给你一个按照非递减顺序排列的整数数组 nums,和一个目标值 target。请你找出给定目标值在数组中的开始位置和结束位置。
如果数组中不存在目标值 target,返回 [-1, -1]。
你必须设计并实现时间复杂度为 O(log n) 的算法解决此问题。
示例 1:
输入:nums = [5,7,7,8,8,10], target = 8
输出:[3,4]
示例 2:
输入:nums = [5,7,7,8,8,10], target = 6
输出:[-1,-1]
示例 3:
输入:nums = [], target = 0
输出:[-1,-1]
提示:
- 0 <= nums.length <= $10^5$
- $-10^9$ <= nums[i] <= $10^9$
- nums 是一个非递减数组
- $-10^9$ <= target <= $10^9$
解析
两次二分查找,分别找左边界和右边界。
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var searchRange = function (nums, target) { function findLeft(nums, target) { let left = 0; let right = nums.length - 1; let result = -1; while (left <= right) { const mid = (left + right) >> 1; if (nums[mid] === target) { result = mid; right = mid - 1; } else if (nums[mid] < target) { left = mid + 1; } else { right = mid - 1; } } return result; }
function findRight(nums, target) { let left = 0; let right = nums.length - 1; let result = -1; while (left <= right) { const mid = (left + right) >> 1; if (nums[mid] === target) { result = mid; left = mid + 1; } else if (nums[mid] < target) { left = mid + 1; } else { right = mid - 1; } } return result; }
return [findLeft(nums, target), findRight(nums, target)]; };
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两次二分查找:找左边界时命中后继续向左收缩,找右边界时命中后继续向右收缩。时间复杂度 O(logn)。