LC34. Find First and Last Position of Element in Sorted Array

Problem Description

LeetCode Problem 34: 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.

Clarification

• array sorted, non-decreasing
• start and end position for target
• there are duplicates

Assumption

Solution

Approach - Binary Search

Use binary search twice, one searches start position and the other searches the end position.

Python

class Solution:
    def searchRange(self, nums: List[int], target: int) -> List[int]:
        left, right = 0, len(nums) - 1
        if right < 0:
            return [-1, -1]

        # Find the start position
        while left < right:
            mid = (left + right) // 2
            if target == nums[mid]:
                right = mid
            elif target > nums[mid]:
                left = mid + 1
            else:
                right = mid - 1

        if nums[left] == target:
            start_pos = left
        else:
            start_pos = -1

        # Find the end position
        left, right = max(0, start_pos), len(nums) - 1

        while left < right - 1:
            mid = (left + right) // 2
            if target == nums[mid]:
                left = mid
            elif target > nums[mid]:
                left = mid + 1
            else:
                right = mid - 1

        if nums[right] == target:
            end_pos = right
        elif nums[left] == target:
            end_pos = left
        else:
            end_pos = -1

        return [start_pos, end_pos]

Complexity Analysis

• Time complexity: \(O(\log n)\)
  Use binary search twice. Each binary search takes at most \(\log n\) steps and total steps are at most \(2 \log n\).
• Space complexity: \(O(1)\)
  Only use several index variables.