Advanced Competitive Programming Interview Test (20 Questions)

1. Which of the following time complexities represents the most efficient algorithm?
A) O(n²)
B) O(2ⁿ)
C) O(log n)
D) O(n log n)

2. What will be the output of the following code?

   def mystery(n):
       if n <= 1:
           return 1
       return n * mystery(n - 1)
   print(mystery(5))
   

3. Write a function to find the longest increasing subsequence in an array using dynamic programming.

4. Explain the difference between BFS and DFS in graph traversal, and when each is preferred.

5. Given a sorted array of integers, which algorithm can be used to find a target value in O(log n) time?
A) Linear search
B) Binary search
C) Bubble sort
D) Merge sort

6. What is the time complexity of the following code snippet?

   for i in range(n):
       for j in range(i, n):
           print(i, j)
   

7. Write a program to implement Dijkstra's algorithm for finding the shortest path in a weighted graph.

8. What does the term "greedy choice property" refer to in greedy algorithms?

9. Which data structure is most suitable for implementing a priority queue efficiently?
A) Stack
B) Queue
C) Binary heap
D) Linked list

10. What will be the output of this code?

    import sys
    sys.setrecursionlimit(10000)
    def f(n):
        if n == 0:
            return 0
        return n + f(n-1)
    print(f(999))
    

11. Implement a recursive function to compute the nth Fibonacci number with memoization.

12. Describe the concept of divide and conquer with an example.

13. What is the space complexity of quicksort in the worst case?
A) O(1)
B) O(log n)
C) O(n)
D) O(n²)

14. Write a function that checks whether a given string is a palindrome using recursion.

15. In the context of competitive programming, what is the purpose of using bit manipulation?

16. What will be the output of the following code?

    s = "abc"
    print(s[1:3] + s[0])
    

17. Design a solution to find the maximum sum subarray using Kadane’s algorithm.

18. Explain the concept of backtracking with an example (e.g., N-Queens problem).

19. Which of the following problems cannot be solved using dynamic programming?
A) Longest common subsequence
B) Matrix chain multiplication
C) Traveling Salesman Problem
D) Binary search

20. Given two strings, write a function to determine if one is a permutation of the other using character frequency counting.

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By: @DataScienceQ 🚀