34. 在排序数组中查找元素的第一个和最后一个位置

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难度系数： 中等
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(logn)O(log n) 的算法解决此问题。

示例 1:

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输入：nums = [5,7,7,8,8,10], target = 8
输出：[3,4]

示例 2:

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输入：nums = [5,7,7,8,8,10], target = 6
输出：[-1,-1]

示例 3:

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输入：nums = [], target = 0
输出：[-1,-1]

提示：

  • 0 <= nums.length <= 10510^5
  • −109-10^9 <= nums[i] <= 10910^9
  • nums 是一个非递减数组
  • −109-10^9 <= target <= 10910^9

解法：

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class Solution {
    public int[] searchRange(int[] nums, int target) {
        int[] result = new int[]{-1, -1};
        int length = nums.length;
        if (nums.length == 0) {
            return result;
        }
        if (nums.length == 1) {
            if (nums[0] ==  target) {
                result[0] = 0;
                result[1] = 0;
            }
            return result;
        }
        int left = 0;
        int right = length - 1;
        int middle;
        while(left <= right) {
            middle = (left + right) / 2;
            if (nums[middle] < target) {
                left = middle + 1;
            } else {
                right = middle - 1;
            }
        }
        if (left >= 0 && left <= length -1 && nums[left] == target) {
            result[0] = left;
        }
        left = 0;
        right = length - 1;
        while(left <= right) {
            middle = (left + right) / 2;
            if (nums[middle] > target) {
                right = middle - 1;
            } else {
                left = middle + 1;
            }
        }
        if (right >= 0 && right <= length - 1 && nums[right] == target) {
            result[1] = right;
        }
        return result;
    }
}

官方解法：

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class Solution {
    public int[] searchRange(int[] nums, int target) {
        int leftIdx = binarySearch(nums, target, true);
        int rightIdx = binarySearch(nums, target, false) - 1;
        if (leftIdx <= rightIdx && rightIdx < nums.length && nums[leftIdx] == target && nums[rightIdx] == target) {
            return new int[]{leftIdx, rightIdx};
        } 
        return new int[]{-1, -1};
    }

    public int binarySearch(int[] nums, int target, boolean lower) {
        int left = 0, right = nums.length - 1, ans = nums.length;
        while (left <= right) {
            int mid = (left + right) / 2;
            if (nums[mid] > target || (lower && nums[mid] >= target)) {
                right = mid - 1;
                ans = mid;
            } else {
                left = mid + 1;
            }
        }
        return ans;
    }
}

原题链接：https://leetcode.cn/problems/find-first-and-last-position-of-element-in-sorted-array/