Heaters

Problem

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.

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.

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.

Solution

O(n^2) time, O(1) space

public class Solution {
    public int findRadius(int[] houses, int[] heaters) {
        Arrays.sort(houses);
        Arrays.sort(heaters);
        int i = 0, res = 0;
        for (int house : houses) {
            while (i < heaters.length - 1 && Math.abs(heaters[i + 1] - house) <= Math.abs(heaters[i] - house)) i++;
            res = Math.max(res, Math.abs(heaters[i] - house));
        }
        return res;
    }
}

Analysis

In this solution, we loop through each house and find the index of its nearest heater
Then we update the res with maximum value
Notice that since we sort the heaters and houses before, we can just have one index
Because if index is far for current house, it must be far for next house as well