Minimum Moves to Pick K Ones

Problem Description

Alice plays a game where she must pick up exactly k ones from a binary array nums using the minimum number of moves. Alice can start at any index where nums[aliceIndex] == 1 and can perform moves to change zeros to ones or swap adjacent elements. The goal is to determine the minimum moves required to achieve this.

Key Insights

• Alice can pick up a one without counting it as a move.
• Alice can either change zeros to ones up to maxChanges times or swap adjacent elements.
• The strategy involves selecting optimal starting positions and efficiently managing moves to reach k ones.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we will utilize a sliding window approach. We will track the positions of ones in the array and calculate the number of moves required to collect k ones based on the current window of indices. We will consider the maxChanges allowed to convert zeros into ones, and adjust the total moves accordingly.

1. Use a sliding window to find contiguous segments of ones.
2. For each segment, calculate the number of moves required to collect k ones, considering how many zeros can be changed based on maxChanges.
3. Keep track of the minimum number of moves encountered.

Code Solutions