1287. Element Appearing More Than 25% In Sorted Array

Given an integer array sorted in non-decreasing order, there is exactly one integer in the array that occurs more than 25% of the time.

Return that integer.

排序的数组里，找到那个出现次数超过1/4的数，保证只有一个。

n的做法可以是for一遍，然后比较arr[i] == arr[i + n // 4]

logn的做法，我们的候选数可能是出现在1/4 2/4 3/4这三个位置。二分一下这几个数在数组里的上下界，就得到了个数，判断一下。

class Solution(object):
    def findSpecialInteger(self, arr):
        """
        :type arr: List[int]
        :rtype: int
        """
        n = len(arr)
        candidates = [arr[n // 4], arr[n // 2], arr[n * 3 // 4]]
        for candidate in candidates:
            l = 0
            r = n - 1
            while l <= r:
                mid = (l + r) // 2
                if arr[mid] < candidate:
                    l = mid + 1
                else:
                    r = mid - 1
            left_index = l
            l = 0
            r = n - 1
            while l <= r:
                mid = (l + r) // 2
                if arr[mid] <= candidate:
                    l = mid + 1
                else:
                    r = mid - 1
            right_index = l
            if right_index - left_index > n // 4:
                return candidate