【数据结构】供暖 heaters

目录

• 供暖 heaters
• 思路
• Tag

供暖 heaters

给出位于同一个水平线上的房屋houses和供暖器heaters的位置。要求设计一个具有最小加热半径的供暖器可以向所有房屋供暖

houses = [1,2,3], heaters = 【2】
1

houses = [1,2,3,4], heaters = [1,4]
1  

思路

因为每个heater的加热半径是一样的，所以求出每一个house到距离它最近的heater的距离，然后在这个距离中找到最大的那个，就可以满足我们的目标。

public int findRadius(int[] houses, int[] heaters) {
        Arrays.sort(heaters);
        int ans = 0;
        for (int i = 0; i < houses.length ; i++) {
            int x = houses[i];
            int j = binarysearch01(heaters,x);
             // left present the distance between houses[i] and  the first heater index bigger than houses[i],
            // if not exist the first bigger element ,
            // left present the distance between houses[i] and the last heater index small than houses[i] .
            int left =Math.abs(x-heaters[j]);
            // right present the distance between house[i] and the former heater.
            // when j equal zero,heater[j-1] is illegal.So choose the bigger one.
            ans = Math.max(ans,Math.min(left,right));
        }
        return ans;
    }

    // find index of the first element bigger than x
    // if exists return index, OR finally return the last index of element that smaller than x.
    public int binarysearch01(int[] arr ,int x){
        int head =0;
        int tail = arr.length-1;
        int mid =0;
        while (head<tail){
            mid = (head+tail)>>1;
            if (arr[mid]>=x){
                tail = mid;
            }
            else{
                head = mid+1;
            }
        }
        return head;
    }

Tag

binary search