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The problem can be solved efficiently using a binary search on the minimum magnetic force. Start by sorting the basket positions, then perform a binary search to find the maximum valid minimum force. The basic idea is to check if it is possible to place all the balls with at least a certain minimum distance (force) between any two of them. If it is possible, try for a larger minimum distance, otherwise try smaller.
Time Complexity: O(n log(n) + log(maxDistance) * n), where n is the number of baskets.
Space Complexity: O(1)
1using System;
2
3class Solution {
4    public bool CanPlaceBalls(int[] position, int m, int minDist) {
5        int count = 1, lastPosition = position[0];
6        for (int i = 1; i < position.Length; i++) {
7            if (position[i] - lastPosition >= minDist) {
8                count++;
9                lastPosition = position[i];
10                if (count >= m) {
11                    return true;
12                }
13            }
14        }
15        return false;
16    }
17    
18    public int MaxDistance(int[] position, int m) {
19        Array.Sort(position);
20        int left = 1, right = position[position.Length - 1] - position[0];
21        int answer = 0;
22        while (left <= right) {
23            int mid = left + (right - left) / 2;
24            if (CanPlaceBalls(position, m, mid)) {
25                answer = mid;
26                left = mid + 1;
27            } else {
28                right = mid - 1;
29            }
30        }
31        return answer;
32    }
33    
34    static void Main() {
35        Solution sol = new Solution();
36        int[] position = {1, 2, 3, 4, 7};
37        int m = 3;
38        Console.WriteLine(sol.MaxDistance(position, m));
39    }
40}The C# solution uses array sorting followed by a binary search approach. The method `CanPlaceBalls` helps verify if balls can be placed with at least `minDist` distance apart for the binary search evaluation.
This approach involves using a binary search for determining the optimal force, aided by a greedy strategy to verify if a particular minimum force is attainable. By iterating over the sorted positions, balls are placed as far apart as possible greedily.
Time Complexity: O(n log(n) + n log(maxDistance)), where n is the number of baskets.
Space Complexity: O(1)
1
The JavaScript code utilizes a blend of greedy placement and binary search to elucidate the optimal magnetic force. The `canPlaceBalls` function ensures viability of specific spacings, driving search adjustments.