# 475. Heaters

## Description

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.

Notice that all the heaters follow your radius standard, and the warm radius will the same.

Example 1:

Input: houses = [1,2,3], heaters = [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: houses = [1,2,3,4], heaters = [1,4]
Output: 1
Explanation: The two heaters were placed at positions 1 and 4. We need to use a radius 1 standard, then all the houses can be warmed.


Example 3:

Input: houses = [1,5], heaters = [2]
Output: 3


Constraints:

• 1 <= houses.length, heaters.length <= 3 * 104
• 1 <= houses[i], heaters[i] <= 109

## Solutions

• class Solution {
public int findRadius(int[] houses, int[] heaters) {
Arrays.sort(heaters);
int res = 0;
for (int x : houses) {
int i = Arrays.binarySearch(heaters, x);
if (i < 0) {
i = ~i;
}
int dis1 = i > 0 ? x - heaters[i - 1] : Integer.MAX_VALUE;
int dis2 = i < heaters.length ? heaters[i] - x : Integer.MAX_VALUE;
res = Math.max(res, Math.min(dis1, dis2));
}
return res;
}
}


• class Solution {
public:
int findRadius(vector<int>& houses, vector<int>& heaters) {
sort(houses.begin(), houses.end());
sort(heaters.begin(), heaters.end());
int left = 0, right = 1e9;
while (left < right) {
int mid = left + right >> 1;
if (check(houses, heaters, mid))
right = mid;
else
left = mid + 1;
}
return left;
}

bool check(vector<int>& houses, vector<int>& heaters, int r) {
int m = houses.size(), n = heaters.size();
int i = 0, j = 0;
while (i < m) {
if (j >= n) return false;
int mi = heaters[j] - r;
int mx = heaters[j] + r;
if (houses[i] < mi) return false;
if (houses[i] > mx)
++j;
else
++i;
}
return true;
}
};

• class Solution:
def findRadius(self, houses: List[int], heaters: List[int]) -> int:
houses.sort()
heaters.sort()

def check(r):
m, n = len(houses), len(heaters)
i = j = 0
while i < m:
if j >= n:
return False
mi = heaters[j] - r
mx = heaters[j] + r
if houses[i] < mi:
return False
if houses[i] > mx:
j += 1
else:
i += 1
return True

left, right = 0, int(1e9)
while left < right:
mid = (left + right) >> 1
if check(mid):
right = mid
else:
left = mid + 1
return left


• func findRadius(houses []int, heaters []int) int {
sort.Ints(houses)
sort.Ints(heaters)
m, n := len(houses), len(heaters)

check := func(r int) bool {
var i, j int
for i < m {
if j >= n {
return false
}
mi, mx := heaters[j]-r, heaters[j]+r
if houses[i] < mi {
return false
}
if houses[i] > mx {
j++
} else {
i++
}
}
return true
}
left, right := 0, int(1e9)
for left < right {
mid := (left + right) >> 1
if check(mid) {
right = mid
} else {
left = mid + 1
}
}
return left
}

• function findRadius(houses: number[], heaters: number[]): number {
houses.sort((a, b) => a - b);
heaters.sort((a, b) => a - b);
const m = houses.length,
n = heaters.length;
let ans = 0;
for (let i = 0, j = 0; i < m; i++) {
let cur = Math.abs(houses[i] - heaters[j]);
while (
j + 1 < n &&
Math.abs(houses[i] - heaters[j]) >= Math.abs(houses[i] - heaters[j + 1])
) {
cur = Math.min(Math.abs(houses[i] - heaters[++j]), cur);
}
ans = Math.max(cur, ans);
}
return ans;
}