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LeetCode Pattern/Prefix Sum/Debugging Subarray Sum: Why Your Prefix Sum + Hash Map Fails

Debugging Subarray Sum: Why Your Prefix Sum + Hash Map Fails

LeetCopilot Team
Dec 22, 2025
10 min read
Prefix SumHash MapDebuggingCommon MistakesInterview Prep
Your subarray sum solution passes some test cases but fails others. Learn the step-by-step debugging process, common bugs, and how to trace through examples to find the issue.
Complete Guide

The Complete Prefix Sum Guide: Master All Patterns, Templates, and Techniques

The ultimate comprehensive guide to prefix sum. Learn all variants (1D, 2D, hash map combinations), when to use each pattern, complete templates in multiple languages, and a systematic approach to solve any prefix sum problem.

Read the complete guide

You've implemented the prefix sum + hash map solution for Subarray Sum Equals K. It works on the examples. You submit.

Wrong Answer on test case 47/93.

You stare at your code. It looks correct. The logic makes sense. But somewhere, there's a bug.

Sound familiar? Debugging prefix sum + hash map solutions is tricky because the bugs are subtle. A missing initialization, wrong update order, or incorrect handling of edge cases can cause failures on specific test cases.

In this guide, you'll learn the step-by-step debugging process, common bugs and their symptoms, and how to trace through examples to find and fix issues fast.

TL;DR

Common bugs:

  1. Missing {0: 1} initialization → Fails on subarrays from index 0
  2. Wrong update order → Counts current element incorrectly
  3. Counting vs finding indices → Using wrong template
  4. Negative numbers → Unexpected behavior with sliding window mindset

Debugging process:

  1. Trace with small example
  2. Check hash map state at each step
  3. Verify prefix sum calculation
  4. Test edge cases

Common Bug 1: Not Initializing {0: 1}

Symptom

Solution fails on test cases where the answer includes subarrays starting from index 0.

Example That Fails

python
# BUGGY CODE
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {}  # BUG: Missing {0: 1}
    
    for num in nums:
        prefix_sum += num
        if prefix_sum - k in sum_count:
            count += sum_count[prefix_sum - k]
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1
    
    return count

# Test
print(subarraySum([1, 2, 3], 6))  # Expected: 1, Got: 0 ❌
print(subarraySum([1, 1, 1], 2))  # Expected: 2, Got: 1 ❌

The Fix

python
# FIXED CODE
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}  # ✓ Initialize with base case
    
    for num in nums:
        prefix_sum += num
        if prefix_sum - k in sum_count:
            count += sum_count[prefix_sum - k]
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1
    
    return count

# Test
print(subarraySum([1, 2, 3], 6))  # 1 ✓
print(subarraySum([1, 1, 1], 2))  # 2 ✓

Why It Works

The {0: 1} represents seeing prefix_sum = 0 once before processing any elements. This allows detection of subarrays starting from index 0.

See detailed guide: Hash Map Initialization

Common Bug 2: Updating Hash Map Too Early

Symptom

Solution counts extra subarrays or gives incorrect counts.

Example That Fails

python
# BUGGY CODE
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}
    
    for num in nums:
        prefix_sum += num
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1  # BUG: Update first
        if prefix_sum - k in sum_count:  # Then check
            count += sum_count[prefix_sum - k]
    
    return count

# Test
print(subarraySum([1], 0))  # Expected: 0, Got: 1 ❌

Why It's Wrong

Trace for nums = [1], k = 0:

code
Initial: sum_count = {0: 1}, prefix_sum = 0

i=0: num=1
  prefix_sum = 1
  Update: sum_count = {0: 1, 1: 1}
  Check: (1 - 0) = 1 in sum_count? Yes!
  count += sum_count[1] = 1
  
Result: 1 (WRONG! No subarray has sum 0)

The bug: We added prefix_sum = 1 to the map, then immediately found it when checking for prefix_sum - k = 1. This incorrectly counts the current element as a valid subarray.

The Fix

python
# FIXED CODE
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}
    
    for num in nums:
        prefix_sum += num
        if prefix_sum - k in sum_count:  # ✓ Check first
            count += sum_count[prefix_sum - k]
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1  # Then update
    
    return count

# Test
print(subarraySum([1], 0))  # 0 ✓

The Rule

Always check before update to avoid counting the current element incorrectly.

Common Bug 3: Counting vs Finding Indices

Symptom

Using the wrong template for the problem type.

