Prefix Sum vs Sliding Window: When to Use Each Pattern

You see a problem: "Find the longest subarray with sum equal to k." You think: "Subarray problem... should I use prefix sum or sliding window?"

This confusion costs interviews. Both patterns solve subarray problems, but they're designed for different scenarios. Use the wrong one, and your solution either fails or is unnecessarily complex.

In this guide, you'll learn when to use each pattern, the key differences, and a decision framework that works every time.

TL;DR

Use Prefix Sum when:

• Multiple range queries on static array
• Exact target sum (can be any value)
• Array has negative numbers
• Counting subarrays with condition

Use Sliding Window when:

• Finding longest/shortest subarray
• All positive numbers (or all non-negative)
• Variable window size with condition
• Maximum/minimum subarray value

Quick decision:

• Target sum + negatives → Prefix Sum + Hash Map
• Longest/shortest + positives → Sliding Window
• Multiple queries → Prefix Sum
• Single pass optimization → Sliding Window

The Core Difference

Prefix Sum: Range Queries

Purpose: Answer "what's the sum from index i to j?"

Approach: Precompute cumulative sums, query in O(1)

Best for:

• Multiple queries
• Exact target sum
• Static array

Example:

# Build once
prefix = [0, 1, 3, 6, 10, 15]

# Query many times in O(1)
sum(2, 4) = prefix[5] - prefix[2] = 15 - 3 = 12

Sliding Window: Contiguous Subarrays

Purpose: Find "longest/shortest subarray meeting condition"

Approach: Expand/shrink window dynamically

Best for:

• Finding optimal subarray
• Variable window size
• Positive numbers only

Example:

# Find longest subarray with sum ≤ k
left = 0
for right in range(n):
    window_sum += nums[right]
    while window_sum > k:
        window_sum -= nums[left]
        left += 1
    max_len = max(max_len, right - left + 1)

Side-by-Side Comparison

Decision Framework

Question 1: Fixed or Variable Size?

Fixed size (k elements):
→ Use Sliding Window (simpler)

Variable size (find optimal):
→ Continue to Question 2

Question 2: Multiple Queries or Single Pass?

Multiple queries:
→ Use Prefix Sum (preprocess once, query many)

Single pass:
→ Continue to Question 3

Question 3: Exact Target or Optimization?

Exact target sum:
→ Continue to Question 4

Longest/shortest/maximum:
→ Use Sliding Window

Question 4: Positive or Negative Numbers?

All positive (or non-negative):
→ Use Sliding Window

Has negative numbers:
→ Use Prefix Sum + Hash Map

Example 1: Maximum Subarray Sum (Fixed Size)

Problem

Find maximum sum of subarray of size k.

When to Use Sliding Window

Input: All numbers (positive or negative)
Goal: Maximum sum
Window: Fixed size k

Solution: Sliding Window

def maxSumFixedWindow(nums, k):
    window_sum = sum(nums[:k])
    max_sum = window_sum
    
    for i in range(k, len(nums)):
        window_sum += nums[i] - nums[i-k]
        max_sum = max(max_sum, window_sum)
    
    return max_sum

Why: Fixed window size, single pass optimization.

When to Use Prefix Sum

If you need multiple queries:

# Answer: "What's max sum for window size 3? 5? 7?"
# Prefix sum allows O(1) per query

Example 2: Subarray Sum Equals K

Problem

Count subarrays with sum equal to k.

When Sliding Window Fails

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

Sliding window approach (WRONG):

# This doesn't work because negatives break monotonicity
left = 0
count = 0
window_sum = 0

for right in range(len(nums)):
    window_sum += nums[right]
    
    while window_sum > k and left <= right:
        window_sum -= nums[left]
        left += 1
    
    if window_sum == k:
        count += 1

# Result: 1 (WRONG! Should be 4)
# Misses: [1,-1,1], [-1,1,1], [1]

Why it fails: Negatives mean window_sum can increase or decrease, breaking the "shrink when too large" logic.

When Prefix Sum + Hash Map Works

Correct approach:

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:
            count += sum_count[prefix_sum - k]
        sum_count[prefix_sum] = sum_count.get(prefix_sum, 0) + 1
    
    return count

# Result: 4 ✓

Why it works: Hash map tracks all previous prefix sums, handles negatives correctly.

Example 3: Minimum Size Subarray Sum

Problem

Find minimum length subarray with sum ≥ target (all positive numbers).

When Sliding Window Works

Input: All positive numbers
Goal: Minimum length
Condition: Sum ≥ target

Solution: Sliding Window

def minSubArrayLen(target, nums):
    left = 0
    window_sum = 0
    min_len = float('inf')
    
    for right in range(len(nums)):
        window_sum += nums[right]
        
        while window_sum >= target:
            min_len = min(min_len, right - left + 1)
            window_sum -= nums[left]
            left += 1
    
    return min_len if min_len != float('inf') else 0

Why: Positive numbers ensure monotonicity—adding elements increases sum, removing decreases it.

