Sliding Window | O(N) | Python3
Intuition\nThe key intuition behind my solution lies in understanding the constraints and opportunities presented by the ability to perform swaps and the limite
# Intuition\nThe key intuition behind my solution lies in understanding the constraints and opportunities presented by the ability to perform swaps and the limited number of changes (from 0 to 1) allowed. The goal is to collect `k` ones with the minimum moves, which may involve strategically positioning oneself and utilizing the `maxChanges` optimally.\n\n1. **Without Step 2 Early Finish:** First, I explore if it\'s possible to achieve the goal without fully utilizing the sliding window, focusing on immediate opportunities around the starting position.\n\n2. **Sliding Window Optimization:** The main intuition here is leveraging a sliding window to find the optimal subset of ones, minimizing the required moves. The optimization comes from carefully selecting which ones to include based on their positions and the cost (in moves) to bring additional ones into this window.\n\n3. **Efficiency through Precomputation:** By precomputing the positions of ones, I reduce the problem to analyzing these positions, rather than the entire array, which significantly simplifies the calculations.\n\n\n# Approach\n\n1. **Early Termination Check:** I initially attempt to find a quick solution by checking if it\'s possible to meet the target `k` with the immediate ones around each position, plus the available `maxChanges`. This checks for edge cases where minimal moves are required.\n   \n2. **Sliding Window Mechanism:** The core of my solution utilizes a sliding window to consider each subset of ones (adjusted for `maxChanges`). You calculate the initial moves required for a base window and then slide this window across the array of ones\' positions, updating the required moves dynamically. This method efficiently finds the window that minimizes the number of moves needed to collect `k` ones.\n\n\n\n# Complexity\n\n- **Time Complexity:** Let `m` be the number of ones in `nums`. The first of solution has a time complexity of \\(O(n)\\) as it iterates through the array once. The sliding window part involves iterating over the array of ones\' positions, leading to a time complexity of \\(O(m)\\) for sliding the window and updating the moves. Therefore, the overall time complexity is \\(O(n + m)\\), which simplifies to \\(O(n)\\) since \\(m \\leq n\\).\n\n- **Space Complexity:** The additional space used is primarily for storing the positions of ones in `arr`, which requires \\(O(m)\\) space. Thus, the space complexity is \\(O(m)\\), where `m` is the number of ones in the array.\n\n\n# Code\n```\nclass Solution:\n    def minimumMoves(self, nums: List[int], k: int, maxChanges: int) -> int:\n        n = len(nums)\n        ans = 1e18\n        # finish without step 2\n        for i in range(n):\n            curr = nums[i]\n            move = 0\n            if i > 0 and nums[i-1] == 1:\n                curr += 1\n                move += 1\n            if i < n-1 and nums[i+1] == 1 and curr < k:\n                move += 1\n                curr += 1\n            if curr + maxChanges >= k:\n                ans = min(ans, move + (k - curr) * 2)\n        \n        if maxChanges >= k:\n            return max(0, ans)\n\n        # sliding window for step2\n        arr = [i for i, v in enumerate(nums) if v == 1]\n        target = k - maxChanges\n        l, r = 0, target-1\n        prev = sum([arr[i] - arr[l] for i in range(target)]) + maxChanges*2\n        ans = min(ans, prev)\n        for i in range(1, len(arr)):\n            diff = arr[i] - arr[i-1]\n            left_count, right_count = i - l, r - i + 1\n            curr = prev + (left_count - right_count)*diff\n            while r + 1 < len(arr) and arr[r+1] - arr[i] <= arr[i] - arr[l]:\n                curr -= arr[i] - arr[l]\n                curr += arr[r+1] - arr[i]\n                r += 1\n                l += 1\n            ans = min(ans, curr)\n            prev = curr\n        return max(0, ans)\n        \n```
['Sliding Window', 'Python3']