10 common binary search interview questions

The importance of the binary search algorithm in technical interviews cannot be overstated. It tests a candidate’s understanding of algorithmic thinking and their ability to optimize solutions. Top tech companies, including Google, Amazon, and Microsoft, frequently include binary search problems in their interviews, making it important for candidates to master this algorithm.

In this blog, we'll explore ten common binary search interview questions. We’ll break down each problem, explain how binary search applies, and provide step-by-step solutions to help you understand the approach. By the end, you'll have a deeper understanding of how to tackle these problems with confidence, making binary search a valuable tool in your coding interview.

Curated list of problems#

The table below lists the top 10 binary search interview questions commonly featured in coding interviews at top tech companies like Google, Facebook, and Netflix. The problems will be selected and arranged based on their difficulty and the extent to which they require modifications to the basic binary search algorithm.

Let’s first look at the basic binary search algorithm. After that, we will explore some of the above problems in detail with algorithm explanation, code solution, and illustrations to explain how the algorithm works.

Binary search#

Binary search is an algorithm to find an element in a sorted array or list. The process involves repeatedly dividing the search interval in half. If the value of the search key is less than the item in the middle of the interval, the algorithm narrows the interval to the lower half. Otherwise, it narrows it to the upper half. The steps are as follows:

1. Initialize: Set two pointers, one at the beginning (left) and one at the end (right) of the array.

2. Calculate the midpoint: Compute the middle index of the current interval as mid = left + (right - left) // 2.

3. Compare: Compare the target value with the value at the middle index.

   1. If they are equal, return the middle index.

   2. If the target value is less than the middle value, adjust the right pointer to mid - 1.

   3. If the target value is greater than the middle value, adjust the left pointer to mid + 1.

4. Repeat: Continue the process until the left pointer exceeds the right pointer, indicating that the target is not in the array.

Code template#

Here’s a code template for binary search in Python, implemented iteratively.

Here’s a code template for binary search in Python, implemented recursively.

This algorithm is efficient with a time complexity of $O(\log n)$, making it suitable for large datasets.

Binary search interview questions list#

This section will cover ten common interview problems that can be efficiently solved using the binary search algorithm. Each problem is selected based on its relevance and frequency in coding interviews, ranging from fundamental to advanced levels.

Problem 1: Search insert position#

This is one of the most basic binary search example problems. It was selected because it extends the basic binary search problem by handling cases where the element is not found. Companies like Amazon and Facebook commonly ask this problem in interviews and consider it easy in terms of difficulty.

Statement: Given a sorted array and a target value, return the index if the target is found. If not, return the index where it would be if inserted in order. You must write an algorithm with $O(\log n)$ runtime complexity.

Solution: Binary search is an algorithm for finding the position of a target value within a sorted array. Here, we will modify the standard binary search to handle cases where the element is not found by returning the index where the target value should be inserted to maintain the order.

Here is the step-by-step explanation of the algorithm:

• Initialization: Start with two pointers, left and right, initialized to the start and end of the array, respectively.

• Iteration:

  • Calculate the middle index mid = left + (right - left) // 2.

  • Compare the target value with the middle element of the array:

    • If the target value equals the middle element, return mid as the index.

    • If the target value is less than the middle element, adjust the right pointer to mid - 1 to continue searching in the left half.

    • If the target value is greater than the middle element, adjust the left pointer to mid + 1 to continue searching in the right half.

• Completion: When the left pointer exceeds the right pointer, the search interval is exhausted. The left pointer will be where the target value should be inserted. Return left as the insert position.

Let’s visualize the above mentioned steps:

Let's implement the solution discussed above:

The time complexity of the algorithm is $O(\log n)$, and the space complexity of the algorithm is $O(1)$.

Problem 2: First and last position of an element in a sorted array#

This problem is selected because it requires finding an element’s first and the last occurrence, a common variation of binary search problems. It is frequently asked in interviews by companies like Google and Microsoft and is considered medium in terms of difficulty.

Statement: Given a sorted array of integers nums and a target value target, return the starting and ending position of target in the array. If target is not found in the array, return [-1, -1]. You must write an algorithm with $O(\log n)$runtime complexity.

