题目

Given an array of integers nums sorted in non-decreasing order, find the starting and ending position of a given target value.

If target is not found in the array, return [-1, -1].

You must write an algorithm with O(log n) runtime complexity.

Example 1:

Input: nums = [5,7,7,8,8,10], target = 8
Output: [3,4]

Example 2:

Input: nums = [5,7,7,8,8,10], target = 6
Output: [-1,-1]

Example 3:

Input: nums = [], target = 0
Output: [-1,-1]

Constraints:

• 0 <= nums.length <= 10^5
• -10^9 <= nums[i] <= 10^9
• nums is a non-decreasing array.
• -10^9 <= target <= 10^9

思路

两次二分查找，第一次查找目标数字的左边界，第二次则查找右边界。

代码

python版本：

class Solution:
    def searchRange(self, nums: List[int], target: int) -> List[int]:
        l, r = 0, len(nums)
        res = [-1, -1]
        while l < r:
            mid = (l+r)//2
            if nums[mid] < target:
                l = mid+1
            else:
                r = mid
        if l >= 0 and l < len(nums) and nums[l] == target:
            res[0] = l
        r = len(nums)
        while l < r:
            mid = (l+r)//2
            if nums[mid] > target:
                r = mid
            else:
                l = mid+1
        if l-1 >= 0 and l-1 < len(nums) and nums[l-1] == target:
            res[1] = l-1
        return res