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This 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 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.
1#include <vector>
2#include <queue>
3#include <iostream>
4using namespace std;
5
6int minKBitFlips(vector<int>& nums, int k) {
7 int flips = 0, flip_count = 0;
8 vector<int> flip(nums.size(), 0);
9 for (int i = 0; i < nums.size(); i++) {
10 if (i >= k) flip_count ^= flip[i - k];
11 if (nums[i] == flip_count % 2) {
12 if (i + k > nums.size()) return -1;
13 flips++;
14 flip_count ^= 1;
15 flip[i] = 1;
16 }
17 }
18 return flips;
19}
20
21int main() {
22 vector<int> nums = {0, 0, 0, 1, 0, 1, 1, 0};
23 int k = 3;
24 cout << minKBitFlips(nums, k) << endl; // Output: 3
25 return 0;
26}In C++, the strategy is similar to C, utilizing a vector to track flips. The iterator checks the effect of previous flips on the current bit using a XOR mechanism to toggle states. A vector is used akin to a flip queue to ensure each flip affects only the appropriate length `k` segment.
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.
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.
This Java solution employs a dynamic-dependent variable `flip` that toggles based on in-place flips denoted by `A[i] += 2`, simulating a local flip state tracker, reducing memory overhead.