Problem Type 1: Counting Subarrays

Correct approach: Store frequency, update every time

python
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}  # Frequency
    
    for num in nums:
        prefix_sum += num
        if prefix_sum - k in sum_count:
            count += sum_count[prefix_sum - k]  # Add frequency
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1  # Always update
    
    return count

Problem Type 2: Finding Longest Subarray

Correct approach: Store earliest index, update only if not seen

python
def maxSubArrayLen(nums, k):
    max_len = 0
    prefix_sum = 0
    sum_index = {0: -1}  # Earliest index
    
    for i, num in enumerate(nums):
        prefix_sum += num
        if prefix_sum - k in sum_index:
            max_len = max(max_len, i - sum_index[prefix_sum - k])
        
        # Only store if not seen before (keep earliest)
        if prefix_sum not in sum_index:
            sum_index[prefix_sum] = i
    
    return max_len

Common Mistake

❌ Using counting template for finding longest:

python
# WRONG: Always updating index
sum_index[prefix_sum] = i  # Should only update if not seen

This keeps the latest index instead of the earliest, giving shorter subarrays.

Common Bug 4: Handling Negative Numbers

Symptom

Solution works for positive numbers but fails with negatives.

Why Negatives Are Tricky

With positive numbers only, you might think sliding window works. But with negative numbers, prefix sums can decrease, breaking sliding window assumptions.

Example

code
nums = [1, -1, 5, -2, 3], k = 3

Prefix sums: 0, 1, 0, 5, 3, 6

Notice: prefix_sum goes 1 → 0 (decreased!)
This is why sliding window fails with negatives.

The Fix

Use prefix sum + hash map, which handles negatives correctly:

python
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}
    
    for num in nums:
        prefix_sum += num  # Can increase or decrease
        if prefix_sum - k in sum_count:
            count += sum_count[prefix_sum - k]
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1
    
    return count

# Test with negatives
print(subarraySum([1, -1, 5, -2, 3], 3))  # Works correctly

See detailed guide: Negative Numbers

Step-by-Step Debugging Process

Step 1: Trace with Small Example

Pick a simple test case and trace through manually.

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

code
Initial: sum_count = {0: 1}, prefix_sum = 0, count = 0

i=0: num=1
  prefix_sum = 0 + 1 = 1
  Check: (1 - 3) = -2 in {0: 1}? No
  sum_count = {0: 1, 1: 1}
  count = 0

i=1: num=2
  prefix_sum = 1 + 2 = 3
  Check: (3 - 3) = 0 in {0: 1, 1: 1}? Yes!
  count += sum_count[0] = 0 + 1 = 1
  Found subarray [1, 2]
  sum_count = {0: 1, 1: 1, 3: 1}
  count = 1

i=2: num=3
  prefix_sum = 3 + 3 = 6
  Check: (6 - 3) = 3 in {0: 1, 1: 1, 3: 1}? Yes!
  count += sum_count[3] = 1 + 1 = 2
  Found subarray [3]
  sum_count = {0: 1, 1: 1, 3: 1, 6: 1}
  count = 2

Result: 2 ✓
Subarrays: [1, 2] and [3]

Step 2: Check Hash Map State

At each iteration, verify:

  • Is the hash map correct?
  • Does it contain expected values?
  • Are frequencies/indices accurate?

Add debug prints:

python
for num in nums:
    prefix_sum += num
    print(f"num={num}, prefix={prefix_sum}, map={sum_count}")
    if prefix_sum - k in sum_count:
        count += sum_count[prefix_sum - k]
        print(f"  Found! count={count}")
    sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1

Step 3: Verify Prefix Sum Calculation

Check that prefix_sum is being calculated correctly:

  • Is it cumulative?
  • Does it handle negatives?
  • Is it reset anywhere (it shouldn't be)?

Step 4: Test Edge Cases

Edge case checklist:

python
# Empty array
assert subarraySum([], 0) == 0

# Single element (match)
assert subarraySum([5], 5) == 1

# Single element (no match)
assert subarraySum([5], 3) == 0

# All zeros
assert subarraySum([0, 0, 0], 0) == 6  # All subarrays

# Negative numbers
assert subarraySum([1, -1, 0], 0) == 3

# Target = 0
assert subarraySum([1, -1, 1, -1], 0) == 4

# Entire array
assert subarraySum([1, 2, 3], 6) == 1

The Correct Template

For Counting Subarrays

python
def subarraySum(nums: List[int], k: int) -> int:
    """
    Count subarrays with sum equal to k.
    Time: O(n), Space: O(n)
    """
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}  # Critical: base case
    
    for num in nums:
        prefix_sum += num
        
        # Check BEFORE update
        if prefix_sum - k in sum_count:
            count += sum_count[prefix_sum - k]
        
        # Update frequency
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1
    
    return count

For Finding Longest Subarray

python
def maxSubArrayLen(nums: List[int], k: int) -> int:
    """
    Find longest subarray with sum equal to k.
    Time: O(n), Space: O(n)
    """
    max_len = 0
    prefix_sum = 0
    sum_index = {0: -1}  # Critical: index before start
    
    for i, num in enumerate(nums):
        prefix_sum += num
        
        if prefix_sum - k in sum_index:
            max_len = max(max_len, i - sum_index[prefix_sum - k])
        
