
Sponsored
Sponsored
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
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.