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You are given a binary array nums of length n, a positive integer k and a non-negative integer maxChanges.
Alice plays a game, where the goal is for Alice to pick up k ones from nums using the minimum number of moves. When the game starts, Alice picks up any index aliceIndex in the range [0, n - 1] and stands there. If nums[aliceIndex] == 1 , Alice picks up the one and nums[aliceIndex] becomes 0(this does not count as a move). After this, Alice can make any number of moves (including zero) where in each move Alice must perform exactly one of the following actions:
j != aliceIndex such that nums[j] == 0 and set nums[j] = 1. This action can be performed at most maxChanges times.x and y (|x - y| == 1) such that nums[x] == 1, nums[y] == 0, then swap their values (set nums[y] = 1 and nums[x] = 0). If y == aliceIndex, Alice picks up the one after this move and nums[y] becomes 0.Return the minimum number of moves required by Alice to pick exactly k ones.
Example 1:
Input: nums = [1,1,0,0,0,1,1,0,0,1], k = 3, maxChanges = 1
Output: 3
Explanation: Alice can pick up 3 ones in 3 moves, if Alice performs the following actions in each move when standing at aliceIndex == 1:
nums[1] becomes 0. nums becomes [1,0,0,0,0,1,1,0,0,1].j == 2 and perform an action of the first type. nums becomes [1,0,1,0,0,1,1,0,0,1]x == 2 and y == 1, and perform an action of the second type. nums becomes [1,1,0,0,0,1,1,0,0,1]. As y == aliceIndex, Alice picks up the one and nums becomes [1,0,0,0,0,1,1,0,0,1].x == 0 and y == 1, and perform an action of the second type. nums becomes [0,1,0,0,0,1,1,0,0,1]. As y == aliceIndex, Alice picks up the one and nums becomes [0,0,0,0,0,1,1,0,0,1].Note that it may be possible for Alice to pick up 3 ones using some other sequence of 3 moves.
Example 2:
Input: nums = [0,0,0,0], k = 2, maxChanges = 3
Output: 4
Explanation: Alice can pick up 2 ones in 4 moves, if Alice performs the following actions in each move when standing at aliceIndex == 0:
j == 1 and perform an action of the first type. nums becomes [0,1,0,0].x == 1 and y == 0, and perform an action of the second type. nums becomes [1,0,0,0]. As y == aliceIndex, Alice picks up the one and nums becomes [0,0,0,0].j == 1 again and perform an action of the first type. nums becomes [0,1,0,0].x == 1 and y == 0 again, and perform an action of the second type. nums becomes [1,0,0,0]. As y == aliceIndex, Alice picks up the one and nums becomes [0,0,0,0].Constraints:
2 <= n <= 1050 <= nums[i] <= 11 <= k <= 1050 <= maxChanges <= 105maxChanges + sum(nums) >= kNeetCode