Introduction

The First Negative Integer in Every Window problem involves finding the first negative number in every window of size k .

Given:

  • an array
  • window size k

the task is to:

  • return first negative integer
    from every sliding window

If no negative number exists:

  • return 0

This problem is one of the most important applications of:

 Sliding Window + Queue

This problem helps in understanding:

  • sliding window traversal
  • queue optimization
  • negative element tracking
  • efficient window processing

Example

Input:arr = [12,-1,-7,8,-15,30,16,28]
k = 3

Output:
[-1,-1,-7,-15,-15,0]

Explanation:
Window 1:
[12,-1,-7]

First negative:
-1

Window 2:
[-1,-7,8]

First negative:
-1

Constraints

1 <= arr.length <= 10^5-10^5 <= arr[i] <= 10^5
1 <= k <= arr.length

Approach 1 : Brute Force

Explanation

The simplest way to solve this problem is:

  1. Traverse every window
  2. Search first negative element
  3. Store answer

This works but repeated scanning increases complexity.

Steps

  1. Traverse all windows.
  2. Scan current window.
  3. Find first negative value.
  4. Store result.
  5. Return answer array.

Dry Run

Input:[12,-1,-7,8,-15,30,16,28]
k = 3

Window:
[12,-1,-7]

First negative:
-1

Window:
[-1,-7,8]

First negative:
-1

Window:
[-7,8,-15]

First negative:
-7

Final Result:
[-1,-1,-7,-15,-15,0]

Brute Force Code

Complexity Analysis

Time Complexity: O(n * k)Explanation:
Every window is scanned completely.

Space Complexity: O(1)
Explanation:
Only result storage is used.

Approach 2 : Queue Based Sliding Window

Explanation

The optimized solution uses:

 Queue of Negative Indices

Idea:

  • store indices of negative elements
  • remove expired indices
  • front always stores
    first negative element

This avoids repeated scanning.

Steps

  1. Create queue.
  2. Store negative indices.
  3. Remove out-of-window indices.
  4. Front stores first negative.
  5. Append result for every window.

Dry Run

Input:[12,-1,-7,8,-15,30,16,28]
k = 3

Process:
12

Queue:
empty

Process:
-1

Queue:
[-1]

Process:
-7

Queue:
[-1,-7]

Window formed
First negative:
-1

Continue traversal...

Final Result:
[-1,-1,-7,-15,-15,0]

Queue Based Sliding Window Code

Complexity Analysis

Time Complexity: O(n)Explanation:
Each index enters and leaves queue at most once.

Space Complexity: O(k)
Explanation:
Queue stores negative indices.

Edge Cases

  1. No negative numbers
  2. All negative numbers
  3. Window size = 1
  4. Window size = array length
  5. Consecutive negative numbers

Why This Problem is Important

First Negative Integer in Window helps in understanding:

  1. Sliding window optimization
  2. Queue-based processing
  3. Negative tracking
  4. Efficient traversal
  5. Window management

It is one of the most important deque and sliding window interview problems.

Real-World Applications

Sliding window concepts are used in:

  1. Stream analytics
  2. Sensor monitoring
  3. Real-time alerts
  4. Financial analysis
  5. Log processing systems

Common Mistakes

  1. Forgetting expired indices
  2. Storing values instead of indices
  3. Incorrect window condition
  4. Missing no-negative case

Interview Tips

Interviewers often expect:

  1. Queue optimization explanation
  2. Sliding window understanding
  3. O(n) traversal reasoning

Always explain:

  • why indices are stored
  • how expired negatives are removed
  • why front stores first negative

Related Questions

  1. Sliding Window Maximum
  2. Shortest Subarray with Sum ≥ K
  3. Constrained Subsequence Sum
  4. Daily Temperatures
  5. Monotonic Queue Problems

Final Takeaway

The First Negative Integer in Every Window problem is a fundamental sliding window and queue optimization problem that teaches efficient window traversal and negative element tracking techniques. Understanding this problem builds a strong foundation for advanced deque and streaming interview problems.