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.
A subarray is a contiguous part of an array.
Example 1:
Input: nums = [0,1,0], k = 1 Output: 2 Explanation: Flip nums[0], then flip nums[2].
Example 2:
Input: nums = [1,1,0], k = 2 Output: -1 Explanation: No matter how we flip subarrays of size 2, we cannot make the array become [1,1,1].
Example 3:
Input: nums = [0,0,0,1,0,1,1,0], k = 3 Output: 3 Explanation: Flip nums[0],nums[1],nums[2]: nums becomes [1,1,1,1,0,1,1,0] Flip nums[4],nums[5],nums[6]: nums becomes [1,1,1,1,1,0,0,0] Flip nums[5],nums[6],nums[7]: nums becomes [1,1,1,1,1,1,1,1]
Constraints:
1 <= nums.length <= 1051 <= k <= nums.lengthThis approach uses a greedy strategy with the help of a queue to track the index of flips. The idea is to traverse through the array and only flip when necessary, using a queue to efficiently track start points of flips that affect the current position. When flipping, add the index to a queue. Dequeue any index that is outside the current consideration (i.e., more than 'k' steps away).
The code uses an auxiliary array `flip` to mark the positions where flips start. The array `flip` is needed to handle the state of whether a bit was flipped or not due to a previous operation. As we iterate through the binary array, we adjust our current state (taking into account the cumulative effect of flips up to `k` positions back) and determine if a flip is necessary. Flips are counted and active flips older than `k` moves are ignored to maintain efficiency.
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The time complexity is O(n), where n is the length of nums, because we make a single pass through the array, and the space complexity is O(n) due to the auxiliary array used to track flips.
This approach utilizes a sliding window technique with a flipping effect flag, which acts as a state tracker for ongoing flip operations. Using an in-place element flipping marker in the array enables this technique to minimize memory usage and avoid using additional data structures to track state.
This implementation uses a simple numeric transition state directly within the input array, marking flips by incrementing values past a threshold. Operation continuity checks thereby use `A[i]` as an in-place modified tracker, optimizing for process space considerations.
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Time complexity is O(n) because only single iteration and local modification are performed, while the space complexity is O(1), assisting state via in-place array manipulation.
| Approach | Complexity |
|---|---|
| Greedy Approach with Queue | The time complexity is O(n), where n is the length of nums, because we make a single pass through the array, and the space complexity is O(n) due to the auxiliary array used to track flips. |
| Sliding Window In-Place Approach | Time complexity is O(n) because only single iteration and local modification are performed, while the space complexity is O(1), assisting state via in-place array manipulation. |
Minimum Number of K Consecutive Bit Flips - Leetcode 995 - Python • NeetCodeIO • 15,507 views views
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