AGGRCOW - Aggressive cows(explanation and soln in cpp )

#1

Farmer John has built a new long barn, with N (2 <= N <= 100,000) stalls. The stalls are located along a straight line at positions x1,…,xN (0 <= xi <= 1,000,000,000).

His C (2 <= C <= N) cows don’t like this barn layout and become aggressive towards each other once put into a stall. To prevent the cows from hurting each other, FJ wants to assign the cows to the stalls, such that the minimum distance between any two of them is as large as possible. What is the largest minimum distance?
Input

t – the number of test cases, then t test cases follows.

  • Line 1: Two space-separated integers: N and C
  • Lines 2…N+1: Line i+1 contains an integer stall location, xi
    Output

For each test case output one integer: the largest minimum distance.
Example

Input:

1

5 3

1

2

8

4

9

Output:

3

#2

SOLUTION AND CODE

Since the range of xi is from 0 to 10^9, one can say that the minimum distance between the cows will lie between the range. The minimum distance between 2 stalls can be 0 (lower bound) and maximum distance is 10^9 (upper bound). So, one can check for each value from lower bound to upper bound.

Let’s say for k minimum distance, we can check if it is possible to place cows in the stall. In case, you have reached the last stall but didn’t have placed all cows, then it is not possible else it is possible.

A point to note is that if, for a k, it is possible to place the cows. Then all the values less than k will be true. Also, if k is false, then all the values greater than k will be false. We can say it is creating a monotonic function and we have to check for the transition from true to false and return that value.

It can be quickly and easily done with Binary Search from the range of 0 to 10^9.

CODE