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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)
1#include <iostream>
2#include <vector>
3#include <algorithm>
4
5bool canPlaceBalls(const std::vector<int>& position, int m, int minDist) {
6 int count = 1, lastPosition = position[0];
7 for (int i = 1; i < position.size(); i++) {
8 if (position[i] - lastPosition >= minDist) {
9 count++;
10 lastPosition = position[i];
11 if (count >= m)
12 return true;
13 }
14 }
15 return false;
16}
17
18int maxDistance(std::vector<int>& position, int m) {
19 std::sort(position.begin(), position.end());
20 int left = 1, right = position.back() - position.front();
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
34int main() {
35 std::vector<int> position = {1, 2, 3, 4, 7};
36 int m = 3;
37 std::cout << maxDistance(position, m) << std::endl;
38 return 0;
39}This C++ solution follows a strategy similar to the C solution. Preprocess by sorting the vector, then apply binary search on the distance. The helper function `canPlaceBalls` checks each valid distance configuration by attempting to place the balls greedily.
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.