Winter is coming! Your first job during the contest is to design a standard heater with fixed warm radius to warm all the houses.

Now, you are given positions of houses and heaters on a horizontal line, find out minimum radius of heaters so that all houses could be covered by those heaters.

So, your input will be the positions of houses and heaters seperately, and your expected output will be the minimum radius standard of heaters.

Note:
Numbers of houses and heaters you are given are non-negative and will not exceed 25000.
Positions of houses and heaters you are given are non-negative and will not exceed 10^9.
As long as a house is in the heaters‘ warm radius range, it can be warmed.
All the heaters follow your radius standard and the warm radius will the same.
Example 1:
Input: [1,2,3],[2]
Output: 1
Explanation: The only heater was placed in the position 2, and if we use the radius 1 standard, then all the houses can be warmed.
Example 2:
Input: [1,2,3,4],[1,4]
Output: 1
Explanation: The two heater was placed in the position 1 and 4. We need to use radius 1 standard, then all the houses can be warmed.

class Solution {
    //check houses, compare maxdist(min(house[i], heaters[j]) : min distance between house[i], heaters[j];   and get max of them; max(min(dist))
    public int findRadius(int[] houses, int[] heaters) {
        int radius = 0;//max
        Arrays.sort(heaters);
        for(int i = 0; i<houses.length; i++){
            int min = Integer.MAX_VALUE;
            //binary search (find first >= houses), target is houses[i]
            int l = 0, r = heaters.length-1;
            while(l <= r){
                int m = (r-l)/2 + l;
                if(heaters[m] >= houses[i]) r = m-1 ;
                else l = m+1;
            }
            //System.out.println(l);
            //l is the index, could be 0, >=heaters.length
            int d1 = l-1>=0 ? (houses[i] - heaters[l-1]) : Integer.MAX_VALUE; 
            int d2 = l<heaters.length ? (heaters[l] - houses[i]): Integer.MAX_VALUE;// handle all the things
            min = d1<d2 ? d1 : d2;
            if(min > radius) radius = min;
        }
        return radius;
    }
}

public class Solution {
    public int findRadius(int[] houses, int[] heaters) {
        Arrays.sort(heaters);
        int result = Integer.MIN_VALUE;
        
        for (int house : houses) {
            int index = Arrays.binarySearch(heaters, house);
            if (index < 0) {
            index = -(index + 1);
            }
            int dist1 = index - 1 >= 0 ? house - heaters[index - 1] : Integer.MAX_VALUE;
            int dist2 = index < heaters.length ? heaters[index] - house : Integer.MAX_VALUE;
        
            result = Math.max(result, Math.min(dist1, dist2));
        }
        
        return result;
    }
}