Problem Understanding

At its core, the Flipping Bits with K-Window problem is about optimizing continuity in a binary sequence.

You are given:

• A binary array nums consisting of only 0s and 1s
• An integer k → the maximum number of 0s you are allowed to flip into 1s

Your task:

Find the maximum number of consecutive 1s you can obtain by flipping at most K zeros.

Breaking Down the Problem

Let’s simplify what this means:

• 1 → already good (no action needed)
• 0 → can be converted (but only up to K times)

So instead of asking:

“Where are the longest 1s?”

We are actually asking:

“Which segment of the array becomes the longest stretch of 1s if we are allowed to fix at most K zeros?”

Observations

1. We are not required to flip exactly K zeros
   → flipping ≤ K zeros is allowed

2. The flips must help create a continuous block
   → scattered flips won’t help unless they form a long segment

3. We are essentially searching for:

   A subarray that contains at most K zeros

Example

Consider:

Now think step-by-step:

• If we flip the two zeros at positions 1 and 4
• The array becomes:

Now the longest consecutive 1s = 5

Visual Interpretation

Think of it like a window sliding over the array**:**

Inside this window:

• We are allowed to keep at most K zeros
• Everything inside can be treated as 1s after flipping

Mathematical Insight

We are looking for:

Longest subarray such that:

And the answer is: