Optimized Sliding Window Approach

Imagine your study streak :

• You move day by day forward (right pointer)
• You allow only K bad days

If bad days exceed K:
You don’t restart from beginning
You just remove earlier days from your streak (move left)

This way:

You always maintain the best valid streak without repeating work

Core Idea (Game Changer)

The brute force method wastes time by restarting again and again.
The sliding window approach fixes this by saying:

“Don’t restart, just adjust the current window.”

Instead of checking every subarray:

• We maintain a continuous window
• Expand it when valid
• Shrink it when invalid

Intuition (Very Simple)

Think like this:

You have a window [left → right]
You are allowed at most K zeros inside this window

• If zeros ≤ K → ✅ valid → expand (move right)
• If zeros > K → ❌ invalid → shrink (move left)

Step-by-Step Working

1. Start with:

2. Move right pointer:

3. If zero_count > K:
   • Move left forward
   • Reduce zero count if needed
4. Update answer:

Dry Run Example

Final Answer = 5

Code

Complexity

• Time Complexity: O(n) ✅
• Space Complexity: O(1) ✅

Each element is visited at most twice

Why This Is Powerful

✔ No repeated work
✔ Real-time adjustment
✔ Works efficiently for large inputs
✔ Most important pattern for exams/interviews