Package g3001_3100.s3086_minimum_moves_to_pick_k_ones

Class Solution

java.lang.Object

g3001_3100.s3086_minimum_moves_to_pick_k_ones.Solution

public class Solution
extends Object

3086 - Minimum Moves to Pick K Ones.

Hard

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:

• Select any index j != aliceIndex such that nums[j] == 0 and set nums[j] = 1. This action can be performed at most maxChanges times.
• Select any two adjacent indices 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:

• At the start of the game Alice picks up the one and nums[1] becomes 0. nums becomes [1, 1 ,1,0,0,1,1,0,0,1].
• Select j == 2 and perform an action of the first type. nums becomes [1, 0 ,1,0,0,1,1,0,0,1]
• Select 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].
• Select 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:

• Select j == 1 and perform an action of the first type. nums becomes [0 ,1,0,0].
• Select 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].
• Select j == 1 again and perform an action of the first type. nums becomes [0 ,1,0,0].
• Select 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 <= 105
• 0 <= nums[i] <= 1
• 1 <= k <= 105
• 0 <= maxChanges <= 105
• maxChanges + sum(nums) >= k

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
long	minimumMoves(int[] nums, int k, int maxChanges)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Solution

public Solution()

Method Details

minimumMoves

public long minimumMoves(int[] nums,
 int k,
 int maxChanges)