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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)
1import java.util.Arrays;
2
3class Solution {
4 public boolean 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 Arrays.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 public static void main(String[] args) {
35 Solution sol = new Solution();
36 int[] position = {1, 2, 3, 4, 7};
37 int m = 3;
38 System.out.println(sol.maxDistance(position, m));
39 }
40}This Java implementation sorts the position array and uses binary search to zero in on the optimal minimum distance. The helper method `canPlaceBalls` determines if it is feasible to place the balls given a distance, supporting the binary search logic.
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
This Java code utilizes a binary search framework to optimize the placement of balls for maximum minimum spacing. The `canPlaceBalls` function checks the placement feasibility at each midpoint level, facilitating the binary adjustments.