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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
class Solution {
public bool CanPlaceBalls(int[] position, int m, int dist) {
int count = 1, last_position = position[0];
for (int i = 1; i < position.Length; ++i) {
if (position[i] - last_position >= dist) {
count++;
last_position = position[i];
if (count == m) {
return true;
}
}
}
return false;
}
public int MaxDistance(int[] position, int m) {
Array.Sort(position);
int left = 1, right = position[position.Length - 1] - position[0];
while (left < right) {
int mid = left + (right - left + 1) / 2;
if (CanPlaceBalls(position, m, mid)) {
left = mid;
} else {
right = mid - 1;
}
}
return left;
}
static void Main() {
Solution sol = new Solution();
int[] position = {5, 4, 3, 2, 1, 1000000000};
int m = 2;
Console.WriteLine(sol.MaxDistance(position, m));
}
}The C# program integrates a greedy and binary search method to establish the maximum value of the minimum magnetic force. The `CanPlaceBalls` method secures the placements iteratively and regulates the search bounds based on feasibility.