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LeetCode Pattern/Prefix Sum/Difference Array Mistakes: Why Your Range Updates Fail

Difference Array Mistakes: Why Your Range Updates Fail

LeetCopilot Team
Dec 22, 2025
9 min read
Prefix SumDifference ArrayCommon MistakesDebuggingInterview Prep
Your difference array solution looks correct but fails test cases. Learn the 4 common bugs, why forgetting the final prefix sum step breaks everything, and how to debug range update problems.
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You've implemented the difference array solution for Range Addition. The logic makes sense. You submit.

Wrong Answer.

The output is completely wrong—just an array of differences instead of the final values. Or maybe the last element is missing. Or the range boundaries are off by one.

Sound familiar? Difference array bugs are subtle because the technique has two distinct phases: applying updates and reconstructing. Miss one step or get the indices wrong, and the entire solution breaks.

In this guide, you'll learn the 4 most common difference array bugs, why they happen, and how to fix them permanently.

TL;DR

Common bugs:

  1. Forgetting final prefix sum → Returns difference array instead of result
  2. Off-by-one in range end → Doesn't update last element of range
  3. Wrong array size → Index out of bounds on diff[end+1]
  4. Updating in wrong order → Applying prefix sum too early

Correct template:

python
# 1. Initialize with size n+1
diff = [0] * (n + 1)

# 2. Apply ALL updates
for start, end, val in updates:
    diff[start] += val
    diff[end + 1] -= val  # Note: end+1

# 3. Reconstruct with prefix sum
result = []
current = 0
for i in range(n):
    current += diff[i]
    result.append(current)

return result  # Not diff!

Common Bug 1: Forgetting the Final Prefix Sum

The Bug

python
# BUGGY CODE
def getModifiedArray(length, updates):
    diff = [0] * (length + 1)
    
    for start, end, val in updates:
        diff[start] += val
        diff[end + 1] -= val
    
    return diff[:length]  # BUG: Returning difference array!

Example That Fails

python
length = 5
updates = [[1, 3, 2], [2, 4, 3]]

Expected: [0, 2, 5, 5, 3]
Got: [0, 2, 3, 0, -5, 0]  # This is the difference array!

Why It Happens

The difference array stores changes, not final values. You must apply prefix sum to reconstruct the actual array.

Trace:

code
After updates:
diff = [0, 2, 3, 0, -5, 0]

This means:
- At index 1: increase by 2
- At index 2: increase by 3 more
- At index 4: decrease by 5

To get final values, apply prefix sum:
result[0] = 0
result[1] = 0 + 2 = 2
result[2] = 2 + 3 = 5
result[3] = 5 + 0 = 5
result[4] = 5 + (-5) = 0

Wait, that gives [0, 2, 5, 5, 0], not [0, 2, 5, 5, 3]

Let me recalculate the updates:
Update [1,3,2]: diff[1]+=2, diff[4]-=2
  diff = [0, 2, 0, 0, -2, 0]
Update [2,4,3]: diff[2]+=3, diff[5]-=3
  diff = [0, 2, 3, 0, -2, -3]

Apply prefix sum:
result[0] = 0
result[1] = 0 + 2 = 2
result[2] = 2 + 3 = 5
result[3] = 5 + 0 = 5
result[4] = 5 + (-2) = 3

Result: [0, 2, 5, 5, 3] ✓

The Fix

python
# FIXED CODE
def getModifiedArray(length, updates):
    diff = [0] * (length + 1)
    
    for start, end, val in updates:
        diff[start] += val
        diff[end + 1] -= val
    
    # ✓ Apply prefix sum to reconstruct
    result = []
    current = 0
    for i in range(length):
        current += diff[i]
        result.append(current)
    
    return result  # Return reconstructed array

How to Remember

Mnemonic: "Difference array stores changes. Prefix sum converts changes to values."

Always ask yourself: "Did I apply prefix sum at the end?"

Common Bug 2: Off-by-One in Range End

The Bug

python
# BUGGY CODE
for start, end, val in updates:
    diff[start] += val
    diff[end] -= val  # BUG: Should be end+1

Example That Fails

python
length = 5
updates = [[1, 3, 2]]

With bug (diff[end]):
diff = [0, 2, 0, -2, 0, 0]
After prefix sum: [0, 2, 2, 0, 0]
Expected: [0, 2, 2, 2, 0]  # Should include index 3!

