How do you solve Minimum Moves to Pick K Ones on LeetCode?

Minimum Moves to Pick K Ones (LeetCode #3086) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using a sliding window helps to efficiently find the best segment of k ones.

What is the time complexity of Minimum Moves to Pick K Ones?

The optimal solution for Minimum Moves to Pick K Ones runs in O(n) time and uses O(n) space. The prefix sum array allows us to quickly calculate the number of ones in any window of size k, leading to linear time complexity.

What is the brute force solution for Minimum Moves to Pick K Ones?

The brute force approach for Minimum Moves to Pick K Ones is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible starting position for Alice and simulating the process of picking up k ones. This method is straightforward but inefficient, as it explores all combinations of moves. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Moves to Pick K Ones?

Minimum Moves to Pick K Ones uses the following concepts: Array, Greedy, Sliding Window, Prefix Sum. The recommended patterns to study are: Sliding Window, Prefix Sum.

What are the interview tips for Minimum Moves to Pick K Ones?

Always think about edge cases, such as when k is larger than the number of ones available. Clarify the problem constraints and how they affect your approach. Practice explaining your thought process as you work through the problem.

What are common mistakes when solving Minimum Moves to Pick K Ones?

Not considering the impact of maxChanges on the number of moves required. Failing to optimize the search for segments of k ones.

#3086

Minimum Moves to Pick K Ones

Hard

ArrayGreedySliding WindowPrefix SumSliding WindowPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal solution uses a sliding window approach combined with prefix sums to efficiently calculate the minimum moves required to collect k ones. This method reduces unnecessary checks and focuses on the most promising segments of the array.

⚙️

Algorithm

3 steps

1Step 1: Create a prefix sum array to count the number of ones in the original array.
2Step 2: Use a sliding window of size k to find the best segment of k ones, calculating the moves needed to convert zeros to ones within this window.
3Step 3: For each window, calculate the number of moves required, considering the maxChanges allowed.

solution.py13 lines

1def minMoves(nums, k, maxChanges):
2    n = len(nums)
3    prefix_sum = [0] * (n + 1)
4    for i in range(n):
5        prefix_sum[i + 1] = prefix_sum[i] + nums[i]
6    min_moves = float('inf')
7    for i in range(n - k + 1):
8        ones_in_window = prefix_sum[i + k] - prefix_sum[i]
9        zeros_in_window = k - ones_in_window
10        moves = zeros_in_window + (ones_in_window - 1)
11        if zeros_in_window <= maxChanges:
12            min_moves = min(min_moves, moves)
13    return min_moves

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Complexity note: The prefix sum array allows us to quickly calculate the number of ones in any window of size k, leading to linear time complexity.

1Using a sliding window helps to efficiently find the best segment of k ones.
2Prefix sums allow for quick calculations of the number of ones in any segment.

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