Max Consecutive Ones III

1. Define the problem

Given a binary array and an integer k, return the longest run of 1s you can make by flipping at most k zeros . Treat zeros as a budget inside the window: grow right, and shrink left whenever the zero count exceeds k.

Constraints

1 ≤ nums.length ≤ 10⁵
nums_i is either 0 or 1
0 ≤ k ≤ nums.length

Example

Inputnums = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0], k = 2

Output6

Explanation Flip the two 0s at indices 5 and 4 (or nearby) to get a run of six 1s.

2. Visualize the solution

Window may hold at most k zeros

Statusvalid

Two zeros so far; zeros = 2 <= k; best = 4.

What happens in this step

window = [0, 3]  [1, 1, 0, 0]

before: zeros = 0 (right = 1)
  right = 2: nums[2] = 0 → zeros = 1
  right = 3: nums[3] = 0 → zeros = 2

Both zeros fit inside the k = 2 flip budget — window valid; best becomes 4.

Step 1 of 4

Steps to visualize

Grow right; if the new value is 0, increment the zero budget used.
While zeros exceed k, advance left and decrement when leaving a zero.
The window always represents a stretch fixable with at most k flips.
Update best with the current window length after each adjustment.
Continue until right reaches the end of the array.

3. Walk through the code

Walk through the code

Same walkthrough, now with the code. Press Next to move one step and watch which lines run.

Window may hold at most k zeros

Statusvalid

Two zeros so far; zeros = 2 <= k; best = 4.

What happens in this step

window = [0, 3]  [1, 1, 0, 0]

before: zeros = 0 (right = 1)
  right = 2: nums[2] = 0 → zeros = 1
  right = 3: nums[3] = 0 → zeros = 2

Both zeros fit inside the k = 2 flip budget — window valid; best becomes 4.

Step 1 of 4

4. Solution

Solution

solution.tsTypeScript

function longestOnes(nums, k) {
  let left = 0;
  let zeros = 0;
  let best = 0;

  for (let right = 0; right < nums.length; right++) {
    if (nums[right] === 0) zeros++;

    while (zeros > k) {
      if (nums[left] === 0) zeros--;
      left++;
    }

    best = Math.max(best, right - left + 1);
  }

  return best;
}

Time: O(n)
Space: O(1)

5. Test cases

Test cases

Input	Expected	Covers
`nums = [1,1,1,0,0,0,1,1,1,1,0], k = 2`	`6`	Docstring example
`nums = [1], k = 0`	`1`	Single one
`nums = [0, 0, 1, 1], k = 2`	`4`	k covers all zeroes
`nums = [1, 1, 1, 1], k = 0`	`4`	All ones
`nums = [0, 0, 0], k = 1`	`1`	All zeroes with k = 1
`nums = [1, 0, 1, 1, 0, 1], k = 0`	`2`	k = 0 is plain max consecutive ones
`nums = [1,1,0,0,1,1,1,0,1,1], k = 2`	`7`	Walkthrough array best length 7

Max Consecutive Ones III