Find First and Last Position of Element in Sorted Array

Problem Summary

• Given a sorted array input, find the starting and ending index of a target number
• If number is not in the input return [-1,-1]

What is Being Asked?

• Do binary search and find the left most and right most value (target)

Approach Taken

• Modification to the regular binary search algorithm: Once found still go either left or right

Main Concepts Used

• Binary Search

Time & Space Complexity

• Time: $O(logn)$ → Reason: Doing the usual binary search
• Space: $O(1)$ → Reason: Just storing pointers

Code

class Solution:
    def searchRange(self, nums: List[int], target: int) -> List[int]:
        left = self.binarySearch(nums, target, True)
        right = self.binarySearch(nums, target, False)
        return [left, right]

    def binarySearch(self, nums: List[int], target: int, left_on_found: bool) -> int:
        l, r = 0, len(nums) - 1
        i = -1
        while l <= r:
            m = (l + r) // 2
            current = nums[m]
            if current == target:
                i = m
                if left_on_found:
                    r = m - 1
                else:
                    l = m + 1
            elif current >= target:
                r = m - 1
            else:
                l = m + 1
        return i

Common Mistakes / Things I Got Stuck On

• Overcomplicated binary searches of target - 1 or target + 1