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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)
1function canPlaceBalls(position, m, minDist) {
2 let count = 1, lastPosition = position[0];
3 for (let i = 1; i < position.length; i++) {
4 if (position[i] - lastPosition >= minDist) {
5 count++;
6 lastPosition = position[i];
7 if (count >= m) {
8 return true;
9 }
10 }
11 }
12 return false;
13}
14
15function maxDistance(position, m) {
16 position.sort((a, b) => a - b);
17 let left = 1, right = position[position.length - 1] - position[0];
18 let answer = 0;
19 while (left <= right) {
20 let mid = Math.floor((left + right) / 2);
21 if (canPlaceBalls(position, m, mid)) {
22 answer = mid;
23 left = mid + 1;
24 } else {
25 right = mid - 1;
26 }
27 }
28 return answer;
29}
30
31const position = [1, 2, 3, 4, 7];
32const m = 3;
33console.log(maxDistance(position, m));The JavaScript function begins by sorting the positions array. By applying a binary search, we determine the greatest minimum separation achievable among balls. The auxiliary function `canPlaceBalls` facilitates the feasibility checks during binary search.
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 C approach employs a binary search over potential forces while utilizing a greedy method to check if balls can be spaced with at least the current middle value as the force. The `canPlaceBalls` function iterates to find feasible placement for balls.