Solution: To solve this problem, we can perform two binary searches: one to find the first occurrence of the target and another to find the last occurrence. By modifying the standard binary search, we can locate these positions.

Here is the step-by-step explanation of the algorithm:

• Finding the first occurrence:

  • Initialize left and right pointers to the start and end of the array, respectively.

  • Use a binary search to find the first occurrence:

    • Calculate the middle index mid = left + (right - left) // 2.

    • If the middle element is greater than or equal to the target, adjust the right pointer to mid - 1.

    • If the middle element is less than the target, adjust the left pointer to mid + 1.

    • If the middle element equals the target, record the index and continue searching in the left half by adjusting right = mid - 1.

• Finding the last occurrence:

  • Reinitialize left and right pointers to the start and end of the array, respectively.

  • Use a binary search to find the last occurrence:

    • Calculate the middle index mid = left + (right - left) // 2.

    • If the middle element is less than or equal to the target, adjust the left pointer to mid + 1.

    • If the middle element is greater than the target, adjust the right pointer to mid - 1.

    • If the middle element equals the target, record the index and continue searching in the right half by adjusting left = mid + 1.

• Completion:

  • After both searches, return the recorded indexes of the first and last occurrences. If either search does not find the target, return [-1, -1].

Let’s visualize the above mentioned steps with an example:

Let’s implement the solution discussed above:

The time complexity of the algorithm is $O(\log n)$ for both find_first and find_last functions, where $n$ is the number of elements in the array. Because both functions are called separately, the total time complexity is $O(\log n) + O(\log n) = O(\log n)$. The space complexity of the algorithm is $O(1)$ because no additional space proportional to the input size is used; only a few variables are maintained.

Problem 3: Peak element in an array#

This problem is selected because it demonstrates the use of binary search in non-trivial array conditions. That showcases its efficiency in finding an element that meets specific criteria beyond simple searching. Companies like Google frequently ask it in interviews, making it important for interview preparation. It is considered medium in terms of difficulty.

Statement: Given an array of integers nums, find a peak element, and return its index. A peak element is an element that is strictly greater than its neighbors. You may imagine that nums[-1] = -∞ and nums[n] = -∞ (for the boundary elements). You must write an algorithm with O(log n) runtime complexity.

Solution: To solve this problem, we use a binary search approach to find a peak element. We continuously narrow down the search space by comparing the middle element with its neighbors and adjusting the search boundaries accordingly.

Here is the step-by-step explanation of the algorithm:

1. Initialization: Start with two pointers, left and right, initialized to the start and end of the array, respectively.

2. Iteration:

   1. Calculate the middle index mid = left + (right - left) // 2.

   2. Compare the middle element with its neighbors:

      1. If the middle element is greater than its right neighbor, it means the peak is on the left side, so adjust the right pointer to mid.

      2. Otherwise, the peak is on the right side, so adjust the left pointer to mid + 1.

3. Completion: When the left pointer meets the right pointer, it points to the peak element. Return left as the index of the peak element.

Let’s visualize the above mentioned steps with an example:

Let’s implement the solution discussed above:

The algorithm’s time complexity is $O(\log n)$, where $n$ is the number of elements in the array. This is because we are using a binary search approach. The algorithm’s space complexity is $O(1)$ because no additional space proportional to the input size is used; only a few variables are maintained.

Further reading#

Educative offers a set of specialized paths to prepare your interview for MAANG companies. Check out some of these paths below, or check out our exhaustive list of paths:

These resources can help solidify your understanding of binary search and prepare you for coding interviews and real-world problem-solving.

Conclusion#

Mastering binary search is essential for excelling in coding interviews. As we've seen through these ten problems, understanding when and how to apply binary search can significantly reduce the time complexity of your solutions. This efficiency not only impresses interviewers but also demonstrates your ability to think critically and solve complex problems. By mastering binary search, you gain a valuable skill that sets you apart from other candidates, giving you a competitive edge in your job search.

Here’s where our mock interviews can become a game changer. We offer a range of mock interviews, including data structures interviews, allowing you to practice with various problem types. During these mock interviews, pay close attention to the interviewer’s feedback. Use the feedback provided to identify areas for improvement and refine your skills.