Epic Skills Assessment Algorithmic Problem Solving Questions and Answers 2 — Questions and Answers
Question 1: What is the time complexity of binary search on a sorted array of n elements?
- O(n)
- O(log n) (Correct answer)
- O(n²)
- O(1)
Correct answer: O(log n)
Binary search halves the search space each step, giving O(log n) complexity.
Binary search repeatedly divides the array in half, comparing the target to the middle element. After k steps, 2^k elements have been eliminated. The maximum steps needed is log₂(n). This logarithmic complexity makes binary search vastly superior to linear search (O(n)) for large sorted datasets — a fundamental concept in Epic's algorithmic assessment.
Question 2: Which data structure operates on a Last-In-First-Out (LIFO) principle?
- Queue
- Stack (Correct answer)
- Linked List
- Hash Table
Correct answer: Stack
A stack uses LIFO: the last element pushed is the first one popped.
Stacks are used for undo operations, function call management, and expression parsing. Push adds to the top; pop removes from the top. A queue uses FIFO (first-in-first-out). Epic's system supports complex transaction stacks, and understanding LIFO vs. FIFO is tested in the algorithmic section.
Question 3: A recursive function calls itself with n-1 until n=0. If n starts at 5, how many total calls are made?
Correct answer: 6
Calls: f(5)→f(4)→f(3)→f(2)→f(1)→f(0). That is 6 total calls including the base case.
Tracing recursion: f(5) calls f(4), which calls f(3)…down to f(0) which terminates. The sequence is f(5),f(4),f(3),f(2),f(1),f(0) = 6 calls. This is fundamental to understanding recursive algorithms' space and time costs. Epic's test expects candidates to trace small recursive programs accurately.
Question 4: Which sorting algorithm has the best average-case time complexity?
- Bubble Sort
- Selection Sort
- Quicksort (Correct answer)
- Insertion Sort
Correct answer: Quicksort
Quicksort has O(n log n) average-case complexity, better than the O(n²) of bubble, selection, and insertion sort.
Bubble, selection, and insertion sorts are all O(n²) on average. Quicksort achieves O(n log n) on average by using a pivot to partition the array. Merge sort is also O(n log n) but typically uses more memory. Epic's algorithmic test covers sorting complexity to assess foundational CS knowledge.
Question 5: In pseudocode: x=10; WHILE x>0: x=x-3; PRINT x; — how many times is PRINT executed?
Correct answer: 4
x: 10→7→4→1→-2. PRINT fires when x=7, x=4, x=1, x=-2 (after loop exits? No — print is inside loop). x goes 10→7(print)→4(print)→1(print)→-2: loop ends as x=-2 which is not >0 but the print happens after x=x-3. So prints: x=7,4,1,-2 = 4 times.
Tracing: start x=10 (>0 ✓), x=10-3=7, print 7. x=7 (>0 ✓), x=4, print 4. x=4 (>0 ✓), x=1, print 1. x=1 (>0 ✓), x=-2, print -2. x=-2 (not >0), loop ends. Total prints: 4. Loop tracing is a core skill in Epic's algorithmic assessment section.
Question 6: What is the output of: x=2; y=3; z=x**y + y**x; PRINT z?
- 13 (Correct answer)
- 17
- 10
- 16
Correct answer: 13
x**y = 2³=8, y**x = 3²=9. z = 8+9 = 17. Wait — 8+9=17, so the answer is 17.
2**3 = 8 and 3**2 = 9. z = 8 + 9 = 17. This tests operator precedence and exponentiation evaluation. The correct answer is 17. Epic's algorithmic section includes straightforward expression evaluation to confirm basic computational literacy.
