[Leetcode] Binary search -- 475. 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.

https://leetcode.com/problems/heaters/#/description

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Solution:

1.  1st try,   naive method.        TLE using python.

          The idea is to try iterate every house in houses  hs,   then we use hs to compare with each heater and get smallest distance "dist".  So we have distance sets "dists"

          find the maximum distance s from dists as the final answer, which is  the minimum radius standard of heaters.

         time complexity o(m*n),  where m = len(houses), n = len(heaters)

 ansMax = 0
        houses.sort()
        heaters.sort()
        for hs in houses:
            minDiff = 2**31   #get min
            for ht in heaters:
                if  abs( hs -ht) < minDiff:
                    minDiff = abs(ht -hs)
            
            if minDiff > ansMax:
                ansMax = minDiff
        return ansMax

      2.    Use binary search. The idea is similar as above. But  it finds the left index of the most closest smaller(equal) ele, the right index closest bigger (equal) ele;   then we compare to get the smallest distance "dist" for each position ;  ( the function same as  the bisect algorithm in python) , then we find the maximum distance s from dists as the final answer, which is  the minimum radius standard of heaters. 

Time complexity is o(mlogm+nlogn + m*lgn)

def binarySearch(lst, ele):
            if len(lst) == 1:
                return (0, 0)
            l = 0
            h = len(lst) - 1
            while (l <= h):
                mid = (l+h)/2
                if lst[mid] == ele:
                    return (mid, mid)
                elif lst[mid] < ele:
                    l = mid + 1
                else:
                    h = mid - 1
            return (l-1, l)            #return left, right index
        
        houses.sort()
        heaters.sort()
        ansMax = 0
        for hs in houses:
            (l, r) = binarySearch(heaters, hs)
            #print('l, r: ', l,r )
            if r > len(heaters)-1:   #only left is valid
                minDiff = abs(hs- heaters[l])
            elif l < 0:             
                minDiff = abs(heaters[r] - hs)
            else:
                minDiff = min(abs(hs - heaters[l]), abs(heaters[r] -hs))
            #print('lminDi: ', minDiff )
            if minDiff > ansMax:
                ansMax = minDiff
        return ansMax