Algorithms Interview Mastery Quiz (2025 Edition) Quiz

Sharpen your algorithmic thinking with this targeted quiz designed for 2025 interviews, featuring conceptual and scenario-based questions on sorting, dynamic programming, complexity analysis, and common data structures. Ideal for candidates aiming to excel in algorithm interviews and assess their core understanding of essential techniques.

1. Sorting Time Complexity

   Which of the following algorithms has the best average-case time complexity for sorting a random unsorted array of 1000 integers?

   1. Merge Sort
   2. Selection Sort
   3. Bubble Sort
   4. Insertion Sort

   Explanation: Merge Sort has an average-case time complexity of O(n log n), making it highly efficient for large random datasets. Bubble Sort, Selection Sort, and Insertion Sort each have average-case complexities of O(n^2), which are significantly slower for arrays of this size. Therefore, Merge Sort outperforms the others in this scenario and is commonly used for its predictable performance.

2. Binary Search Preconditions

   What must be true about an array before binary search can correctly find the index of an item within it?

   1. The array must be in reverse order.
   2. The array must have no duplicate elements.
   3. The array must contain only integers.
   4. The array must be sorted.

   Explanation: Binary search only works correctly if the array is sorted, as it relies on order to eliminate half the possible elements with each step. Having duplicate elements does not prevent binary search from working, though it may not always find the first occurrence. The array does not have to contain only integers or be in reverse order; any order works as long as it is consistently sorted.

3. Dynamic Programming Identification

   Which scenario best illustrates a problem that can be optimized using dynamic programming?

   1. Finding the minimum number of coins to make change for a value using given denominations.
   2. Printing all elements of a tree in pre-order traversal.
   3. Swapping adjacent values to sort an array.
   4. Searching for a value in an unsorted list by checking each element one by one.

   Explanation: The minimum coin change problem involves overlapping subproblems and optimal substructure, key properties for dynamic programming optimization. Linear search in an unsorted list and sorting by swapping are not dynamic programming problems, as they lack overlapping subproblems and can be solved more directly. Pre-order traversal is a tree traversal technique that does not involve optimization or managing subproblems.

4. Time Complexity Analysis

   If an algorithm processes each element of an n-element array exactly twice in two separate loops, what is its overall time complexity?

   1. O(n)
   2. O(log n)
   3. O(n^2)
   4. O(2n)

   Explanation: Even though the algorithm loops through the array twice, each loop processes n elements, resulting in 2n operations. In time complexity analysis, constant coefficients like 2 are omitted, so the result simplifies to O(n). O(n^2) would be correct only for nested loops, and O(log n) does not match this scenario. O(2n) is not conventionally used because the constant factor is ignored in Big O notation.

5. Hash Table Operations

   When using a hash table to store and access data by key, what is the average-case time complexity for inserting or searching for an element, assuming a good hash function and low load factor?

   1. O(log n)
   2. O(n log n)
   3. O(1)
   4. O(n)

   Explanation: With an effective hash function and a low load factor, hash table operations like insertion and search take constant time on average, or O(1). O(n) time would apply only in the worst case, such as high collision scenarios. O(log n) complexity is typical of tree-based structures, while O(n log n) is common in efficient sorting algorithms but not relevant to hash table lookups.