        # Only store if not seen (keep earliest)
        if prefix_sum not in sum_index:
            sum_index[prefix_sum] = i
    
    return max_len

Real Debugging Example

The Bug

python
# Student's code (has a bug)
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}
    
    for num in nums:
        if prefix_sum - k in sum_count:  # BUG: Check before update
            count += sum_count[prefix_sum - k]
        prefix_sum += num  # BUG: Update after check
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1
    
    return count

Finding the Bug

Test case: nums = [1], k = 1

Expected: 1 (the subarray [1])
Got: 0

Trace:

code
Initial: sum_count = {0: 1}, prefix_sum = 0, count = 0

i=0: num=1
  Check: (0 - 1) = -1 in {0: 1}? No  ← Checking with old prefix_sum!
  prefix_sum = 0 + 1 = 1  ← Update after check
  sum_count = {0: 1, 1: 1}
  count = 0

Result: 0 (WRONG!)

The issue: We check with the old prefix_sum (0), then update to the new prefix_sum (1). We should update first, then check.

The Fix

python
# FIXED CODE
def subarraySum(nums, k):
    count = 0
    prefix_sum = 0
    sum_count = {0: 1}
    
    for num in nums:
        prefix_sum += num  # ✓ Update first
        if prefix_sum - k in sum_count:  # ✓ Then check
            count += sum_count[prefix_sum - k]
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1
    
    return count

Debugging Checklist

When your solution fails, check:

  • Initialization: Did you add {0: 1} or {0: -1}?
  • Update order: Check before update, not after?
  • Prefix sum calculation: Is it cumulative? Updated correctly?
  • Template type: Counting (frequency) or finding (index)?
  • Edge cases: Empty array, single element, all zeros, negatives?
  • Hash map type: Using dict/map, not set?
  • Return value: Returning count/length, not the hash map?

Practice Problems

Debug your skills with these problems:

Beginner:

  1. Subarray Sum Equals K (#560) - Basic template
  2. Running Sum of 1d Array (#1480) - Simpler variant

Intermediate:
3. Continuous Subarray Sum (#523) - Modulo arithmetic
4. Contiguous Array (#525) - Transform to sum = 0
5. Maximum Size Subarray Sum Equals k (#325) - Finding longest

Advanced:
6. Subarray Sums Divisible by K (#974) - Negative remainders
7. Count Number of Nice Subarrays (#1248) - Transform problem

FAQ

Q: My solution works on examples but fails on submission. What should I check first?

A: Check initialization ({0: 1}) and edge cases (empty array, single element, negatives).

Q: How do I know if I should use {0: 1} or {0: -1}?

A: Counting subarrays → {0: 1}. Finding longest → {0: -1}. See Hash Map Initialization.

Q: My solution gives a count that's too high. What's wrong?

A: Likely updating the hash map before checking. Always check first, then update.

Q: My solution gives a count that's too low. What's wrong?

A: Likely missing {0: 1} initialization, which causes you to miss subarrays from index 0.

Q: How do I debug if I can't see the failing test case?

A: Create your own edge cases:

  • Empty array
  • Single element (match and no match)
  • All same values
  • Negative numbers
  • Target = 0
  • Entire array sums to target

Q: Should I use a set or a dict/map?

A: Use dict/map to store frequency or index. Use set only for existence checks (rare).

Conclusion

Debugging prefix sum + hash map solutions requires systematic thinking and understanding of common pitfalls.

Key debugging steps:

  1. Trace manually with a small example
  2. Check hash map state at each iteration
  3. Verify prefix sum calculation
  4. Test edge cases thoroughly

Common bugs:

  • Missing {0: 1} initialization
  • Wrong update order (update before check)
  • Using wrong template (counting vs finding)
  • Not handling negatives correctly

The correct template:

python
count = 0
prefix_sum = 0
sum_count = {0: 1}  # Initialize

for num in nums:
    prefix_sum += num  # Update
    if prefix_sum - k in sum_count:  # Check
        count += sum_count[prefix_sum - k]
    sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1  # Store

return count

Master this debugging process, and you'll fix prefix sum bugs in minutes. For more on this pattern, see Prefix Sum + Hash Map, Hash Map Initialization, and the complete guide.

Next time your solution fails, trace it step-by-step. The bug will reveal itself.

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