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 be 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 heaters were placed in the position 1 and 4. We need to use radius 1 standard, then all the houses can be warmed.
Approach:
I spent a long time thinking about this problem, trying several methods without success. Then I saw a hint and it dawned on me: the main point is to find the two nearest heaters for each house and take the maximum value. Use the houses as the traversal point and the heaters as auxiliary units. Although I solved it, I still only vaguely understand it. (Marked)
public class Solution { public int findRadius(int[] houses, int[] heaters) { Arrays.sort(houses); Arrays.sort(heaters); int i = 0, j = 0, res = 0; while (i < houses.length) { while (j < heaters.length - 1 && Math.abs(heaters[j + 1] - houses[i]) <= Math.abs(heaters[j] - houses[i])) { j++; } res = Math.max(res, Math.abs(heaters[j] - houses[i])); i++; } return res; } } I found a relatively easy-to-understand method online:
public class Solution { public int findRadius(int[] houses, int[] heaters) { Arrays.sort(houses); Arrays.sort(heaters); int result = 0; int temp = 0; int j = 0; for (int i = 0; i < houses.length; i++) { while (j < heaters.length && heaters[j] < houses[i]) j++; if (j == heaters.length) temp = houses[i] - heaters[j - 1]; else if (j == 0) temp = heaters[j] - houses[i]; else if (heaters[j] > houses[i]) temp = Math.min(heaters[j] - houses[i], houses[i] - heaters[j - 1]); if (temp > result) result = temp; } return result; } } This siteOriginal articleAll follow "Attribution-NonCommercial-ShareAlike 4.0 License (CC BY-NC-SA 4.0)Please retain the following annotations when sharing or adapting:
Original author:Jake Tao,source:"475. Heaters"
