8.10 - hard - 38

164. Maximum Gap: 试了一下bucket sort，好像不太行，看了答案，发现是自己的思路问题，bucket的设定想错的。bucket装的是差值小于最小可能值的值，所以只要存储左边界和右边界就可以了还有一种radix sort的解法，还要研究一下。

class Solution(object):
    def maximumGap(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        N = len(nums)
        if (N < 2):
            return 0
        imin = min(nums)
        imax = max(nums)
        M = max(1, int(1.0 * (imax - imin) / (N - 1))) # 找出max difference的最小可能值
        buckets = [None] * ((imax - imin) / M + 1) # 做出buckets，每个bucket之间的差距是M
        for x in nums:
            i = (x - imin) / M
            bucket = buckets[i] # 提取出当前x所在的bucket
            if bucket is None:
                buckets[i] = {'min': x, 'max': x}
            else:
                bucket['min'] = min(bucket['min'], x) # 这两步就是设定bucket的边界，左边界和有边界，因为bucket本身也是有长度M的
                bucket['max'] = max(bucket['max'], x)
        gap = 0
        prev = buckets[0]
        for i in range(1, len(buckets)):
            if buckets[i] is None:
                continue
            # 因为如果两个值在同一个bucket里面，那么就说明它们的差值小于M，就不可能是解
            # 所以要求当前左边界和上一个的有边界之间的差值
            gap = max(gap, buckets[i]['min'] - prev['max'])
            prev = buckets[i]
        return gap