Why It Happens

The plateau effect: We want to add val from start to end inclusive.

  • diff[start] += val starts the plateau
  • diff[end+1] -= val ends the plateau after index end

If we use diff[end] -= val, the plateau ends at index end, not after it.

Visual:

code
Want to add 2 to range [1, 3]:

Correct (end+1):
diff = [0, 2, 0, 0, -2, 0]
       [0, 2, 2, 2,  0, 0]  ← Plateau from 1 to 3 ✓

Wrong (end):
diff = [0, 2, 0, -2, 0, 0]
       [0, 2, 2,  0, 0, 0]  ← Plateau from 1 to 2 only ❌

The Fix

python
# FIXED CODE
for start, end, val in updates:
    diff[start] += val
    diff[end + 1] -= val  # ✓ Correct: end+1

How to Remember

Think: "I want the value to stop increasing after index end, so I decrement at end+1."

Common Bug 3: Not Initializing Array Size

The Bug

python
# BUGGY CODE
diff = [0] * length  # BUG: Too small!

for start, end, val in updates:
    diff[start] += val
    diff[end + 1] -= val  # Index out of bounds when end = length-1!

Example That Fails

python
length = 5
updates = [[0, 4, 1]]  # Update entire array

diff = [0] * 5  # Size 5
diff[0] += 1    # OK
diff[5] -= 1    # IndexError: list index out of range!

Why It Happens

When end = length - 1, we need to access diff[end+1] = diff[length]. If the array only has size length, this is out of bounds.

The Fix

python
# FIXED CODE
diff = [0] * (length + 1)  # ✓ Extra space for end+1

for start, end, val in updates:
    diff[start] += val
    diff[end + 1] -= val  # Safe even when end = length-1

How to Remember

Rule: Always initialize difference array with size n + 1.

Common Bug 4: Updating in Wrong Order

The Bug

python
# BUGGY CODE
result = [0] * length
current = 0

for start, end, val in updates:
    diff[start] += val
    diff[end + 1] -= val
    
    # BUG: Applying prefix sum after each update
    for i in range(length):
        current += diff[i]
        result[i] = current

Why It's Wrong

This applies prefix sum k times (once per update) instead of once at the end. It's inefficient and gives wrong results because you're accumulating the difference array multiple times.

The Fix

python
# FIXED CODE
diff = [0] * (length + 1)

# Apply ALL updates first
for start, end, val in updates:
    diff[start] += val
    diff[end + 1] -= val

# Then reconstruct ONCE
result = []
current = 0
for i in range(length):
    current += diff[i]
    result.append(current)

How to Remember

Two-phase approach:

  1. Phase 1: Apply all updates to difference array
  2. Phase 2: Reconstruct final array with prefix sum

Never mix the phases!

Step-by-Step Debugging Process

Step 1: Check Array Size

python
# Should be length + 1
assert len(diff) == length + 1

Step 2: Verify Update Logic

python
# Print difference array after updates
print("Difference array:", diff)

# Should see:
# - Positive values at start indices
# - Negative values at end+1 indices

Step 3: Check Prefix Sum Application

python
# Trace prefix sum manually
current = 0
for i in range(length):
    current += diff[i]
    print(f"i={i}, diff[i]={diff[i]}, current={current}")

Step 4: Test Edge Cases

python
# Edge case 1: Update entire array
updates = [[0, length-1, 1]]

# Edge case 2: Update single element
updates = [[0, 0, 1]]

# Edge case 3: Overlapping updates
updates = [[0, 2, 1], [1, 3, 2]]

# Edge case 4: Negative values
updates = [[0, 2, -1]]

The Correct Template

Python

python
def range_addition(length: int, updates: List[List[int]]) -> List[int]:
    """
    Apply multiple range updates efficiently.
    Time: O(n + k), Space: O(n)
    """
    # Step 1: Initialize difference array (size n+1)
    diff = [0] * (length + 1)
    
    # Step 2: Apply all updates
    for start, end, val in updates:
        diff[start] += val
        diff[end + 1] -= val
    
    # Step 3: Reconstruct with prefix sum
    result = []
    current = 0
    for i in range(length):
        current += diff[i]
        result.append(current)
    
    return result

JavaScript

javascript
function rangeAddition(length, updates) {
    // Step 1: Initialize
    const diff = new Array(length + 1).fill(0);
    
    // Step 2: Apply updates
    for (const [start, end, val] of updates) {
        diff[start] += val;
        diff[end + 1] -= val;
    }
    
