maximum-tastiness-of-candy-basket.py

# Time:  O(nlogr), r = max(price)-min(price)
# Space: O(1)

# binary search, greedy
class Solution(object):
    def maximumTastiness(self, price, k):
        """
        :type price: List[int]
        :type k: int
        :rtype: int
        """
        def check(x):  # max cnt if smallest absolute difference >= x
            cnt = prev = 0
            for i in xrange(len(price)):
                if prev and price[i]-prev < x:
                    continue
                cnt += 1
                if cnt == k:
                    break
                prev = price[i]
            return cnt >= k

        price.sort()
        left, right = 1, price[-1]-price[0]
        while left <= right:
            mid = left + (right-left)//2
            if not check(mid):
                right = mid-1
            else:
                left = mid+1
        return right