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## Problem

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

Every house can be warmed, as long as the house is within the heater’s warm radius range.

Given the positions of houses and heaters on a horizontal line, return the minimum radius standard of heaters so that those heaters could cover all houses.

Example 1:

Input: houses = [1,2,3], heaters = 
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: houses = [1,2,3,4], heaters = [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.


Example 3:

Input: houses = [1,5], heaters = 
Output: 3


Constraints:

• 1 <= houses.length, heaters.length <= 3 * 10^4
• 1 <= houses[i], heaters[i] <= 10^9

## Code

class Solution {
public int findRadius(int[] houses, int[] heaters) {
TreeSet<Integer> set = new TreeSet<>();

for (int h : heaters) {
}

int res = 0;

for (int house : houses) {
Integer ceiling = set.ceiling(house);
Integer floor = set.floor(house);

int d1 = ceiling == null ? Integer.MAX_VALUE : ceiling - house;
int d2 = floor == null ? Integer.MAX_VALUE : house - floor;

res = Math.max(res, Math.min(d1, d2));
}

return res;
}
}

class Solution {
public int findRadius(int[] houses, int[] heaters) {
Arrays.sort(houses);
Arrays.sort(heaters);

int index = 0;
int res = 0;

for(int i = 0; i < houses.length; i++){
int curr = houses[i];

while (index < heaters.length - 1 &&
Math.abs(heaters[index] - curr) >= Math.abs(heaters[index + 1] - curr)) {
index++;
}

res = Math.max(res, Math.abs(heaters[index] - curr));
}

return res;
}
}

class Solution {
public int findRadius(int[] houses, int[] heaters) {
Arrays.sort(heaters);
int res = 0;

for (int house : houses) {
int index = Arrays.binarySearch(heaters, house);

if (index < 0) {
index = -(index + 1);
}

int d1 = index - 1 >= 0 ? house - heaters[index - 1] : Integer.MAX_VALUE;
int d2 = index < heaters.length ? heaters[index] - house : Integer.MAX_VALUE;

res = Math.max(res, Math.min(d1, d2));
}

return res;
}
}