Minimum Number of K Consecutive Bit Flips

Problem Description

You are given a binary array nums and an integer k. A k-bit flip is choosing a subarray of length k from nums and simultaneously changing every 0 in the subarray to 1, and every 1 in the subarray to 0. Return the minimum number of k-bit flips required so that there is no 0 in the array. If it is not possible, return -1.

Key Insights

• Flipping a subarray of length k changes multiple elements in one operation.
• The challenge is to determine the number of flips needed to turn all 0s into 1s.
• Once a flip is made, the effect can be tracked to avoid unnecessary future flips.
• A greedy approach is optimal since we want to flip the leftmost 0 as soon as we encounter it.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

The algorithm uses a greedy approach with a sliding window technique. We maintain a count of flips and use a difference array to track where flips start and end. As we iterate through the array, we keep adjusting the current value based on the cumulative effect of flips. If we encounter a 0 that is not yet flipped, we perform a flip starting from that position. If a flip can't be performed because it would exceed the bounds of the array, we return -1.

Code Solutions