefix sum and a hash map of seen sums. For each position, check if currentSum - k exists in the map to count valid subarrays. This approach avoids nested loops and reduces time complexity, leveraging the array scanning plus hash lookup pattern efficiently.
Problem Statement
Given an integer array nums and an integer k, determine the total number of contiguous subarrays whose sum equals k. Each subarray must consist of consecutive elements in nums.
For example, with nums = [1,1,1] and k = 2, there are 2 subarrays that meet the criteria. Implement an efficient solution that handles large arrays without checking all possible subarrays explicitly.
Examples
Example 1
Input: nums = [1,1,1], k = 2
Output: 2
Example details omitted.
Example 2
Input: nums = [1,2,3], k = 3
Output: 2
Example details omitted.
Constraints
- 1 <= nums.length <= 2 * 104
- -1000 <= nums[i] <= 1000
- -107 <= k <= 107
Solution Approach
Prefix Sum with Hash Map
Maintain a running prefix sum and use a hash map to store how many times each sum has occurred. For each element, increment the count by the number of times (currentSum - k) appears in the map. This exploits the array scanning plus hash lookup pattern and avoids nested iteration.
Iterative Single Pass
Scan through nums once, updating the current cumulative sum and consulting the hash map in each iteration. Add currentSum to the map after counting. This ensures O(n) time and captures all valid subarrays without recomputation.
Edge Case Handling
Initialize the hash map with {0:1} to account for subarrays starting at index 0. Carefully handle negative numbers and zeros, as they may influence the prefix sums and hash lookups, ensuring correctness across all integer ranges.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n) since each element is processed once and hash map lookups are constant on average. Space complexity is O(n) due to storing prefix sums in the hash map.
What Interviewers Usually Probe
- Checks if candidate considers brute-force inefficiency with nested loops.
- Looks for use of prefix sum combined with hash lookup to count subarrays.
- Observes whether edge cases like negative numbers and zero sums are handled correctly.
Common Pitfalls or Variants
Common pitfalls
- Forgetting to initialize hash map with 0:1, causing missed subarrays starting at index 0.
- Using nested loops which lead to O(n^2) performance and timeouts.
- Neglecting negative numbers or zeros which can invalidate prefix sum assumptions.
Follow-up variants
- Return all subarrays themselves instead of just the count using a similar prefix sum map.
- Find the longest subarray with sum equal to k, adjusting the map to store earliest indices.
- Count subarrays with sum less than or equal to k, modifying lookup logic to handle ranges.
How GhostInterview Helps
- Highlights the array scanning plus hash lookup pattern for immediate implementation.
- Detects common pitfalls like incorrect initialization or overlooked negatives and zeros.
- Offers fast, step-by-step guidance to translate the problem into an efficient O(n) solution.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the most efficient approach for Subarray Sum Equals K?
Use a prefix sum combined with a hash map to count occurrences of currentSum - k, achieving O(n) time complexity.
Can negative numbers be handled in this problem?
Yes, the prefix sum plus hash map approach works with negative numbers because it tracks cumulative sums accurately.
Why not use a brute-force nested loop?
Nested loops lead to O(n^2) time and will fail on large arrays; prefix sum with hash lookup is necessary for efficiency.
How do I account for subarrays starting at index 0?
Initialize the hash map with {0:1} to count subarrays that sum to k from the beginning of the array.
What pattern does this problem exemplify?
It exemplifies the array scanning plus hash lookup pattern where cumulative sums are mapped to frequencies for quick subarray counting.
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Open problem page