When Prefix Sum is Overkill

Prefix sum approach would work but is more complex:

# Requires binary search or two pointers on prefix array
# Sliding window is simpler and more intuitive

Example 4: Longest Substring Without Repeating Characters

Problem

Find longest substring with all unique characters.

Why Prefix Sum Doesn't Apply

This isn't a sum problem!

Solution: Sliding Window + Hash Set

def lengthOfLongestSubstring(s):
    left = 0
    seen = set()
    max_len = 0
    
    for right in range(len(s)):
        while s[right] in seen:
            seen.remove(s[left])
            left += 1
        seen.add(s[right])
        max_len = max(max_len, right - left + 1)
    
    return max_len

Pattern: Sliding window works for any condition, not just sums.

Common Mistakes

Mistake 1: Using Sliding Window with Negatives

❌ Wrong:

# Array has negatives
nums = [1, -1, 5, -2, 3]
# Using sliding window for "sum equals k"
# Will miss valid subarrays!

✅ Correct:

# Use prefix sum + hash map

Mistake 2: Using Prefix Sum for "Longest"

❌ Wrong:

# Finding longest subarray with sum ≤ k (all positive)
# Using prefix sum + binary search
# Overcomplicated!

✅ Correct:

# Use sliding window (simpler)

Mistake 3: Confusing "Exact Sum" with "At Most"

Exact sum = k: Prefix sum + hash map
Sum ≤ k (positives): Sliding window
Sum ≥ k (positives): Sliding window

When to Use Prefix Sum

✅ Use Prefix Sum When:

1. Multiple range queries on static array
2. Exact target sum with any numbers
3. Counting subarrays with sum condition
4. Array has negative numbers
5. Need O(1) query time after preprocessing

Example problems:

• Range Sum Query (#303)
• Subarray Sum Equals K (#560)
• Continuous Subarray Sum (#523)

When to Use Sliding Window

✅ Use Sliding Window When:

1. Finding longest/shortest subarray
2. All positive numbers (or non-negative)
3. Variable window size with condition
4. Maximum/minimum value in subarray
5. Single pass optimization

Example problems:

• Minimum Size Subarray Sum (#209)
• Longest Substring Without Repeating Characters (#3)
• Max Consecutive Ones III (#1004)

Visual Decision Tree

Subarray/Substring Problem
         |
         v
   Multiple queries?
    /           \
  YES            NO
   |              |
   v              v
Prefix Sum   What's the goal?
             /      |      \
        Exact    Longest  Maximum
         Sum    /Shortest   Value
          |        |          |
          v        v          v
    Negatives?  Positives? Sliding
      /    \       |       Window
    YES    NO      v
     |      |   Sliding
     v      v   Window
  Prefix  Sliding
   Sum    Window
  +Hash
   Map

Practice Problems

Prefix Sum Problems

1. Range Sum Query - Immutable (#303)
2. Subarray Sum Equals K (#560)
3. Continuous Subarray Sum (#523)
4. Subarray Sums Divisible by K (#974)

Sliding Window Problems

1. Minimum Size Subarray Sum (#209)
2. Longest Substring Without Repeating Characters (#3)
3. Max Consecutive Ones III (#1004)
4. Fruit Into Baskets (#904)

Could Use Either (Choose Wisely)

1. Maximum Average Subarray I (#643) - Fixed size → Sliding Window
2. Find All Anagrams in a String (#438) - Fixed size → Sliding Window

FAQ

Q: Can I use sliding window with negative numbers?

A: Only if you're finding longest/shortest with a monotonic condition (e.g., sum ≥ k). For exact sum with negatives, use prefix sum + hash map.

Q: Which is faster?

A: Sliding window is O(n) time, O(1) space. Prefix sum is O(n) time, O(n) space. Sliding window is more space-efficient when applicable.

Q: Can I combine both patterns?

A: Rarely needed. They solve different problem types. Choose one based on the problem requirements.

Q: What if I need multiple queries AND have negatives?

A: Use prefix sum. Build once, query many times with hash map lookups.

Q: How do I remember which to use?

A: Mnemonic: "Exact sum + negatives → Prefix. Longest + positives → Sliding."

Conclusion

Prefix sum and sliding window solve different types of subarray problems.

Key differences:

• Prefix sum: Range queries, exact sums, negatives OK
• Sliding window: Longest/shortest, positives only, variable size

Decision rules:

1. Multiple queries → Prefix Sum
2. Exact sum + negatives → Prefix Sum + Hash Map
3. Longest/shortest + positives → Sliding Window
4. Fixed window size → Sliding Window

The patterns:

Prefix Sum:

prefix_sum = 0
sum_count = {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

Sliding Window:

left = 0
for right in range(n):
    # Expand window
    window_sum += nums[right]
    
    # Shrink if needed
    while condition_violated:
        window_sum -= nums[left]
        left += 1
    
    # Update result
    max_len = max(max_len, right - left + 1)

Master this distinction, and you'll choose the right pattern instantly. For more, see the complete prefix sum guide, sliding window guide, and when prefix sum fails.

Next time you see a subarray problem, ask: "Exact sum or longest? Negatives or positives?"