In the universe Earth C-137, Rick discovered a special form of magnetic force between two balls if they are put in his new invented basket. Rick has n empty baskets, the ith basket is at position[i], Morty has m balls and needs to distribute the balls into the baskets such that the minimum magnetic force between any two balls is maximum.
Rick stated that magnetic force between two different balls at positions x and y is |x - y|.
Given the integer array position and the integer m. Return the required force.
Example 1:
Input: position = [1,2,3,4,7], m = 3 Output: 3 Explanation: Distributing the 3 balls into baskets 1, 4 and 7 will make the magnetic force between ball pairs [3, 3, 6]. The minimum magnetic force is 3. We cannot achieve a larger minimum magnetic force than 3.
Example 2:
Input: position = [5,4,3,2,1,1000000000], m = 2 Output: 999999999 Explanation: We can use baskets 1 and 1000000000.
Constraints:
n == position.length2 <= n <= 1051 <= position[i] <= 109position are distinct.2 <= m <= position.lengthThe 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.
This C solution implements a binary search method to find the maximum minimum force. We first sort the basket positions, then binary search for the largest possible minimum distance using a helper function `canPlaceBalls` which checks if we can place all balls with at least `minDist` distance apart.
C++
Java
Python
C#
JavaScript
Time Complexity: O(n log(n) + log(maxDistance) * n), where n is the number of baskets.
Space Complexity: O(1)
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.
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.
C++
Java
Python
C#
JavaScript
Time Complexity: O(n log(n) + n log(maxDistance)), where n is the number of baskets.
Space Complexity: O(1)
| Approach | Complexity |
|---|---|
| Binary Search on Answer | Time Complexity: O(n log(n) + log(maxDistance) * n), where n is the number of baskets. |
| Greedy with Binary Search | Time Complexity: O(n log(n) + n log(maxDistance)), where n is the number of baskets. |
Magnetic Force Between Two Balls | Simple Thought Process | Leetcode 1552 | codestorywithMIK • codestorywithMIK • 11,163 views views
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