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.
\n
Example 1:
\n\nInput: nums = [1,1,0,0,0,1,1,0,0,1], k = 3, maxChanges = 1
\n\nOutput: 3
\n\nExplanation: 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 [1,1,1,0,0,1,1,0,0,1].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:
\n\nInput: nums = [0,0,0,0], k = 2, maxChanges = 3
\n\nOutput: 4
\n\nExplanation: 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].\n
Constraints:
\n\n2 <= n <= 1050 <= nums[i] <= 11 <= k <= 1050 <= maxChanges <= 105maxChanges + sum(nums) >= k2 moves. Hence except for the immediate neighbors of the index where we move all the ones, we should try to use change operations.",
"For some subset of ones, it is always better to move the ones to the median position.",
"We only need to be concerned with the indices where nums[i] == 1."
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