    // Step 3: Reconstruct
    const result = [];
    let current = 0;
    for (let i = 0; i < length; i++) {
        current += diff[i];
        result.push(current);
    }
    
    return result;
}

Java

java
public int[] rangeAddition(int length, int[][] updates) {
    // Step 1: Initialize
    int[] diff = new int[length + 1];
    
    // Step 2: Apply updates
    for (int[] update : updates) {
        int start = update[0], end = update[1], val = update[2];
        diff[start] += val;
        diff[end + 1] -= val;
    }
    
    // Step 3: Reconstruct
    int[] result = new int[length];
    int current = 0;
    for (int i = 0; i < length; i++) {
        current += diff[i];
        result[i] = current;
    }
    
    return result;
}

Real Debugging Example

The Student's Code

python
def getModifiedArray(length, updates):
    diff = [0] * length  # BUG 1: Size should be length+1
    
    for start, end, val in updates:
        diff[start] += val
        diff[end] -= val  # BUG 2: Should be end+1
    
    return diff  # BUG 3: Should apply prefix sum

Test Case

python
length = 5
updates = [[1, 3, 2], [2, 4, 3]]
expected = [0, 2, 5, 5, 3]

Debugging Process

Step 1: Run the code

python
result = getModifiedArray(5, updates)
print(result)  # [0, 2, 3, -2, -3]
# Wrong! Expected [0, 2, 5, 5, 3]

Step 2: Identify bugs

  1. Size is 5, should be 6 (might cause index error)
  2. Using diff[end] instead of diff[end+1]
  3. Returning diff instead of applying prefix sum

Step 3: Fix bugs

python
def getModifiedArray(length, updates):
    diff = [0] * (length + 1)  # ✓ Fix 1
    
    for start, end, val in updates:
        diff[start] += val
        diff[end + 1] -= val  # ✓ Fix 2
    
    # ✓ Fix 3: Apply prefix sum
    result = []
    current = 0
    for i in range(length):
        current += diff[i]
        result.append(current)
    
    return result

Step 4: Verify

python
result = getModifiedArray(5, updates)
print(result)  # [0, 2, 5, 5, 3] ✓

Debugging Checklist

When your difference array solution fails:

  • Array size: Is it length + 1?
  • Range end: Using end + 1, not end?
  • Prefix sum: Applied at the end?
  • Return value: Returning result, not diff?
  • Update order: All updates before reconstruction?
  • Edge cases: Tested with full array update?

Practice Problems

Debug your skills with these problems:

  1. Range Addition (#370) - Basic template
  2. Corporate Flight Bookings (#1109) - 1-indexed variant
  3. Car Pooling (#1094) - Capacity checking
  4. Brightest Position on Street (#2021) - Event-based

FAQ

Q: Why do I need size n+1?

A: To safely access diff[end+1] when end = length-1.

Q: What if I forget to apply prefix sum?

A: You'll return the difference array (changes) instead of the final values. The output will be completely wrong.

Q: Can I apply prefix sum in-place?

A: Yes:

python
for i in range(1, length):
    diff[i] += diff[i-1]
return diff[:length]

Q: What if updates are 1-indexed?

A: Convert to 0-indexed:

python
diff[start - 1] += val
diff[end] -= val  # end is already +1 after conversion

Q: How do I know if my difference array is correct before applying prefix sum?

A: Check:

  • Positive values at start indices
  • Negative values at end+1 indices
  • Sum of all values = sum of all update values

Conclusion

Difference array bugs are subtle but avoidable with the right checklist.

Key mistakes:

  1. Forgetting final prefix sum
  2. Using end instead of end+1
  3. Array size n instead of n+1
  4. Applying prefix sum too early

The correct process:

  1. Initialize diff = [0] * (n + 1)
  2. Apply all updates: diff[start] += val; diff[end+1] -= val
  3. Reconstruct with prefix sum
  4. Return result, not diff

The template:

python
diff = [0] * (length + 1)
for start, end, val in updates:
    diff[start] += val
    diff[end + 1] -= val

result = []
current = 0
for i in range(length):
    current += diff[i]
    result.append(current)
return result

Master this checklist, and you'll never fail a difference array problem again. For more, see Difference Array, Off-by-One Errors, and the complete guide.

Next time you implement difference arrays, remember: size n+1, end+1, prefix sum at the end.

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