Optimized Solution for the Aggressive Cows Problem Using Binary Search

[vickashu]

Summary:

This pull request adds a Java solution for the Aggressive Cows Problem, which aims to place cows in stalls such that the minimum distance between any two cows is maximized. The solution utilizes a binary search approach to find the largest possible minimum distance between the cows.

Approach (Binary Search + Greedy Placement):

1. Sorting:

   • The stall positions are sorted to ensure we place cows in a linear and increasing order.

2. Binary Search:

   • The possible minimum distances between cows range from 1 to the maximum distance (difference between the first and last stall).
   • Binary search is used to check the feasibility of placing cows with a middle distance (mid) between them.

3. Greedy Placement (canWePlace() function):

   • For each middle distance (mid), the function checks if it's possible to place all k cows such that the minimum distance between any two cows is at least mid.
   • It starts placing the first cow at the first stall, then attempts to place each subsequent cow in the next stall that satisfies the distance condition.

4. Final Output:

   • The maximum possible minimum distance between any two cows is the answer, which is found using binary search over possible distances.

Key Changes:

• Greedy Placement Strategy (canWePlace function): Added a method to check if cows can be placed with at least a given minimum distance.
• Binary Search Implementation (aggressiveCows function): Introduced binary search over the possible distance range to efficiently determine the largest minimum distance that satisfies the placement condition.
• Input Handling: The stalls array is sorted to facilitate the linear greedy placement of cows.