【leetcode】Heaters

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 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 heater was placed in the position 1 and 4. We need to use radius 1 standard, then all the houses can be warmed.

本题属于Easy级别，最常规的方法是用两层循环遍历houses和heaters数组，得到每个house与所有heaters的距离的最小值，然后取出所有最小值中的最大值即为radius。但是这种解法时间复杂度是O(n^2),会导致Time Exceed Limited。

仔细想想，其实根本不需要每个house和所有的heaters进行比较，只需要比较一左一右相邻的两个heaters即可。如何快速找到两个相邻的heaters，可以先对heaters进行排序，再利用二分查找的原理。

参考代码如下：

class Solution(object):
    def binSearch(self,l,n):
        low = 0
        high = len(l)-1
        while low < high:
            mid = (low + high)/2
            if n == l[mid]:
                return 0
            elif n < l[mid]:
                if mid - 1 >= 0 and n >= l[mid-1] :
                    return min(abs(n-l[mid]),abs(n-l[mid-1]))
                else:
                    high = mid - 1
            elif n > l[mid]:
                if mid + 1 <= len(l)-1 and n <= l[mid +1]:
                    return min(abs(n-l[mid]),abs(n-l[mid+1]))
                else:
                    low = mid + 1
        return abs(n - l[low])
    def findRadius(self, houses, heaters):
        """
        :type houses: List[int]
        :type heaters: List[int]
        :rtype: int
        """
        radius = 0
        heaters.sort()
        for i in houses:
            minDis = self.binSearch(heaters, i)
            print minDis
            if minDis != -1 and radius < minDis:
                radius = minDis
        return radius