What is the optimal time complexity of solving Binary Search?

The optimized solution achieves a time complexity of O(log n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Binary Search?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Binary Search?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Binary Search?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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DSA SectionEasy

Binary Search

Learn how to solve the 'Binary Search' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given an array of integers nums which is sorted in ascending order, and an integer target, write a function to search target in nums. If target exists, then return its index. Otherwise, return -1.

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

Constraints

•1 <= nums.length <= 10^4
•-10^4 < nums[i], target < 10^4
•All the integers in nums are unique.
•nums is sorted in ascending order.

Examples

Example 1

Input

nums = [-1,0,3,5,9,12], target = 9

Output

Explanation

9 exists in nums and its index is 4

Example 2

Input

nums = [-1,0,3,5,9,12], target = 2

Output

-1

Explanation

2 does not exist in nums so return -1

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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