Binary Search

LeetCode 792 | Difficulty: Easy

Easy

Problem Description

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.

Example 1:

Input: nums = [-1,0,3,5,9,12], target = 9
Output: 4
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

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.

Topics: Array, Binary Search

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Approach

Binary Search

Binary search reduces the search space by half at each step. The key insight is identifying the monotonic property — what condition lets you decide to go left or right?

When to use

Sorted array, or searching for a value in a monotonic function/space.

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Solutions

Solution 1: C# (Best: 154 ms)

Metric	Value
Runtime	154 ms
Memory	40.2 MB
Date	2021-11-25

Solution

public class Solution {
    public int Search(int[] nums, int target) {
     int lo = 0, hi = nums.Length - 1;
     while(lo <= hi)
     {
         int mid = lo + (hi-lo)/2;
         if(nums[mid] == target)
         {
             return mid;
         }
         else if(target > nums[mid])
         {
             lo = mid+1;
         }
         else
         {
             hi = mid-1;
         }
     }
        
     return -1;
   }
    
}

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Complexity Analysis

Approach	Time	Space
Binary Search	$O(log n)$	$O(1)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• Precisely define what the left and right boundaries represent, and the loop invariant.